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This article aims to investigate the 3D morpho-sedimentary dynamics of two gravel beaches in relation to hydrodynamic forcing, using a multi-sensor approach. Study sites, namely Etretat and Hautot-sur-Mer, are both located in Normandy, France. Thus, they face similar wave conditions of the English channel's eastern side, with megatidal ranges and channelized wave orientations. However, they differ in gravel size (D50 Etretat = 5.2 cm; D50 Hautot-sur-Mer = 7.0 cm), vertical composition (Etretat is a purely gravel beach, Hautot-sur-Mer is a composite one with a low tide terrace) and wave exposure (Etretat is an embayed beach, oriented 47°N, Hautot-sur-Mer is a semi-open beach, oriented 71°N). Used data include shoreline positions automatically extracted from coastal Video Monitoring Systems (VMS) images between 2018 and 2020, wave data provided by the WaveWatch 3 model, and gravel size maps derived from UAV-imagery at different dates (one in Etretat, three in Hautot-sur-Mer). First, an Empirical Orthogonal Function (EOF) analysis was performed on the shoreline position data to extract the Principal Components (PC) describing mechanisms of morphological changes in the shoreline shape at different elevations (−2 to +3 m in Etretat and + 1 to +3 m in Hautot-sur-Mer). Four mechanisms spread within five PCs were found in Etretat: cross-shore translation (PC1), rollover (PC2), scale/elevation dependent rotation (PC3 and PC4) and breathing (PC5). Four PCs describing three mechanisms were identified in Hautot-sur-Mer: right-centered beach cell rotation (PC1), left-centered beach cell rotation (PC2), large scale rotation (PC3) and rollover (PC4). Interpretation of the PCs were supported by significant correlations with morphological parameters such as average beach width (BW), beach orientation angle (BOA) and beach slope (BS). The main mid-term morphological periods of variability include 2, 3, 5 and 8+ months in Etretat and 2, 3 and 6 months in Hautot-sur-Mer (all parameters included), which essentially corresponds to the variability of the wave energy. Finally, the analysis of surface grain size spatial variability revealed the presence of textural patterns with spatial and temporal variations in sorting and average grain size up to 1 cm in two months.
Content may be subject to copyright. - Accepted manuscript
Antoine Soloya, Imen Turkia, Nicolas Lecoqa, Carlos Lopez Solanoa, Benoit Laignela
a Normandie Univ, UNIROUEN, UNICAEN, CNRS, M2C, 76000 Rouen, France
Corresponding author: Antoine Soloy,
©2022. This manuscript version is made available under the CC-BY-NC-ND 4.0
Shoreline variability; pebble beach; cross-shore translation; beach rotation; beach breathing; beach rollover
This article aims to investigate the 3D morpho-sedimentary dynamics of two gravel beaches in relation to
hydrodynamic forcing, using a multi-sensor approach. Study sites, namely Etretat and Hautot-sur-Mer, are both located
in Normandy, France. Thus, they face similar wave conditions of the English channel's eastern side, with megatidal
ranges and channelized wave orientations. However, they differ in gravel size (D50 Etretat = 5.2 cm; D50 Hautot-sur-
Mer = 7.0 cm), vertical composition (Etretat is a purely gravel beach, Hautot-sur-Mer is a composite one with a low tide
terrace) and wave exposure (Etretat is an embayed beach, oriented 47°N, Hautot-sur-Mer is a semi-open beach, oriented
71°N). Used data include shoreline positions automatically extracted from coastal Video Monitoring Systems (VMS)
images between 2018 and 2020, wave data provided by the WaveWatch 3 model, and gravel size maps derived from
UAV-imagery at different dates (one in Etretat, three in Hautot-sur-Mer). First, an Empirical Orthogonal Function (EOF)
analysis was performed on the shoreline position data to extract the Principal Components (PC) describing mechanisms
of morphological changes in the shoreline shape at different elevations (−2 to +3 m in Etretat and + 1 to +3 m in Hautot-
sur-Mer). Four mechanisms spread within five PCs were found in Etretat: cross-shore translation (PC1), rollover (PC2), - Accepted manuscript
scale/elevation dependent rotation (PC3 and PC4) and breathing (PC5). Four PCs describing three mechanisms were
identified in Hautot-sur-Mer: right-centered beach cell rotation (PC1), left-centered beach cell rotation (PC2), large scale
rotation (PC3) and rollover (PC4). Interpretation of the PCs were supported by significant correlations with
morphological parameters such as average beach width (BW), beach orientation angle (BOA) and beach slope (BS).
The main mid-term morphological periods of variability include 2, 3, 5 and 8+ months in Etretat and 2, 3 and 6 months
in Hautot-sur-Mer (all parameters included), which essentially corresponds to the variability of the wave energy. Finally,
the analysis of surface grain size spatial variability revealed the presence of textural patterns with spatial and temporal
variations in sorting and average grain size up to 1 cm in two months.
1. Introduction
Monitoring, understanding and predicting coastal dynamics are key issues in coastal engineering in order to
cope with coastal risks, especially in the context of climate change and sea level rise. It is a challenging task, as coastal
morphodynamics are the complex result of non-linear interactions between hydrodynamic forcing (currents, waves,
tides) and local characteristics (sediment size, embayment, intertidal zone structuration, etc.). Over the past few decades,
great progress has been made in this regard thanks to improved monitoring technologies, which now allow the study of
coasts at different scales, from the global and regional ones through satellite imagery, to the local scale through ground
surveys and Video Monitoring Systems (VMS).
Satellite techniques rely on data provided by optical or radar sensors to identify coastal features at a regional or
larger scale, at a daily to weekly measuring frequency constrained by orbital parameters (Salameh et al., 2019; Vos et
al., 2020). “Ground surveys” gather all the methods for in situ measurement of a site’s topography at a defined moment,
including lidar, total stations, differential GNSS (dGNSS) and photogrammetry (Andriolo et al., 2018; Lee et al., 2013;
Mason et al., 2000; Morton et al., 1993). Among them, the profiling methods (dGNSS and total stations) are particularly
used for long term repeated measurements as the method is relatively versatile and can provide morphological
monitoring records down to the hourly scale. Nevertheless, measurements are most often carried out on a weekly to
monthly frequency and sometimes even shorter, depending on research-specific needs (Lacey and Peck, 1998; Larson
and Kraus, 1994; Turner et al., 2016).
The use of VMS is a popular methodology that made it possible to monitor the shoreline of specific study sites
on the long term, during daylight, with high resolution (from centimeters to meters), applying a commonly used sampling
time step of 10 min (Davidson et al., 2007; Holman and Stanley, 2007; Silva et al., 2009; Turner et al., 2004). The idea
is to georeference the moving shoreline visible on images, using its pixel coordinates associated with the local water
level, assuming a good knowledge of the cameras' position and orientation relative to the environment in their field of
view (Aarninkhof et al., 2003). Using this technique makes it possible to monitor the intertidal morphology with a
repeatability up to the tidal cycle, although consistently delineating the shoreline over long periods can be challenging
due to the high variability of image-taking conditions (light, weather, sea states, boats, users, camera lens cleanness,
etc.). Authors report vertical biases ranging from 10 to 34 cm on reconstructed intertidal digital elevation models, - Accepted manuscript
depending on the site, hardware, dataset and delineation method used (Plant et al., 2007; Soloy et al., 2021; Uunk et al.,
VMS data are often processed with an Empirical Orthogonal Function (EOF) statistical analysis in order to
decompose the complex movements of the shoreline through time into simpler components of variability, each of which
summarizes a certain part of the total variability. By doing this, authors were able to identify mechanisms such as cross-
shore translation, beach rotation (Blossier et al., 2017; Harley et al., 2015; Robinet et al., 2020; Turki et al., 2013),
breathing (Blossier et al., 2017; Ratliff and Murray, 2014; Robinet et al., 2020), boundary effect of cross-shore structures
(Miller and Dean, 2007), nourishment effects (Lemke and Miller, 2017) and even geological variations (Hapke et al.,
2016). However, this improvement in monitoring techniques has mostly benefited the understanding of sandy coastal
systems, and our knowledge of gravel ones remains relatively modest in comparison, despite the fact that they represent
a significant - although unknown - part of the world's coastline (Buscombe and Masselink, 2006; Jennings and
Shulmeister, 2002; Mason and Coates, 2001; Van Wellen et al., 2000). The main reason for this discrepancy is probably
the cost and difficulty of measuring the spatial variability of gravel particle size, as well as its temporal variability,
although this information is thought to be essential to understand and model the dynamics of gravel beaches (Buscombe
and Masselink, 2006). Indeed, the spatial variability of gravel sizes and shapes as well as their temporal variabilities
play a significant role in the reciprocal relationship between sediment transport, hydrodynamic processes, and
morphological changes (Bluck, 1967; Buscombe and Masselink, 2006; Flemming, 1964; Isla, 1993; Orford, 1975;
Williams and Caldwell, 1988).
To address this disparity and take the variability of sediment characteristics into account, the present study aims
to investigate the geomorphodynamics and gravel size variability of two coastal systems, Etretat and Hautot-sur-Mer, a
purely gravel beach and a composite one, respectively, both located in Normandy, France (Figure 1). Using the
methodology developed by Soloy et al. (2021) and applied to nearly two years of VMS image data, it was possible to
automatically monitor the shoreline position on both beaches on various elevations within the tidal range. Combined
with the other recently developed algorithm from Soloy et al. (2020), with the aim of mapping the distribution of surface
gravel particle size at different times, this paper intends to propose a first analysis of the morpho-sedimentary
relationship of two pebble beaches of Normandy.
The extracted information will help us answer different questions regarding morphodynamics and sedimentary
variability of gravel beaches in Normandy, including: (1) How does the shoreline shape change through time? (2) Are
changes homogeneous at all elevations? (3) Are there specific mechanisms of shoreline change and what are their typical
temporal period of variability? (4) What physical phenomena are responsible for morphological changes? (5) What is
the shoreline's fabric made of? (6) How do the fabric's properties vary over time? (7) Can we link the morphological
variability to the sedimentary one?
To bring relevant solutions to this questioning, an Empirical Orthogonal Function (EOF) analysis was performed
using VMS-derived intertidal bathymetry datasets in order to identify the different mechanisms describing the shoreline
variability at various elevations. Then, a wavelet analysis was used to identify and compare the main periods of - Accepted manuscript
variability of morphological parameters (beach width, beach orientation angle and beach slope) with hydrodynamic ones
(wave energy, current velocity, and tidal range), and determine the main acting physical forcing processes. Finally, the
spatial and temporal variability of gravel size were analyzed in light of the results brought by previous analysis.
This study is articulated around 5 sections, the first of which is this introduction. Section 2 presents the study
sites and is succeeded by a material and methods description in section 3. Results are presented and discussed in section
4, and conclusive remarks are provided in the fifth and final section.
2. Study sites
The present study focuses on the shoreline dynamics of the pebble beaches of Hautot-sur-Mer and Etretat. These
two sites are located along the coast of Normandy, France, on the Southeast side of the English Channel (Figure 1). The
funnel morphology of the Channel produces extreme tidal ranges called megatidal (up to 15 m at Mont Saint Michel,
Bonnefille (1968); Chabert D’Hières and Le Provost (1978); Levoy et al. (2000); SHOM (1953)) and orient the wave
propagation in the channel extension’s direction (SW - NE).
Hautot-sur-Mer is a composite beach (Jennings and Shulmeister, 2002) with a steep slope (>10%) pebble ridge
(measured D50 = 7.1 cm) laying on sandy low tide terrace (measured D50 = 0.18 mm) (Figure 2). It is a 1100 m long
semi-open beach with a linear plan-form shape, installed in the hollow of a valley and surrounded by chalk cliffs. The
beach has nine groins installed perpendicularly to a seawall oriented at 71°N. The tidal range measured at Dieppe (4.5
km East of the study site) varies from 2.96 m in neap to 9.86 m in spring tide, with an average amplitude of 6.79 m
(Table 1). The gentle slope of the sandy low tide terrace (1.3%) allows the water to retreat over 210 m away from the
seawall at the lowest tides. The average wave height is 0.79 m heading 130°N, with a yearly maximum of 3.55 m for
the year 2019.
Etretat is a 1000 m long embayed purely gravel beach with a parabolic plan-form shape, installed at the outlet
of a valley and surrounded by chalk cliffs. The beach is composed of a steep slope (>12 %) pebble ridge (measured D50
= 5.2 cm) (Figure 2). A subtidal sandy substrate (measured D50 = 0.8 mm) (Soloy et al., 2020) appears on rare occasions
when the beach becomes mainly sandy after long repetitive heavy storm conditions. The beach is crossed by 4 groins
installed against the seawall, which has a mean orientation of 47°N. In the intertidal zone, bedrock emerges at low tide
on the sides of the bay. The tidal range varies from 3.2 m to 9.13 m, with an average of 6.08 m. At low tide, the beach
width can reach 150 m (Table 1). The average wave height is 0.89 m heading 145°N, with a yearly maximum of 4.44 m
for the year 2019. - Accepted manuscript
Figure 1 - Location maps of the study sites (a); Satellite Images of Etretat (b) and Hautot-sur-Mer (c). White frames indicate the area of
interest on the beaches, the coast orientation is displayed with an arrow.
Figure 2 - Conceptual model of the cross-shore composition profile of Etretat and Hautot-sur-Mer's beaches (angles and proportions are not
to scale). HT = High Tides, LT = Low Tides - Accepted manuscript
Table 1 - Morphological characteristics of beaches in Etretat and Hautot-sur-Mer
6.08 m
6.79 m
9.13 m
9.86 m
3.20 m
2.96 m
-4.80 m
-4.45 m
1000 m
1100 m
150 m
210 m
> 12 %
> 10 %
60 mm
75 mm
0.80 mm
0.18 mm
3. Material and Methods
3.1. Nearshore Hydrodynamics
The hydrodynamic parameters of this study were used to serve two different purposes: (1) estimating the
beaches’ 3D morphology using VMS-derived waterlines of known elevation (water level), and (2) comparing
morphodynamics with hydrodynamics (wave energy, tidal currents, tidal ranges).
For measuring the morphology (georeferencing the waterlines) in Hautot-sur-Mer, water level data was provided
by the tide gauge ran by the French Naval Hydrographic and Oceanographic Service (Service Hydrographique et
Oceanographique de la Marine, SHOM) and located in the harbor of Dieppe (49° 55' 45.0114"N, 1° 5' 4.1634"E), 4.2 km
North East from the VMS ( 10.17183/REFMAR#24). Unfortunately, there exist no other hydrodynamic
observation stations near the study sites. Hence, other hydrodynamic parameters were extracted from hindcast model
As there is no tidal gauge anywhere near Etretat, water levels (tide and surge) used for estimating the morphology
of the beach were provided by the Hycom2D model (Chassignet et al., 2007). The model’s output is given on a
curvilinear grid with a resolution ranging from 2 km far from the coast to 500 m close to the coasts. The time series was
extracted from the point of coordinates 49° 42' 45.7194"N, 0° 11' 34.4394"E. The maximum error on the water elevation
is expected to happen during high surge with an underestimation of 10 cm, while the tidal phase difference uncertainty
is 12 min (Pasquet et al., 2014). A comparison between Hycom2D and the water level gauge in Dieppe shows a Root
Mean Square Error (RMSE) of 0.26 m and a coefficient of determination () of 0.98 (0.13 m and 0.53 for surge alone).
Figure 3a presents the time series of water elevations in Etretat used in this study. Elevations are centered around zero
and vary from ± 2 m to ±5 m during the tidal cycle, with a maximum amplitude of 9.13 m. It is worth mentioning that
setup elevations are not considered by Hycom2D. Consequently, morphological data are projected with a bias that tends
to reduce their elevation by an order of magnitude of a few centimeters. - Accepted manuscript
Figure 3 - Hydrodynamical parameters in Etretat from July 2018 to December 2020: Water level (datum: mean water level) (a) ; Wave
Significant Height (b) ; Wave Peak Period (c) ; Roses of Wave Significant Height during Summer (April October) (d) and Winter (October
April) (e) periods.
Wave data were provided by the implementation of the WaveWatch 3 model (Tolman, 2009) by Ifremer (French
Research Institute for Exploitation of the Sea) over the English channel called PREVIMER_WW3-NORGAS-UG
(Dumas et al., 2014). The output is given on an unstructured grid with a resolution varying from 2 min of arc off the
shore to 200 m near the coast. Data were extracted at the point 49° 42' 53.7114"N, 0° 10' 58.35"E for Etretat - Accepted manuscript
(depth h = 21 m), and at the point 49° 56' 55.5936"N, 1° 1' 2.7042" for Hautot-sur-Mer (depth h = 17.5 m). This model
has been extensively validated with data from buoys and satellite altimeters (Michaud et al., 2015) showing an RMSE
of 25 cm and an of 0.94 on the sea surface wave significant height parameter (Hs) (Castelle et al., 2020). Output
parameters used in this study include Hs and wave direction, from July 2018 to November 2020.
Figure 3b and c present the wave significant height and period respectively in Etretat, as used in the present
study. During the period 2018 2020, the average Hs was 0.88 m with a maximum of 4.44 m, and the average peak
period was 7.0 s with a maximum of 18.2 s. Both parameters show a seasonality with higher values during winter
(October to April) and lower values during summer (April to October). Energetic events take place mainly during winter
seasons including Storm Ciara recorded on 10th of February 2020, when waves reached 4.44 m in height.
Wave roses presented in Figure 3e and f show that there are two main incoming wave directions: West and
North. During winter, 71.6 % of waves are coming from the Western sector (250°N - 310°N), and especially 50.0 %
come from directions ranging between 270°N and 290°N, with a maximum height of 4.44 m. The Northern sector (0°N
- 30°N) hosts 14.0 % of the waves with a maximum wave height of 2.76 m. On the other hand, summer waves are
coming from the Western sector 59.6 % of the time, 49.3% of the waves being concentrated between directions 270°N
to 290°N, with a maximum wave height of 3.30 m. The Northern sector hosts 26.1 % of the waves with a maximum
height of 3.16 m.
For each site, wave characteristics were used to calculate the energy flux .
    
Where  is the total wave energy determined using
, and is the wave group velocity
given by
, is the water depth, is the wave number   
, is the wavelength, and is the
wave celerity in transitional water   
 , g is the acceleration of gravity of 9.81 m/s, and T is the wave period.
This allows us to project  along the cross-shore and longshore local axis of the beach:
 
 
Where  and  represent the cross-shore and the longshore projections respectively, and is the angle
between the incoming waves and the beach orientation.
3.2. Shoreline Variability
Video Monitoring Systems (VMS) were installed in June and December of 2018 respectively in Etretat and
Hautot-sur-Mer. The VMS implementation and operational processing are presented and discussed in detail in a - Accepted manuscript
dedicated article (Soloy et al., 2021). For each site, 3 video cameras cover a panoramic view of the beaches (Figure 4),
recording time-averaged images (timex) every 10 min and over 10 min during daylight. A Mask R-CNN segmentation
model (He et al., 2017) is used to automatically delineate the waterline on images. Produced lines are then georeferenced
and clustered per tidal cycle in order to generate daily intertidal point-clouds. RMSE values show a vertical elevation
mean uncertainty of 22 cm in Etretat and 29 cm in Hautot-sur-Mer, which are within the range of values calculated by
authors for other sites (Plant et al., 2007; Uunk et al., 2010).
Figure 4 - Panoramic composition of the 3 camera views in Hautot-sur-Mer (top) and Etretat (bottom) (modified after Soloy et al. 2021).
On both sites, the morphological variability of the beach was evaluated through the analysis of three
morphological indices: the beach width (BW), the beach slope (BS) and the beach orientation angle (BOA). These
indices were extracted from our VMS-derived point clouds datasets.
BW is obtained by measuring the cross-shore distance separating waterlines to a predefined baseline along cross-
shore transects (Figure 5). In total, the beaches are segmented into 211 and 114 transects for Etretat and Hautot-sur-Mer,
respectively. Each transect starts from a perpendicular baseline located along the beach’s seawall where it is separated
by 2 m from its neighbors. Transects are all 100 m long while heading towards the sea and do not cross each other. BW
is the horizontal distance separating the baseline to a point of fixed elevation along each transect. Target elevations range
from -2 m to +3 m in Etretat (0 m being the local mean water level), and from +1 m to +3 m in Hautot-sur-Mer, and are
vertically separated by 1 m. When no waterline was recorded at the exact target elevation, an interpolated value between
the neighbor waterlines was used. Elevation limits indicated below were constrained by data availability throughout the
tidal cycle. The lower number of elevations in Hautot-sur-Mer is due to the difficulty of identifying a clearly contrasted
shoreline on the lower part of the composite system (z < +1 m).
BS was computed as the slope 
 along each transect, and between neighboring target elevation.
BOA is calculated by approximating the shoreline to a parabola. The orientation angle is then calculated as the
angle between the seawall and the parabola’s tangent of a selected transect. On both sites, the transects located at the
center between two groins were chosen to compute the BOA: P050 in Etretat and P075 in Hautot-sur-Mer. - Accepted manuscript
For all parameters, values were averaged at a daily time scale, and gaps were filled with linearly interpolated
ones. On both sites a malfunction disabled the right-side camera in November 2019 in Etretat and in June 2020 in Hautot-
sur-Mer. Consequently, the lateral extension of the beach being monitored changed through time. Thus, our analysis
will focus only on the profiles that remained in the left and center camera frames in Etretat, i.e., transects from P20 to
P114 (from July 2018 to June 2020), and only take into account the dates at which the right camera was still working in
Hautot-sur-Mer, i.e., from December 2018 to June 2020 (with transects from P20 to P99), in order to maximize both the
duration and beach lateral extension being analyzed.
This approach allows the study of one beach cell bounded with two groins on the sides and the sea wall at the
back for the two sites, which is here considered a local morphological unit whose evolution remains a good approximate
to the one of the larger scale coastal system. In Hautot-sur-Mer, the available data covers the halves of two different
boxes siding the groin located at P50 instead of a full one. Assuming that morphodynamics can be considered consistent
from one box to its direct neighbors as long as they remain similar in size, shape, composition and orientation, it is
assumed that results are representative of a full unit. The studied beach cell length is 188 m long in Etretat and are
100 and 140 m long in Hautot-sur-Mer for both the West and the East cells, respectively. - Accepted manuscript
Figure 5 - Cross-shore transects used for discretizing the shoreline position along the beach of Etretat (a) and Hautot-sur-Mer (b).
P100 - Accepted manuscript
3.3. Grain size mapping
The spatial variability of the sediment size was measured using the methodology developed by Soloy et al.
(2020). This method relies on the use of the Mask R-CNN algorithm to automatically detect and classify the non-
overlapping clasts visible on an image at the pixel scale. The size of the detected clasts can then be measured along the
long and short axis of the ellipse that fits the best to their contour. Using georeferenced ortho-imagery, it is possible to
map the spatial spread of sediment size over large areas (typically a few tens of thousands of square meters), at the scale
of single clasts. Measurements provided by this method were validated with = 0.98 and RMSE = 3.9 mm using
pebbles from Hautot-sur-Mer.
Ortho-images were produced using Structure from Motion (SfM) techniques applied on UAV data (Westoby et
al., 2012). The UAV measurement campaigns took place on 2020/06/10 in Etretat, and on 2019/04/09, 2019/06/04 and
2020/06/09 in Hautot-sur-Mer. The maps used for this study were produced by averaging the sediment long axis size
using a grid of resolution 1 m x 1 m.
3.4. Statistical approaches
The analysis of the evolution of the beaches’ morphology was performed using Empirical Orthogonal Functions
(EOF). This statistical method was proven relevant to extract spatio-temporal variability patterns in time series of
shoreline position (Aubrey, 1979; Medina et al., 1994, 1993; Turki et al., 2013; Winant et al., 1975).
The objective of this approach is to extract variability modes along both spatial and temporal dimensions, and
to quantify their dependance from the original time series of 2D shoreline positions . To do so, a map of linear
regressions and correlations is calculated, the axis of maximum amplitudes determines the first spatial and temporal
eigenfunctions, and , respectively. The first functions’ variability is then subtracted from the time series,
and the same procedure is applied again to define the second eigenfunctions along an orthogonal axis. The methodology
is iteratively repeated from    to   , where n is reached when the cumulative variance explained by all
eigenfunctions reaches a previously defined threshold. Therefore can be described as a series of linear
combinations of both spatial and temporal eigenfunctions.
 
Along with the EOF, the correlation factor was often used in this paper to evaluate the linear links between
different parameters.
  
Where  is the covariance between two vectors and , as calculated by 
. - Accepted manuscript
values can range from -1 to 1. However, as there was no need to discriminate negative from positive
correlations along this study, here refers as the absolute correlation value, therefore varying from 0 to 1. Correlation
values superior to 0.5 were considered significant.
The temporal evolution of signals was also investigated using a wavelet analysis. The wavelet transform is a
high-resolution frequency analysis technique that consists of decomposing a signal in both time and frequency in order
to describe both periodic and non-periodic changes.
A wavelet transform is used to decompose the signal based on children wavelet, which correspond to scaled and
translated versions of a reference parent wavelet. Each wavelet has a finite length (a scale) and is localized in time. The
parent wavelet includes two parameters for time-frequency exploration: a scale parameter and a temporal localization
parameter .
The parameterization in scales and the translation of the children wavelet allows the detection of the different
frequencies composing the signal. The continuous wavelet transform of a signal S(t) produces a local wavelet spectrum,
as defined by 
 . The local wavelet spectrum allows a description and visualization of the
power distribution (color axis) along the different frequencies/periods (y axis) over time (x axis).
The wavelet power can then be averaged at each period to obtain the global wavelet spectrum (GWS), which
highlights the periods (modes) of variability present in the signal.
4. Results and discussions
4.1. Morphological Changes in shoreline position
The spatial and temporal variability of the shoreline position of Etretat and Hautot-sur-Mer beaches was
investigated using 2 years of daily observations. The shoreline position at elevations ranging -2 m to +3 m (1 m step)
from mid-2018 to late 2020 in Etretat, and at elevations +1 m to +3 m from early 2019 to mid-2020 in Hautot-sur-Mer,
are presented in Figure 6a and b, respectively. Time series of the average BW at each elevation are shown in Figure 6c
and d, as well as the average planform shape of the shoreline in Figure 6e and f. - Accepted manuscript
Figure 6 - Planform evolution of the +2 m elevation shoreline position in Etretat (a) and Hautot-sur-Mer (b), from July 2018 to November 2020. Time series of average beach width between elevations -2
m and +3 m in Etretat (c), and from +1 and +3 m in Hautot-sur-Mer (d), with 1 m of span. Average planform shape of the shoreline at the same elevations in Etretat (e) and Hautot-sur-Mer (f). The position
of groin structures is indicated with black dashed lines. - Accepted manuscript
As a first observation, the shorelines’ planform shapes visible on Figure 6a, b, e, and f differ
from one site to the other. In Etretat, the shoreline adopts the shape of a parabola with a center part being
closer to the seawall than both of its ends near Groins 1 and 2. The shape is more linear in Hautot-sur-
Mer where the right side of a cell (left side of groins) is on average farther from the seawall than the left
one (right side of groins). Regarding cross-shore slopes, Figure 6e shows the increasing slope with
elevation, from around 0.14 between -2 m and -1 m, to 0.25 between +2 and +3 m. The small bump
visible at each elevation on a diagonal from P70 at -2 m to P80 at +3 m corresponds to a small
discrepancy in camera alignments that is also visible on Figure 6a. In Hautot-sur-Mer (Figure 6f), the
average slope is 0.10 between +1 m and +2 m, and 0.12 between +2 m and +3 m. Although the smaller
number of elevations does not allow for the lower profile to be evaluated here, a slope of 0.013 was
measured on the sandy substrate by Soloy et al. (2020).
On Figure 6a and b, the succession of reddish and blueish colors corresponds to a series of
advance and retreat movements. Changes are differently manifested along the beach, especially in
Hautot-sur-Mer where the wide side changes from west to east through time. This variation is likely
associated with a beach planform rotation around a pivotal point generated by the wave diffraction near
the groins and its obliquity responsible for a longshore transport. Figure 6b suggests a seasonality in the
rotation mechanism with an alternance between two main beach orientations: (1) a wider side to the left
of the beach cell (beach facing NE) from April to August, and (2) a wider side to the right (beach facing
NW) throughout the rest of the year.
In Etretat, the time series of average BW Figure 6c do not show any clear seasonal pattern. The
+3 m beach width consistently retreats from 30 m in July 2018 to 20 m in December 2019. It then
suddenly reaches its low around 12 m where it remains from December to April 2020 before advancing
to 30 m again by April May, where it remained until the end of the time series. The period of retreated
shoreline observed from December to April 2020 corresponds to a cluster of severe winter storms.
During this cluster of storms, an old groin (Figure 7) that is usually covered by sediment emerged around
P60 in Etretat, thanks to erosion, and the top of the beach even became sandy for a few weeks. At the
bottom of the beach, the -2 m beach width consistently remained around 60 m, with no significant change
during winter 2020, but advancing towards 63 m on average at the end of the storm period. - Accepted manuscript
Figure 7 Sand covering the beach in Etretat, normally covered with gravel (2020/02/16). An old rocky and usually
buried groin is visible on a, as well as old wooden groin poles on b.
In Hautot-sur-Mer, a subtle seasonality pattern is visible in the time series of beach width with
values evolving from 25 m in December to 30 m in July, at +3 m of elevation and from 33 to 38 m at 0
m at the same dates. The amplitude of daily changes also evolves with 2 to 3 m on average during
summer seasons up to 7 to 8 m during winter ones. However, the early 2020 cluster of storm events in
Hautot-sur-Mer did not provoke a period of minimum beach width as was observed in Etretat, although
large variations are visible during this period.
Buried Groin
Groin 1
Old wooden
groin poles - Accepted manuscript
Despite their proximity, both sites present significant morphodynamical differences. The
difference in shoreline planform shapes is first explained by the difference in openness between both
coastlines: embayed/enclosed beaches like Etretat naturally adopt a concave shape while open beaches
are more linear at a large scale. At the scale of the beach cell, groin structures also play a role in the
shoreline shape by accumulating the alongshore-drifted sediment on one side while creating a deficit on
the other side. The effect of groins on the shoreline planform shape was modeled by Leont’yev (2018,
2007), who showed that the planform shape consecutive to the presence of groins can be summarized
as a linear function describing the accumulative side of the groin, and as a sinusoid for the erosive one.
The extent of the groin’s influence zone depends on both groin characteristics (size, elevation, spacing,
etc.) and the longshore sediment flux characteristics (i.e., sediment discharge, flux channel size,
etc.). The author explains that if the distance between groins is lower than the extent of the groin’s
influence on one of its sides given a certain sediment flux, the erosive side of a groin will interact with
the accumulative side of its neighbor. This interaction limits the development of a sinusoid pattern,
resulting on a more linear shoreline such as what can be observed in Hautot-sur-Mer. The average left-
facing planform shoreline orientation also suggests an asymmetric longshore drift in a West to East
direction, which is confirmed by the observations of Costa et al. (2015). The location of Etretat near the
Cape of Antifer - where the sediment alongshore drift asymmetry is lower (Costa et al., 2015) - allows
the average planform shoreline between groins to be more parabolic, thanks to the more even
permutations between accumulative and erosive sides of groins (Leont’yev, 2018).
Etretat seems to be more sensitive to the impact of storms than Hautot-sur-Mer, and especially
clustered ones. The influence of storm clustering on the eroded sediment volume was shown by
Karunarathna et al. (2014) to be largely higher than the influence of the sum of each individual storms
on sandy beaches. Assuming that the same phenomenon happens with coarser sediment, it could explain
the observed retreat in Etretat. The reason why Hautot-sur-Mer does not experience the same retreat is
probably due to the protection offered by the dissipative low tide terrace. Indeed, Almeida et al. (2014)
were able to compare the offshore significant wave height to the onshore one on different types of
beaches and showed that storm wave height was reduced by a factor of 2 to 2.5 on composite beaches
due to the low tide terrace dissipative effect, while wave height was not reduced and even be slightly
increased on purely gravel beaches.
The transition from gravel to sand by erosion in Etretat during the storm period changed the
properties of the fabric exposed to the waves, likely lowering its permeability (Krumbein and Monk,
1943) while still offering a reflective profile to incoming waves, although more gently slopped. Hay et
al. (2014) reported similar observations on a mixed sand gravel beach of Canada, with a decrease in
surficial sediment median diameter when the wave energy was increasing. The consecutive relative - Accepted manuscript
stability of the +2 m and +3 m beach width at this period while lower elevations present a higher
variability is a phenomenon observed by Karunarathna et al. (2012), who explained that composite
beaches may become unstable during storms due to the cutback of the upper beach during a previous
storm. Although Etretat’s beach is considered purely gravel, this transition from gravel to sand makes it
somewhat comparable to a composite one. Our hypothesis is that the gravel sediment eroded from the
top of the beach was deposited at the subtidal bottom, unmonitored, thus building the beach step and
providing a focus point to stabilize the runup extent and the swash to lower elevations, thus protecting
the upper beach, as already evidenced on a gravel beach by Poate et al. (2013).
4.2. Principal components of variability
EOF were calculated using time series of average beach width at the various selected elevations
with the aim of extracting principal components (PC) of morphological variability to characterize the
beaches’ spatiotemporal morphodynamics. Each PC describes a percentage of the shoreline’s total
variability in space and time between -2 m and +3 m in Etretat (Figure 8), and from +1 m to +3 m in
Hautot-sur-Mer (Figure 9). Linear correlation coefficients were then calculated between different
components and morphological parameters (BW, BS, BOA and PCs), and with hydrodynamical ones
(wave energy, current velocity, and tidal range). The result correlation matrices are presented in Figure
10. In all cases, the significance threshold is set to 0.5 which was selected as the conventional value for
rejection of the null hypothesis (absence of correlation). Figure 11 presents a conceptual model, which
describes how each PC is related to one or several mechanisms, and to which spatial extent.
Table 2 presents the percentage of the total variability explained by each PC. Results show that
up to six PCs are necessary to explain at least 90% of the total variability of Etretat’s shoreline position.
In Hautot-Mer, the number of PCs required to reach the same threshold is 14, thus showing higher
complexity. Therefore, the threshold of cumulated explained variability was lowered to 80% for this
site, although it still includes up to 7 PCs. However, PC6 in Etretat and PC5 to 7 in Hautot-sur-Mer are
considered residual in further discussion as their behavior is erratic and their relative variability remains
low. For both sites, the first PC explains around half of the total variability, with 62.4% in Etretat and
46.1% in Hautot-sur-Mer. Further PCs account for significantly lower amounts, although similar from
site to site. - Accepted manuscript
Table 2 - Percentage of the total variability explained by the EOF components in Etretat and Hautot-sur-Mer.
Principal Components
Figure 8 presents the results of the EOF in Etretat. Both spatial () and temporal
() eigenfunctions are presented at the top and at the bottom of each PC’s subfigure, respectively.
Elevations are displayed on an inversed axis to make the figure’s top correspond to the sea side, while
the bottom is the land side. Dashed black lines locate the position of groin structures, and the black line
represents the stability line (i.e., line of zero variability). The red line on figures of is the equivalent
stability through time.
4.2.1. Etretat PC 1 Cross-shore translation
On Figure 8a, shows consistent positive values with no crossing of the stability
line, which indicates that the entire region moves all together in the same direction, either seaward or
landward. The magnitude of variability is larger towards the high elevation left side than the low right
side. Therefore, PC1 depicts a cross-shore translation mechanism, with an alternation between advances
and retreats. McCarroll et al. (2019) observed that cross-shore mechanisms tend to become significant
on embayed beaches longer than 1 km, which agrees with our observation. However, the subtle
longshore gradient indicating slightly larger magnitudes on the left side than the right one suggests that
the observed translation could be a related to a rotation mechanism at the scale of the entire beach. A
small drop is visible around the buried groin at the highest elevations, which tends to show the structure’s
influence on the cross-shore variability.
Although does not show a specific seasonal variability, it resembles the time series of BW
(Figure 6c), including a period of significantly lower values between December 2019 and April 2020,
which corresponds to the storm period mentioned in section 4.1. Positive values correspond to advanced
shoreline positions while negative ones reflect a retreated state.
PC1 is primarily correlated to BW with values ranging from 0.72 to 0.96 (Figure 8a), and to a
lower extent is also correlated to BOA with values from 0.52 to 0.56 (except for elevation -2 m with
= 0.38 and 0.36, respectively). The link observed between PC1 and BOA remains difficult to explain
with our data alone, although it could be the manifestation of an alongshore gradient in the cross-shore
wave energy such as the one observed by Harley et al. (2015) on a sandy beach. - Accepted manuscript
Regarding hydrodynamics (Figure 8c), none of Etretat’s PCs is significantly correlated to any
of the considered parameters at the 0.5 threshold. It is generally accepted that hydrodynamics alone are
not enough information to the shoreline position change of gravel systems, and that the spatial dispersion
of gravel sizes and shapes and their temporal variability are necessary to be considered (Buscombe and
Masselink, 2006), therefore low correlation values between hydro- and morphodynamical parameters is
not surprising. PC 2 Rollover
Figure 8b presents PC2, which describes an alternation between states of advanced shorelines
at low elevations while high elevations shorelines are retreated, and the opposite. This would correspond
to a mechanism of beach rollover (Buscombe and Masselink, 2006) affecting the beach slope, whose
axis of rotation would be located around elevations 0 m and +1 m, according to the alongshore-extended
stability line’s location on the subfigure. To the authors’ knowledge, it is the first time
that a rollover mechanism is identified using an EOF analysis applied on a shoreline position dataset,
although this process is important especially for gravel beaches (Austin and Masselink, 2006; Buscombe
and Masselink, 2006), and was often described in the literature (e.g. Isla and Bujalesky (2000); Odezulu
et al. (2018); Talavera et al. (2018)).
shows a negative trend that could be interpreted as a decreasing tendency of the beach
slope throughout the two years of monitoring. Positive values translate a steep slope and negative values
correspond to a gentle slope. Buscombe and Masselink (2006) described the rollover process as a
response to storms, which seems to be the case on , for instance with the storm of January 2020
that significantly lowered the slope. But variability appears to be more complex, especially
considering the negative trend, and it is likely that other factors might be responsible for a significant
part of it such as climate parameters (e.g. Sea Level Pressure, see Montaño et al., 2020), intrinsic
characteristics (e.g. granulometry, permeability, etc.), or larger scale mechanisms (e.g. global rotation).
Regarding correlations to morphological parameters, PC2 is expectedly well correlated to BS
( = 0.82). However, it also shows significant correlations with BW at -1 m and -2 m ( = 0.6 and 0.83,
respectively), while these elevations were the ones presenting the lowest correlations between BW and
PC1. This observation shows that the lower the elevation, the lesser the response of the shoreline to
cross-shore translation processes, and the larger its link with rollover processes. - Accepted manuscript
21 PC 3 Breathing
Figure 8c presents PC3, a breathing mechanism, first described by Ratliff and Murray (2014),
and defined as “changes in shoreline curvature as [sediment] move from the middle of the [beach cell]
to the edges, and back”. Indeed, draws two stability lines developed in the alongshore
direction and separating the site into 3 alongshore extended regions: high (z > +1 m), intermediate (-1 <
z < +1 m), and low elevations (z < -1 m). When both high and low elevations’ shorelines are retreated,
intermediate ones are advanced, and vice versa. The “eye” shape of this pattern tends to show that the
lowest stability line could be extended further to the left towards elevations lower than -2 m, although
not monitored here.
Interestingly, PC3 shows a cross-shore curvature simultaneous to the longshore one, but with
an even higher magnitude of variability. To the authors’ knowledge, this type of cross-shore component
in a breathing mechanism was not yet described in the literature. This shows that sediment mostly moves
along the cross-shore direction, from low and high elevations towards intermediate ones (i.e., around
the mean sea level) and back.
Regarding , positive values of correspond to a “deflated” state (i.e., concave cross-shore
profile), negative values represent an “inflated” state. The time series presents a seasonal dynamic with
on average deflated states during winter and inflated ones during summer. The daily variability is also
higher during the winter season. Similar variability was observed in breathing mechanisms by Ratliff
and Murray (2014) and Robinet et al. (2020) on embayed beaches, and by Blossier et al. (2017) on a
barline. Concerning correlations, presents no significant correlation with any of the tested
parameters. PC 4 Large scale rotation
PC4 shown in Figure 8d is the first mainly longshore mechanism. It is evidenced by the presence
of a cross-shore oriented stability line separating two compartments on , the left one of
which is retreated when the right one is advanced, and vice versa. This can be understood as a
mechanism of rotation, which generally takes place around a pivotal point and defines retreat
movements at one end and advance ones at the other end. The pivotal point was defined by Short et al.
(2000) as the point of minimal variability along the beach which here corresponds to the stability line.
On present results, the stability line is formed by the succession of pivotal points forms at different
elevations. - Accepted manuscript
The stability line starts from P90 at the top of the beach (+3 m) and goes towards the left to P50
at 0 m, and then goes back towards the right to P80 at -2 m, although one would expect it to be vertical.
The change in direction of the stability line at elevation 0 m highlights the existence of a symmetrical
process centered on 0 m, with a wider variability at the lowest elevations. These observations indicate
that this specific rotation mechanism is likely related to the effect of tides. Indeed, Masselink and Short
(1993) showed that tides shift horizontally and vertically the position where processes such as shoaling,
surf and swash happen and dissipate the wave energy. Moreover, authors explain that the relative amount
of time that the profile is impacted by each process also depends on the tidal range and phasis: Swash
has two maximums at both turns of tides. Hence the lowest and highest regions being more variable than
the center one. In addition, the oblique stability line could be the result of a change in relative the relative
influence of the longshore projection of the swash, due to the same effect. The position of groins does
not seem related to any pattern on , the rotation mechanism described by PC4 thus
probably describes a mechanism of larger spatial scale than one of the beach cell.
Regarding , positive values along correspond to a clockwise orientation, negative
ones reflect a counterclockwise orientation. The variability is higher during the winter season although
there is no clear seasonal pattern: the beach was on average oriented towards opposite directions between
January and July of 2019 than between the same period of 2020. In terms of correlations, PC4 is only
corelated to BOA at -2 m and -1 m ( = 0.54 and 0.52, respectively), correlation values then decrease
with the elevation, under the significance threshold of 0.5, which confirms our previous observations. PC 5 Beach cell rotation
PC5, Figure 8e, represents another longshore mechanism of rotation, this time influenced by the
presence of groin structures. Indeed, the left beach cell - bounded by Groins 1 and 2 - is divided into
mainly two lateral compartments, the left one of which follows the dynamics of the area located on the
right side of Groin 2 (i.e., the left side of the unmonitored beach cell at the right extremity).
The stability line adopts the same shape as the one of PC4, except that instead of connecting
both cross-shore sides, it connects between the two beach cells and forms a thin string of warmer colors
at elevation -1 m. This string translates the presence of a local change in the slope at the lowest elevations
provoked by a difference of cross-shore translation rates between elevations -1 m and -2 m. This
phenomenon is thought to be the result of sediment by passing Groin 2, which is rarely exposed to water
under 0 m, contrary to Groin 1. In addition, the stability line follows the direction of Groin 2, which
once more highlights the influence of groins on the sediment dynamics. Similar observations on a beach
of North Carolina, USA were made by Miller and Dean (2007). - Accepted manuscript
Considering the temporal evolution, present a periodic variability with cycles from a few
weeks up to 3 months, that do not correspond to the ones of the larger scale rotation . Positive
values correspond to a clockwise orientation, while negative ones are relative to a counterclockwise
orientation. is correlated with BOA at +1 m, +2 m and +3 m which is the opposite of PC4 and
confirms that rotation is affected by the presence of groin structures, hence the need for 2 modes to
describe this mechanism while including or excluding groins.
Figure 8 - Results of the EOF analysis applied to Etretat’s shoreline position from elevations -2 m to +3 m. Principal
Components 1 to 5 are presented in frames a to e, respectively. Top surface plots are presenting the spatial eigenfunction
, the Y axis was inversed so the sea side is towards the figure’s top and the land side is towards the bottom.
Groin structures were marked with black dashed lines, and the contour of zero variability (i.e. stability line) was drawn as a - Accepted manuscript
solid black line. Bottom time series show the temporal eigenfunction associated with each component, the red line
highlights the minimum of variability.
4.2.2. Hautot-sur-Mer PC 1 Right-centered beach cell rotation
Figure 9 presents the results of the previous methodology applied to Hautot-sur-Mer.
, displayed in Figure 9a, opposes both left and right sides of the beach cells with a quasi-
vertical stability line located towards the right and a maximum of variability to the left. PC1 is therefore
characterizing a longshore rotation mechanism with a stability/pivot line located around transects P90
and P30 for the right and left beach cells, respectively. Another cross-shore oriented stability line can
be seen at the position of Groin 2, which shows that this rotation mechanism is limited to the beach cell
spatial scale.
shows a very clear seasonality pattern with negative values from April to September, and
positive ones from September to April, following a near binary evolution with values averaging either
+50 or -50, and rarely others. This situation translates the presence of two main stable shoreline
orientations: counterclockwise when values are negative, and clockwise when they are positive,
while most states in between seem to be transitory.
Regarding correlations (Figure 10), PC1 shows high correlations with both BW and BOA, the
first of which increases with elevation ( = 0.72, 0.83 and 0.87 for +1 m, +2 m, and +3 m, respectively)
when the second decreases ( = 0.88, 0.86 and 0.84 for +1 m, +2 m, and +3 m, respectively). The reason
for such high correlation values with BW being related to a beach rotation mode is the unbalance in size
and relative variability between both sides of the cell. With a higher magnitude of variability to the left
and a wider region where this variability applies, losses in the left side are not fully compensated by
right side’s gains, resulting in a rotation-induced cross-shore translation: an overall advance/retreat that
will be simultaneous to the rotation event (Figure 11).
When compared with morphodynamics, BW is the only parameter to show any significant
correlation, with = 0.53 and 0.5 for elevations +3 m and +2 m, respectively. Regarding hydrodynamics,
correlation with the longshore wave energy ( = 0.45) and both the cross-shore and total wave energy
( = 0.39) remain relatively high compared with other parameters despite being bellow the significance
threshold of 0.5. This tends to indicate that PC1 and more specifically its cross-shore translation aspect
is likely linked to wave dissipation processes. - Accepted manuscript
25 PC 2 Left-centered beach cell rotation
in Figure 9b exhibit a very similar spatial variability as PC1 although this time,
the stability line present at +3 m and +2 m does not go all the way down to +1 m and stops when reaching
the groin and is located towards the left of the beach cells with a maximum of variability to the right.
We interpret PC2 as the expression of a second mode of beach cell rotation mechanism, less influential
than PC1, especially acting at high elevations, and with a stability/pivotal line to the left around P70 and
P20 for the right and left beach cells, respectively. At +1 m, the shoreline essentially migrates a cross-
shore movement with higher magnitudes of variability towards the left of the beach cells.
In , positive values correspond to a clockwise orientation, and negative values represent a
counterclockwise one. The time series does not present any remarkable pattern such as seasonality or
opposed binary states similar to the ones observed with PC1. When calculating correlation values
(Figure 10), PC2 does not show any significant relationship with the tested parameters. PC 3 Large scale rotation
(Figure 9c) presents an opposition between the left and right sides of the
monitored region, with a large near zero variability area around Groin 2, which is shown by the apparent
chaotic behavior of the stability line, although it overall separates both left and right compartments. It
therefore translates a third mode of rotation mechanism, at a larger spatial scale than the previous ones.
does not seem to show any significant seasonality or opposed binary states either. Positive
values refer to a counterclockwise orientation while negative ones are relative to a clockwise one. In
terms of correlation, no significant link was found between PC3 and any of the tested parameters. PC 4 Rollover
PC4 presented in Figure 9d highlights a mainly cross-shore gradient of variability although the
stability line shown on is not straight. This means that PC4 encapsulates information
about the slope and thus translates a mechanism of rollover, whose variability varies in the longshore
direction, in this case within a center of rotation located at lower elevation near the groins and at higher
elevation around the middle of the beach cell.
shows a slight seasonal alternation of negative values (gentle/dissipative slope) between
May and October (i.e., summer), and positive (steep/reflective slope) the rest of the time. However, the
minimum (most gentle slope) is reached in January 2020, i.e., during the storm period. Regarding - Accepted manuscript
correlations, PC4 is significantly correlated with BS, which confirms our interpretation of this mode
being a characterization of a rollover mechanism.
Figure 9 - Results of the EOF analysis applied to Hautot-sur-Mer’s shoreline position from elevations +1 m to +3 m.
Principal Components 1 to 4 are presented in frames a to d, respectively. Top surface plots are presenting the spatial
eigenfunction , the Y axis was inversed so the sea side is towards the figure’s top and the land side is towards
the bottom. Groin structures were marked with black dashed lines, and the contour of zero variability (i.e. stability line) was
drawn as a solid black line. Bottom time series show the temporal eigenfunction associated with each component, the
red line highlights the minimum of variability. - Accepted manuscript
Figure 10 - Correlation matrix between morphodynamical parameters including beach width (BW), beach orientation
angle (BOA) and beach slope (BS) and the temporal eigenfunction of the principal components (PC) resulting from the EOF
analysis applied to Etretat’s shoreline position from elevations -2 m to +3 m (a), and to Hautot-sur-Mer from elevations +1
m to +3 m (b). c and d present the same operation calculated with hydrodynamic parameters including wave energy, current
velocity and tidal range. - Accepted manuscript
Figure 11 - Conceptual model of the isolated mechanisms of beach morphological variability in Etretat (left) and Hautot-
sur-Mer (right), associated with their corresponding principal component (PC). - Accepted manuscript
4.3. Periods of variability and morphological response to hydrodynamic conditions
The temporal variability of the different shoreline’s morphological parameters (BW, BOA and
BS) was assessed using a wavelet analysis. For each elevation, the wavelet power was temporally
averaged (GWS), thus highlighting the period(s) carrying the most variability. Due to the limited length
of the time series, only shorter periods than approximately 6 months in Hautot-sur-Mer and 8 months in
Etretat fell within the wavelet’s cone of influence, which are therefore the longest periods to be analyzed.
Results are presented in Figure 12a to f. For comparison, the same analysis was performed using time
series of different hydrodynamic parameters including wave energy, current velocities, and tidal range
(Figure 12e to j). Table 3 summarizes the main periods of variability identified on Figure 12.
For both sites, most of the variability is located towards the longest periods (6 to 8 months),
regardless of the parameter or the elevation. Morphological variability is also depending on the
elevation, especially for longer periods than 5 months (Figure 12). This corresponds to the observations
made by multiple authors (Lemos et al., 2018; Reeve et al., 2007) although investigations are usually
carried out over longer timeframes (typically decades using monthly measurements). Interestingly, the
magnitude of BOA’s variability in Etretat is not proportional to the absolute elevation but rather to the
relative elevation compared to the mean sea level. This observation suggests that the amplitude of beach
rotation is minimal towards z = 0 m and increases at both higher and lower elevations, which was not
reported in the literature, to the authors’ knowledge.
In Etretat, identified periods of morphological variability include 2, 3, 5 and 8+ months, all
parameters and elevations considered (Figure 12, Table 3). In Hautot-sur-Mer, periods were identified
at 2 and 6 months for all parameters, with an additional period at 3 months for BS alone. The observed
periods correspond to medium-scales components of variability, which are usually related to seasonal
or near-seasonal hydrodynamic processes (Loureiro and Ferreira, 2020). More specifically, the wave
exposure and the occurrence of storms are often documented as the main process responsible for
medium-term morphological changes (McCarroll et al., 2019; Ruiz de Alegria-Arzaburu and Masselink,
2010; Turki et al., 2013). Hydrodynamics’ spectral patterns remain very similar from one site to the
other. The wave energy spectrum presents two main periods at 2 and 8+ months in Etretat, and at 2 and
6 months in Hautot-sur-Mer. The tidal range spectrum shows two main periods at 1 month and 2 weeks,
the latter also being the only period identified on the current velocity spectrum. These periods
respectively correspond to the monthly lunar (Mm, T = 27.5 d) and the fortnightly lunar (Mf, T = 13.6 d)
tidal components. Although tidal ranges play an essential role in distributing the wave energy along
beach profiles (Masselink and Short, 1993), and tidal energy converted into currents is proportional to
the tidal amplitude squared (Hammons, 1993), investigated tidal processes do not modulate a significant - Accepted manuscript
part of the beaches’ morphodynamical variability for shorter periods than 6 to 8 months. Thus, the wave
energy is the only parameter to show common periods of variability with morphodynamics, meaning
that wave processes are in good part responsible for temporal changes of BW, BOA and BS signals.
These results tend to agree with findings from Stark and Hay (2016), who showed that the bottom stress
of tidal currents in a mega-tidal context was too low to significantly move single gravel.
These results provide insights into the possible processes responsible for the beach changes ;
These insights remain limited by availability in time and quality of data. Indeed, wave breaking and
swash were specifically shown to be linked with morphological processes especially for gravel beaches
(Guest and Hay, 2021) although their variability is expected to be more significant at longer time scales
(Almeida et al., 2014; Buscombe and Masselink, 2006; Karunarathna et al., 2012; Poate et al., 2013;
Ratliff and Murray, 2014).
Table 3 - Summary of the identified temporal periods of variability in morphological (yellow) and hydrodynamical (blue)
signals in Etretat and Hautot-sur-Mer. Parameters include beach width (BW), beach orientation angle (BOA), beach slope
(BS), wave energy (WE), current velocity (CS), and tidal range (TR).
X - Accepted manuscript
Figure 12 - Global Wavelet Spectrum (GWS) calculated from beach width (a, b), beach orientation angle (c, d), beach
slope (e, f), wave energy (g, h), current velocity (i, j) and tidal range (k, l) time series in Etretat (left) and Hautot-sur-Mer
(right). - Accepted manuscript
4.4. Spatio-temporal variability of the surficial gravel size
Gravel beaches’ ability to dissipate wave energy through infiltration was shown to be a function
of the permeability associated with the local size distribution of the gravel fabric (McCall et al., 2012,
2015). Other studies reported results suggesting that the surface roughness is also and maybe even more
important than permeability as a controlling factor of the wave energy dissipation and reflection, and
thus of the beaches’ response to hydrodynamics (Jennings and Shulmeister, 2002; Mason et al., 1997;
Powell, 1990). Moreover, at each instant the mobilizable gravels on a beach are expected to be the
surficial ones, as they are the ones receiving most of the drag force due to waves while remaining
relatively free to move, which can be summarized by the concept of entrainment threshold (Brayne et
al., 2020; Lorang, 2000). Surficial gravels tend to get sorted by size and shape, thus forming a patchwork
of so called clast assemblages, each of which corresponds to a “discrete population of gravel clasts
which is characterized by textural unity” (Bluck, 1999). The presence of assemblages on the beach face
highlights the spatial variability of surface roughness (Stark et al., 2014). Position, orientation, size,
shape, and composition of assemblages are the result of antecedent conditions of sediment supply
availability, and sediment sorting processes (Buscombe and Masselink, 2006). Their temporal
variability could potentially be used as a proxy of surface sediment transport processes, as was
demonstrated by Guest and Hay (2021) using remote sensing techniques applied on 14 days of high
frequency video images, over a 2.7 m longshore span.
In this section, we aim to characterize some components of spatial and temporal variability of
surficial grain size at the scale of the beach cell, and to associate them with morphodynamics given a
relatively limited dataset composed of one map of mean grain size in Etretat (2020/06/10, Figure 13a)
and three in Hautot-sur-Mer (2019/04/09, 2019/06/04 and 2020/06/09, Figure 13b, c and d,
respectively). Importantly, although variability of gravel shapes is thought to play an important role in
gravel system’s dynamics (Buscombe and Masselink, 2006), shapes are not investigated in this study.
In Table 4, the commonly used grain size values related to each campaign are presented (D16, D50,
D84, mean size and std) along with other statistical factors.
4.4.1. Mean Grain Size
The mean grain size is lower in Etretat (5.6 cm ± 1.7) than Hautot-sur-Mer (7.2 cm ± 2.8 to 8.2
cm ± 2.9). Indeed, Etretat’s pebbles are resupplied less often due to the lower erosion rate of its chalk
cliffs (source of the flint supply), while being kept trapped on an embayed beach without the protection
of dissipative low tide terrace like in Hautot-sur-Mer (Costa et al., 2015). Therefore, Etretat’s pebble
tend to shrink down through abrasion to a lower diameter that is more at the equilibrium with the local - Accepted manuscript
conditions of higher wave energy, lower longshore mobility and lower resupply fluxes (Bertoni et al.,
In Hautot-sur-Mer, the mean sediment size varies between 8.2 cm ± 0.29 on 2019/04/09 and 7.2
cm ± 2.6, on 2019/06/04. This temporal variability corresponds to 32% change of volume in 2 months
(considering spheres with a diameter equivalent to the averaged measured clast’ surface). A temporal
decrease in gravel size on beaches was documented by Bertoni et al. (2016), who measured an average
weight loss of almost 20% after an 8- to 10-month period, and 60% after 13 months on 240 retrieved
marked marble pebbles, at Pisa’s beach, in Italy. Considering these results, 32% of volume difference
due to abrasion in only two spring months seems high, especially with flint material. Another
explanation could be the occurrence of a local size sorting mechanism such as rotation (measured
rotation of 5° clockwise between the two dates) and mixing. In addition, the occurrence of percolation
through the oscillatory forcing of swash could have a segmentary effect by burying/uncovering selected
size ranges of clasts (“Brazil Nut Effect” (BNE) and “Reverse BNE” (RBNE)(Nadler, 2012; Ulrich et
al., 2007)).
4.4.2. Sedimentary patterns
On Figure 13, in general, the average clast length tends to increase from higher to lower
elevations. Two main types of sedimentary patterns can be identified on the maps, namely clast
assemblages and cusps, with spatial and temporal variabilities in the order of one to several centimeters.
Assemblages are textural zonation that can be located anywhere on the beach face and extend in any
direction, with a typical scale of several tens of meters. For example, a 50 m long assemblage (Average
size > 10 cm, surrounding size < 8 cm) can be seen at the bottom of the beach face in Hautot-sur-Mer
on 2020/06/09 (Figure 13d) and a similar one (Average size > 7 cm, surrounding size < 6 cm) at the
northeast side of Etretat’s beach cell (Figure 13a), one day later. Such patterns, located bellow the
elevation of the last tide, were likely formed (at least partly) within hours to days, depending on the
antecedent conditions of wave energy. Higher elevation patterns such as the accumulations at the top
east corner of the beach cells of Hautot-sur-Mer are likely due to older events. Groin structures seem to
attract larger thus clasts forming groin assemblages at various elevations, generally asymmetrically.
Interestingly, assemblages in Hautot-sur-Mer are in general periodic from beach cell to beach cell, which
suggests that their conditions of formation are influenced by the presence of groins, even at the beach
cell’s center.
Gravel cusps are described by Buscombe and Masselink (2006) as quasi-periodic topographic
oscillations of the shoreline provoked by swash flows, forming cross-shore extended horns with coarser - Accepted manuscript
clasts and bays with smaller ones. Although no cusp is observed in Etretat, they are present at every
measured date in Hautot-sur-Mer with varying wavelengths and amplitude. Their presence and
characteristics seem to be largely responsible for the quality of size sorting: the more developed the
cusps, the poorer the sorting at the scale of the beach cell. However, despite being supposedly well
correlated to the swash energy (Guest and Hay, 2019; Jennings and Shulmeister, 2002), our limited
dataset doesn’t allow to draw a strict relationship between the characteristics of cusps and simultaneous
incoming waves.
The similarity in size sorting between both sites in June 2020 (hardly visible to no visible cusps,
50 m long assemblages at the bottom of the beach face) contrasts with the high temporal variability
evidenced in Hautot-sur-Mer. It suggests that similar wave climate led to the appearance of similar
spatial types of sorting patterns between groins, despite the differences in sediment supply (available
volume, gravel size), and general context (embayment, low tide terrace, vertical structure (e.g., porosity
and permeability)).
Table 4 - Grain size results in meters for each UAV measurement campaign.
0.028 - Accepted manuscript
Figure 13 - Maps of mean clast length measured in Etretat on 2020/06/10 (a) and Hautot-sur-Mer on 2019/04/09 (b),
2019/06/04 (c) and 2020/06/09 (d). Contour lines of elevation are indicated for each round elevation with a vertical
separation of 1 m. Hydrodynamic conditions are provided for a 30-day period centered on the UAV measurement campaign
including the wave significant height (blue line, left y axis) and the wave direction (orange dots, right y axis). - Accepted manuscript
5. Conclusion
The morphological evolution of two pebble beaches, including a purely gravel one in Etretat
and a composite one in Hautot-sur-Mer, was investigated using an Empirical Orthogonal Function
(EOF) analysis applied to a 2-year time series of shoreline positions at different elevations. The EOF’s
Principal Components (PC) highlighted the existence of at least four mechanisms of shoreline change
including rotation, cross-shore translation, rollover and breathing. Despite their relative proximity, the
two beaches present different sets of modes: 88.5% of Etretat’s shoreline position variability is explained
by cross-shore translation (PC1, 62.4%), rollover (PC2, 14.1%), breathing (PC3, 5.8%), large scale
rotation (PC4, 3.9%) and beach cell rotation (2.3%). The first mode could be related to a rotation at the
scale of the entire embayment, whose pivotal point would be located out of the monitored area. The
variability of Hautot-sur-Mer’s shoreline position is explained at 72.2% by right-centered rotation (PC1,
46.1%), left-centered rotation (PC2, 14.8%), large scale rotation (PC3, 7%) and rollover (PC4, 4.3%).
The interpretation of most of the PCs was confirmed when calculating correlation coefficient between
PCs and morphological parameters including beach width (BW), beach orientation angle (BOA) and
beach slope (BS). Moreover, the analysis showed that elevation plays a significant role in all
mechanisms of shoreline position change, and that the influence of groin structures is more important
in Hautot-sur-Mer, where it plays a role in every single PC, than in Etretat, where it is only visible in
Comparison between time series of morphological and hydrodynamic parameters did not show
any significant linear correlation. The hydrodynamic data used in this study consists of offshore waves
provided by the WaveWatch 3 model, therefore non-linear nearshore transformations are not taken into
account, which significantly limits the observed correlations. Nevertheless, a wavelet analysis
highlighted common temporal periods of variability at a mid-term scale including 2, 3, 5, 6 and 8+
months. Periods of 2, 6 and 8+ months also identified in signals of wave energy, however tidal range
and current velocity did not share any common period of variability with the considered
morphodynamical parameters.
Analyzing the granulometric spatial dispersion of surface gravel particles was possible thanks
to a segmentation methodology applied to UAV-derived ortho-imagery. Gravel size was measured once
in Etretat, and at three different dates in Hautot-sur-Mer, allowing for some first order estimate of
temporal variability to be investigated on the latter site as well, under summer conditions. In general,
both sites present different gravel size with D50 values of 5.2 cm in Etretat 7.0 cm in Hautot-sur-Mer
(time averaged). The spatial dispersion generally evidenced the presence of patterns such as a cross-
shore gradient, cusps and clast assemblages whose periodicity from one beach cell to its neighbors - Accepted manuscript
demonstrates the impact of groin structures. The temporal analysis highlighted differences through time
in both the average granulometry and the presence and position of patterns. For instance, an average
difference of -1 cm in all recorded sizes (mean, D16, D50 and D84) was observed between April and
June 2019, while the only significant morphological change of the beach was its orientation (5°).
Possible explanations include seasonal abrasion and the presence of physical processes leading to
sorting, such as percolation and processes related to rotation. The influence of cusp variability on the
sediment distribution variability was also highlighted. As the need for better knowledge and
understanding in the granulometric spatio-temporal variability is widely acknowledged by the
community of coastal scientists, this methodology shows promising results in regard to this matter.
However, the length and sampling frequency of time series need to be improved in order to precisely
characterize the reciprocal relationship existing between hydrodynamics, morphodynamics and
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Full-text available
On mixed sand–gravel beaches, impacts from gravel- and cobble-sized grains—mobilized by the energetic shorebreak—limit the utility of in situ instrumentation for measuring the small-scale response of the beach face on wave period time scales. We present field observations of swash zone morpho-sedimentary dynamics at a steep, megatidal mixed sand–gravel beach using aeroacoustic and optical remote sensing. Coincident observations of bed level and mean surficial sediment grain size in the swash zone were obtained using an array of optical cameras paired with acoustic range sensors. Lagrangian tracking of swash-transported cobbles was carried out using an additional downward-oriented camera. The principal objective of the study was to investigate linkages between sediment grain size dynamics and swash zone morphological change. In general, data from the range sensor and camera array show that increases in bed level corresponded to increases in mean grain size. Finer-scale structures in the bed level and mean grain size signals were observable over timescales of minutes, including signatures of bands of coarse-grained material that migrated shoreward with the leading edge of the swash prior to high tide berm formation. The direction and magnitude of cobble transport in the swash varied with cross-shore position, and with the composition of the underlying bed. These results demonstrate that close-range remote sensing techniques can provide valuable insights into the roles of cobble-sized versus sand-sized particle dynamics in the swash zone on mixed sand–gravel beaches.
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Coastal systems are extremely dynamic environments exposed to many hazards, making accurate and regular monitoring a major challenge, particularly in the context of global change and sea level rise. In this frame of reference, high-frequency, high-resolution coastal Video Monitoring Systems (VMS) have been installed on three megatidal (tidal amplitude > 9 m) sites of Normandy (France) including a sandy beach at Villers-sur-Mer, a pebble beach at Etretat and a composite beach at Hautot-sur-Mer. This article proposes the use of Mask R-CNN to process images acquired at these sites and perform the automatic segmentation of the visible bodies of water in order to extract the waterline. The extracted waterlines are associated with a measured water level, which makes it possible to reconstruct the topography of the beaches at the scale of the tidal cycle. After training the neural network on manually labeled data, the segmentation by Mask R-CNN is very efficient by achieving a satisfactory segmentation on 69.87% of the images of Villers-sur-Mer, on 67.11% at Hautot-sur-Mer, and on 97.33% at Etretat. Once the waterlines have been extracted and georeferenced, the reproduction of the beaches’ morphology is satisfactory (averaged vertical RMSE = 28 cm). These results confirm that segmentation by Mask R-CNN is a particularly powerful tool that allows efficient and low-cost monitoring of the evolution of beach morphology, particularly in response to marine conditions. Its capabilities to detect and segment bodies of water while not being affected by the various sources of noise make it a remarkably effective tool for coastal science applications.
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Sandy beaches are highly dynamic environments buffering shores from storm waves and providing outstanding recreational services. Long-term beach monitoring programs are critical to test and improve shoreline, beach morphodynamics and storm impact models. However, these programs are relatively rare and mostly restricted to microtidal alongshore-uniform beaches. The present 16-year dataset contains 326 digital elevation models and their over 1.635 × 10⁶ individual sand level measurements at the high-energy meso-macrotidal rip-channelled Truc Vert beach, southwest France. Monthly to bimonthly topographic surveys, which coverage progressively extended from 300 m to over 2000 m to describe the alongshore-variable changes, are completed by daily topographic surveys acquired during a 5-week field campaign. The dataset captures daily beach response at the scale of a storm to three large cycles of interannual variability, through the impact of the most energetic winter since at least 75 years and prominent seasonal erosion/recovery cycles. The data set is supplemented with high-frequency time series of offshore wave and astronomical tide data to facilitate its future use in beach research.
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This article proposes a new methodological approach to measure and map the size of coarse clasts on a land surface from photographs. This method is based on the use of the Mask Regional Convolutional Neural Network (R-CNN) deep learning algorithm, which allows the instance segmentation of objects after an initial training on manually labeled data. The algorithm is capable of identifying and classifying objects present in an image at the pixel scale, without human intervention, in a matter of seconds. This work demonstrates that it is possible to train the model to detect non-overlapping coarse sediments on scaled images, in order to extract their individual size and morphological characteristics with high efficiency (R 2 = 0.98; Root Mean Square Error (RMSE) = 3.9 mm). It is then possible to measure element size profiles over a sedimentary body, as it was done on the pebble beach of Etretat (Normandy, France) in order to monitor the granulometric spatial variability before and after a storm. Applied at a larger scale using Unmanned Aerial Vehicle (UAV) derived ortho-images, the method allows the accurate characterization and high-resolution mapping of the surface coarse sediment size, as it was performed on the two pebble beaches of Etretat (D50 = 5.99 cm) and Hautot-sur-Mer (D50 = 7.44 cm) (Normandy, France). Validation results show a very satisfying overall representativity (R 2 = 0.45 and 0.75; RMSE = 6.8 mm and 9.3 mm at Etretat and Hautot-sur-Mer, respectively), while the method remains fast, easy to apply and low-cost, although the method remains limited by the image resolution (objects need to be longer than 4 cm), and could still be improved in several ways, for instance by adding more manually labeled data to the training dataset, and by considering more accurate methods than the ellipse fitting for measuring the particle sizes.
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The steepness of the beach face is a fundamental parameter for coastal morphodynamic research. Despite its importance, it remains extremely difficult to obtain reliable estimates of the beach-face slope over large spatial scales (1000’s of km of coastline). In this letter, a novel approach to estimate this slope from time-series of satellite-derived shoreline positions is presented. This new technique uses a frequency-domain analysis to find the optimum slope that minimises high-frequency tidal fluctuations relative to lower-frequency erosion/accretion signals. A detailed assessment of this new approach at 8 locations spanning a range of tidal regimes, wave climates and sediment grain sizes shows strong agreement (R = 0.9) with field measurements. The automated technique is then applied across 1000’s of beaches in eastern Australia and California USA, revealing similar regional-scale distributions along these two contrasting coastlines and highlights the potential for new global-scale insight to beach-face slope spatial distribution, variability and trends.
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Beaches around the world continuously adjust to daily and seasonal changes in wave and tide conditions, which are themselves changing over longer time-scales. Different approaches to predict multi-year shoreline evolution have been implemented; however, robust and reliable predictions of shoreline evolution are still problematic even in short-term scenarios (shorter than decadal). Here we show results of a modelling competition, where 19 numerical models (a mix of established shoreline models and machine learning techniques) were tested using data collected for Tairua beach, New Zealand with 18 years of daily averaged alongshore shoreline position and beach rotation (orientation) data obtained from a camera system. In general, traditional shoreline models and machine learning techniques were able to reproduce shoreline changes during the calibration period (1999–2014) for normal conditions but some of the model struggled to predict extreme and fast oscillations. During the forecast period (unseen data, 2014–2017), both approaches showed a decrease in models’ capability to predict the shoreline position. This was more evident for some of the machine learning algorithms. A model ensemble performed better than individual models and enables assessment of uncertainties in model architecture. Research-coordinated approaches (e.g., modelling competitions) can fuel advances in predictive capabilities and provide a forum for the discussion about the advantages/disadvantages of available models.
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With high anthropogenic pressure and the effects of climate change (e.g., sea level rise) on coastal regions, there is a greater need for accurate and up-to-date information about the topography of these systems. Reliable topography and bathymetry information are fundamental parameters for modelling the morpho-hydrodynamics of coastal areas, for flood forecasting, and for coastal management. Traditional methods such as ground, ship-borne, and airborne surveys suffer from limited spatial coverage and temporal sampling due to logistical constraints and high costs which limit their ability to provide the needed information. The recent advancements of spaceborne remote sensing techniques, along with their ability to acquire data over large spatial areas and to provide high frequency temporal monitoring, has made them very attractive for topography and bathymetry mapping. In this review, we present an overview of the current state of spaceborne-based remote sensing techniques used to estimate the topography and bathymetry of beaches, intertidal, and nearshore areas. We also provide some insights about the potential of these techniques when using data provided by new and future satellite missions.
In a simple definition, beach rotation is the opposing movement of the shoreline along the two ends of an embayed beach, driven by longshore and/or cross-shore sediment transport in response to seasonal or periodic changes in wave direction and/or gradients in wave energy. However, when considered in detail, the mechanisms, drivers and timescales of beach rotation are complex, resulting from non-linear interactions of cross-shore and alongshore hydrodynamic forcing, sediment transport and morphological change, developed over single or combined timescales that range from storm events to decadal rotation driven by climate-forced changes in wave conditions. In the context of global change, morphodynamic complexity of beach rotation processes is further compounded by rising sea levels and changes in wave climate, and impacted by artificial modification of beach environments along increasingly engineered coastlines. The spatial and temporal complexity of beach rotation mechanisms creates significant challenges to morphodynamic modelling and management of embayed beaches.
Brayne, R.P.; Lorang, M.S.; Naylor, L.A., and Reinhardt, L., 2020. Field-based observation of the entrainment threshold of cobbles with motion loggers. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 392–397. Coconut Creek (Florida), ISSN 0749-0208. Beaches composed of pebble to boulder-sized material are a common feature of coastal regions and provide effective protection against wave attack. The wave-related entrainment threshold of these coarse particles is of utmost importance to defining the onset of dynamic beach behavior. Wave-competence equations derived to predict the boundary between particle stability and entrainment when acted on by waves (e.g. Lorang, 2000) are useful when designing artificial gravel beaches as shore protection structures because they help inform the size of material required to mimic the dynamic behavior of their natural counterpart. The objective of this study is to use motion loggers embedded within native cobbles to measure the entrainment threshold during storm wave events to provide much-needed field data with which to test the accuracy of the Lorang (2000) equations. The movement of 14 cobbles were observed over a range of conditions (0.10 m < HS < 0.52 m) during five separate 1.5-hour-long experiments on coarse pebble/cobble beach at Flathead Lake, Montana, USA. The entrainment threshold was positively related to wave power and was accurately predicted by the Lorang (2000) equations using significant wave height, mean period and beach slope to estimate swash velocities and run-up height as driving variables. More experiments are required to constrain the value(s) used for the beach stability coefficient Kr, although the values found here correspond with the widely used Hudson Formula (Hudson, 1952). Alternatively, directly quantifying swash velocities and run-up elevations from video analysis would greatly improve the results rather than estimating these primary variables. These results provide a unique insight into the wave-competence approach to designing dynamic revetments and artificial gravel beaches as shore protection alternatives to rip-rap and seawalls at a time when rising sea level and a potential increase in storm intensity are likely to increase the wave impact on coastal regions.