Small-Scale Morpho-Sedimentary Dynamics in the Swash Zone
of a Megatidal Mixed Sand–Gravel Beach
Tristan B. Guest *,† and Alex E. Hay
Citation: Guest, T.B.; Hay, A.E.
Dynamics in the Swash Zone of a
Megatidal Mixed Sand–Gravel Beach.
J. Mar. Sci. Eng. 2021,9, 413.
Academic Editors: Troels Aagaard
and Gerben Ruessink
Received: 28 February 2021
Accepted: 9 April 2021
Published: 13 April 2021
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Department of Oceanography, Dalhousie University, Halifax, NS B3H 4R2, Canada; email@example.com
† Current address: Luna Sea Solutions Inc., Lunenburg, NS B0J 2C0, Canada.
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.
Keywords: swash zone; sediment dynamics; grain size sorting; bed level change; cobble transport
Inter-relationships between bed level change and sediment properties in the swash
zone are difﬁcult to establish due to the challenges inherent in obtaining observations of
bed level and sediments on the time scale of the swash forcing. Applying novel in situ
sensing techniques—based on multi-element conductivity insertion probes—has led to
important advances in our understanding of swash zone sediment transport on sandy
]. However, such methods are not suitable for coarse-grained beaches, where
the high velocity impacts from gravel- and cobble-sized grains mobilised by the energetic
shorebreak pose a major hazard to instrumentation. Remote sensing methods provide a
potential alternative. The recent application of remote sensing to the swash zone, including
acoustic range sensors for observing bed level change [
] and image-based methods for
estimating sediment grain size [
], has also advanced our understanding of sediment
transport processes in the swash. However, previous efforts have been largely limited to
pure sand or gravel beach types, with mixed sand–gravel (MSG) beaches receiving much
The use of ultrasonic range sensors to obtain remote observations of bed level in the
swash zone has provided insight into the dynamics of beach proﬁle change. An important
result borne of swash timescale bed level monitoring during the last 15 years is that of
the inter-swash timescale of net bed level change, wherein a tendency toward a dynamic
J. Mar. Sci. Eng. 2021,9, 413. https://doi.org/10.3390/jmse9040413 https://www.mdpi.com/journal/jmse
J. Mar. Sci. Eng. 2021,9, 413 2 of 23
equilibrium proﬁle (see [
]) is achieved via a balance between onshore and offshore sedi-
ment ﬂuxes over many swash events [
]. This is contrary to the previously prevailing
notion that beach face equilibrium is the result of a balance between individual uprush and
downrush events (i.e., intra-swash timescales). The use of arrays of bed level sensors has
allowed for more comprehensive investigations of volume change across the beach proﬁle,
including the swash zone, than was previously possible [
]. Studies of bed level change
at swash or near-swash timescales on MSG beaches are rare: Kulkarni et al.
manual post-and-ruler surveying method to examine bed level change on a MSG beach
at time intervals of minutes; Horn and Walton
used a similar post-and-ruler method
to measure bed level every 10–25 s over a three hour period spanning high tide. They
reported increases in bed elevation on the rising tide and decreases on the falling tide,
with high frequency (i.e., one time step) bed level variations being nearly as large as the
overall bed level change. No MSG beach studies exist, to the knowledge of the authors,
that make use of ultrasonic bed level sensors to obtain sub-swash timescale observations of
bed level and swash height.
Digital grain sizing methods enable the collection of grain size data non-intrusively
with high temporal resolution. There are many automated methods for estimating a grain
size distribution from optical imagery. Under the scheme proposed by
Buscombe et al. 
these methods can be broadly classiﬁed as ‘geometrical’ or ‘statistical’. Geometrical meth-
] employ image processing techniques (e.g., segmentation, thresholding) to identify
major and minor axis lengths of individual grains. Statistical methods (e.g., [
make use of time series analysis techniques (e.g., autocorrelation and Fourier or wavelet
transforms) in the space domain to characterise texture in the image without attention
to individual grains. Recent statistical methods [
], which characterise the grain size
distribution in terms of Fourier or wavelet derived power spectra, do not require calibration
speciﬁc to a sediment population. Using wavelet transforms has the beneﬁt of not requiring
the input data to be stationary, making wavelet-based grain sizing methods more suitable
for applications involving inhomogeneous or poorly sorted sediments .
Though digital imaging techniques have been applied widely across the geological
sciences, few studies have applied such methods to the swash zone. The only study to
do so that the authors are aware of is that of Austin and Buscombe
, who applied the
method to images captured in the subaerial swash zone of a meso-macrotidal
gravel beach. Austin and Buscombe
used mean grain size data, collected at a minimum
of 5 min sampling intervals from both subaerial digital imagery and subaqueous physical
samples to compare with bed level change from a manual, in situ surveying method.
The extent to which the image-derived grain size data were used in their analysis is unclear.
Theirs is also the only study the authors are aware of in the gravel beach literature which
includes simultaneous observations of bed level and sediment properties in the swash
zone. Their cross-shore bed level and sediment sampling transects were separated by 2 m
alongshore. Austin and Buscombe
observed that temporal changes in the grain size
signal at several locations on the beachface were related to the morphological response:
sediment coarsening being associated with accretion at the berm and step crest, and ﬁning
associated with accretion seaward of the step. They note, however, that distinct phases of
the observed morphological change were not generally reﬂected in the grain size signal.
Lagrangian tracers have a long history of use for characterising sediment dynamics
on beaches. In the gravel beach literature, particle tagging with ﬂuorescent paint [
or radio frequency identiﬁcation tags (RFID; [
]) has lead to improved characterisations
of transport dynamics on tide-to-tide timescales. No studies, to the authors’ knowledge,
have made use of cobble-sized tracers to investigate transport in the swash on runup
timescales on a coarse-grained or MSG beach.
Here, results are presented from a ﬁeld study at Advocate Beach, Nova Scotia.
The study made use of collocated observations of bed level and swash height using
ultrasonic range sensors, and mean surﬁcial grain size using digital imagery in the swash
zone, at subsecond to several seconds resolution. The digital imagery and observations of
J. Mar. Sci. Eng. 2021,9, 413 3 of 23
bed and swash level were both obtained using low-cost, commercially available sensing
equipment. The observations are presented in the context of berm formation and evolution
over two high-tide cycles. The objectives of this study are: (1) to investigate the coevolution
of bed level and mean surﬁcial grain size, seeking insight into the phenomenological role
of grain size on swash zone morphological evolution, (2) to investigate the dynamics of
individual particles in swash ﬂows using video-based Lagrangian particle tracking, and (3)
to assess the utility of low cost range sensing and video-based methods for quantifying
bed level and mean grain size change in the swash zone.
2.1. Site Description
Advocate Beach is a mixed sand–gravel–cobble barrier beach located near the head of
the Bay of Fundy in Nova Scotia, Canada (Figure 1). Based on the 8–12 m tidal range, Ad-
vocate beach can be classed as megatidal rather than macrotidal [
]. The beach separates
the headlands of Cape Chignecto to the west and Cape D’Or to the southeast, and is 5 km
long with a nearly linear shoreline. The beach face is steep (approximately 1 in 10 slope)
and the sediments poorly sorted, ranging from medium sand to cobbles to boulders greater
than 20 cm in diameter. From the lower beach face to beneath lowest low water, the sedi-
ment composition transitions from mixed sand–gravel–cobble to cobble and boulder-sized
material. From the southwest, the beach is exposed to the full 500 km fetch of the Bay of
Fundy and adjacent Gulf of Maine, but from other directions is more fetch-limited. At low
tide, the beach is uniformly planar with crest to low water distance as much as 100 m in
spring tides (see Figure 1c, and [
]). The large tidal range results in high rates of change
in the shoreline position; during maximum ﬂood or ebb, the rate of change of water level is
as much as 3 m h−1, or roughly 0.5 m min−1across-shore.
During and after fairweather forcing, an active high tide berm is commonly observed
near the high water line. The berm composition is generally of coarser material than that
found in the intertidal zone, consisting of relatively well sorted gravel and cobbles. Fol-
lowing periods of energetic wave forcing, the beach appears free of distinct morphological
features, and when exposed at low tide the beach surface sediments are predominantly
sandy. Conversely, the beach surface sediments are generally coarser following periods
of low energy forcing. The combination of a steep beach slope and typically short pe-
riod, wind-generated incident waves result in a highly energetic shore break for offshore
signiﬁcant wave heights of ca. 0.5 m and larger .
J. Mar. Sci. Eng. 2021,9, 413 4 of 23
) Map of the Maritimes region of Canada and the northeastern United States. The location
of Advocate Beach is indicated by the red box in the map inset. (
) Photograph of Advocate Beach
at mid-tide, taken from near the high tide level facing westward. Northwest is alongshore to the
right, as indicated by the arrow at the bottom right of the photo. (
) The mean proﬁle of the beach,
averaged over the duration of the 2018 ﬁeld experiment. Mean High Water (MHW) and Mean Low
Water (MLW) are both indicated, also as averages over the experiment’s duration. The location of a
pressure transducer (PT) used to obtain wave and tide data is indicated by the green dot. The inset
plot shows the difference in each tide’s proﬁle from the mean proﬁle, highlighting the upper beach
proﬁle near the high water line as the region of greatest morphological change.
2.2. Experiment Overview
The ﬁeld experiment was conducted between 14 and 27 October (yeardays 287–300),
2018. The experiment spanned 27 tides, which are hereafter referred to by their sequential
low tide index, 1 through 27 (Figure 2). The goal of the experiment was to investigate the
coevolution of bed level and mean surﬁcial grain size, with an emphasis on swash zone
processes. Data were collected using a four-element array of collocated ultrasonic range
sensors and cameras, along with an overhead camera used for tracking the movements
of tracer cobbles in the swash. Both systems were modular, and could be handled by
two people. The frames were positioned immediately shoreward of the high water line
J. Mar. Sci. Eng. 2021,9, 413 5 of 23
during periods of low to moderate energy forcing conditions such that the instruments
were suspended over the swash zone.
Summary of (
) tidal elevation, (
) signiﬁcant wave height, and (
) peak wave period
during the experiment. Tides 19 and 27—the tides analysed in this paper—are indicated by the light
Wave and tide data were obtained using a pressure transducer located on the lower
beach face between the mid-tide and mean low water levels (see Figure 1c). The pressure
transducer housing was secured to a heavily weighted frame such that the sensing element
was ca. 10 cm above bed level. A real-time kinematic (RTK) GPS receiver was used to
survey the instrument locations, as well as for beach-scale surveying of bed level and grain
size on a tide-to-tide basis. Results from the survey component are outside the scope of
this paper, and are presented in Guest .
The local coordinate system is deﬁned such that
is alongshore, positive to the north-
is across-shore increasing to seaward, and
is positive upward. Local longshore (
and cross-shore (
) coordinates reported in this paper are relative to the intersection of the
mean high water shoreline, computed for the tides encompassed by the 2018 experiment,
and the ﬁxed across-shore line along which the beach proﬁle was surveyed each tide.
Vertical coordinates are reported as orthometric elevations referenced to the vertical datum
used by the RTK GPS (Figure 1c).
2.2.1. Range Sensor and Camera Array
Coincident evolution of bed level and mean surﬁcial grain size was investigated using
an array of collocated Maxbotix MB7384 ultrasonic range sensors (range resolution of ca.
1 mm) and 5 megapixel Raspberry Pi cameras. The array consisted of four downward-
facing range sensor and camera pairs, cantilevered approximately 2 m horizontally over the
swash on an instrument frame that could be moved as shoreline position changed with the
tide. The array frame and instrument conﬁguration are shown in Figure 3. The four array
elements are hereafter referred to as elements A through D, where A is the southernmost
element of the array, and D the northernmost element. The pairs were separated by 0.9 m
alongshore resulting in a 2.7 m total longshore span at a nominal elevation of 0.75 m above
the bed. The range data were sampled at 6 Hz, and the video images at 0.2 Hz. Each of
the four array element pairs were controlled by a Raspberry Pi single board computer,
which also served as the data logger. A wireless router, connected to the Raspberry Pis
via ethernet, enabled Wi-Fi communication with the Pis to initiate and terminate data
J. Mar. Sci. Eng. 2021,9, 413 6 of 23
logging. The four computers were time-synchronised using network time protocol (NTP),
and powered from a 12 V marine battery.
The range sensor and camera array and frame. (
) Four array elements, labelled A through
D, each containing a downward-oriented ultrasonic range sensor and a camera, were cantilevered
over the swash to observe bed level change and mean grain size. Each pair was separated by
0.9 m in the alongshore from its nearest neighbour, at a nominal elevation of 0.75 m above the bed.
(b) Drawing of a single array element, with positions of the range sensor and camera.
J. Mar. Sci. Eng. 2021,9, 413 7 of 23
The alongshore orientation of the four range sensor-camera elements on the array
frame was chosen to capture the development of incipient beach cusps and other three-
dimensional morphology in the alongshore. The geometry of the frame (i.e., the ﬁeld of
view in relation to the base, which was in contact with the beach surface) was chosen
so that the mid-swash zone could be sampled without the base of the instrument frame
interfering either with the data collection, or with the swash processes being observed.
When conditions were favourable, the instrument frame was assembled and posi-
tioned near the high water line and data were collected during the transition from late
ﬂood tide to early ebb. Sampling was initiated prior to the maximum swash runup position
passing beneath the array, and continued until the swash runup was no longer in the
instruments’ ﬁeld of view. The frame remained stationary thoughout. The aim of the
deployments was to position the frame such that the mean shoreline position coincided
with the instruments’ ﬁelds of view at high tide, such that bed level and grain size could
be measured at the intermittently exposed bed. The position of each array element was
recorded using RTK GPS during each deployment.
2.2.2. Overhead Camera
An overhead Raspberry Pi camera, also network-connected via the wireless router,
was used for monitoring the positions of tracer cobbles in the swash. This camera was
mounted to a second instrument frame, consisting of a stationary base which could be
moved with the changing shoreline position, and a movable arm which supported the
camera allowing it to view the swash zone from a height of ca. 3 m without the frame base
being in the image. The frame and camera are shown in Figure 4. The camera ﬁeld of view
at the beach surface was approximately 2.4 by 4.3 m, longshore by cross-shore.
Prior to the initial deployment, cobbles were sieved into three different size classes:
22.4 to 31.5 mm, 31.5 to 45 mm, and 45 to 63 mm. The cobbles in these size classes were
painted blue, orange, and yellow, respectively. The number of cobbles in each class varied
from 10 to 30 in a given deployment, depending on how many were recovered during the
The overhead camera frame was generally deployed alongside the array frame during
periods of fairweather forcing. As with the array frame, the overhead camera frame was
assembled and positioned near the high water line during late ﬂood tides. The bed within
the camera’s view was ‘seeded’ with the painted tracer cobbles prior to the maximum
swash runup position entering the camera’s ﬁeld of view. Video was captured as the
cobbles were redistributed by the swash. When the camera’s ﬁeld of view no longer
contained the mean shoreline position, the frame was moved to a more seaward ‘station’,
and the cobbles that had been stranded by the translating shoreline were reintroduced
to the swash. The overhead camera frame typically occupied 3 to 5 stations during a
deployment. A minimum of three ground control points were captured at each station
using RTK GPS to provide a scaling between pixel and ground coordinates.
J. Mar. Sci. Eng. 2021,9, 413 8 of 23
) The overhead camera frame, with downward-looking camera to monitor the transport
of painted tracer cobbles in the swash. The camera was elevated approximately 3 m above the bed.
) Sample imagery captured by the camera during the development of a high tide berm (tide 19).
The images represent intermediate and late stages of the berm’s development, beginning with the
initial deployment of the cobble tracers. The decreased number of cobbles visible in (
) is a result
2.3. Data Processing
2.3.1. Range Data: Bed Level and Swash Height
The data from the ultrasonic range sensors represent ﬁrst returns (i.e., the distance
to the nearest object within the
(10 cm) radius beam pattern), which were either from
the exposed beach surface in the absence of swash, or from the water surface when swash
was present. Processing of the range time series was carried out to isolate the bed level
and swash signals. Spurious returns of 0.5 and 5 m—the sensors’ minimum and maximum
sensing distances—made an additional processing step necessary. The spurious returns
were attributed to diminished or scattered acoustic reﬂections from aerated swash at
leading edge of the swash front. No return, or returns not within the 0.5–5 m sensing range
of the instruments, result in range output of 0.5 or 5 m.
J. Mar. Sci. Eng. 2021,9, 413 9 of 23
The bed level was extracted from the range time series by identifying sequences of
samples in which no sample differed from the ﬁrst sample in the sequence by more than a
predeﬁned range threshold.
was set to 9 samples (1.5 s), and the range threshold set to
5 mm. For analysis applications requiring a uniformly sampled bed level time series, gaps
in the series associated with swash were ﬁlled via linear interpolation.
The swash thickness was extracted from the range time series by isolating all values
at ranges less than the range to the interpolated bed level, minus a buffering threshold of
2 mm to eliminate spurious low amplitude values due to instrument noise. The isolated
segments were deﬁned to be swash events if they had a minimum duration of 5 samples
(0.83 s) and a local maximum within the segment (excluding the endpoints) at least 15 mm
above the bed. These criteria were implemented to exclude spurious events in the swash
time series that did not exhibit the anticipated shape of a runup event (i.e., a sequence
of increase, maximum, and decrease in swash height). A sample elevation time series,
with the extracted bed level and swash height maxima, is shown in Figure 5.
) Time series of swash and bed elevation, from data recorded during high tide of tide 19
by the range sensor in array element A. Orange dots represent the extracted bed level, blue dots the
swash height maxima. (b) Subset of the time series in (a).
Bed level change between swash runup events was computed by differencing the
ﬁnal values in each bed level segment in the (non-interpolated) bed level signal, where a
segment consisted of contiguous points meeting the exposed bed criteria described above.
This deﬁnition of bed level change was chosen to be conceptually consistent with the
deﬁnition proposed by Blenkinsopp et al. .
2.3.2. Array Cameras: Digital Grain Sizing
A wavelet-based digital grain sizing (DGS) package [
], implemented in Python,
was used to estimate grain size statistics from the camera array imagery. The DGS algo-
rithm does not require calibration, and takes as input a grain-resolving image containing
The image sets from the four array-frame cameras were manually curated to include
only those images with fully exposed bed in the region of the image used for analysis. Each
image was cropped to half width and height in the centre of the image, corresponding
to a ﬁeld of view at the bed of 1.42
0.85 m, for a 0.75 m camera height above the bed.
Sample images processed by the DGS algorithm are shown in Figure 6. Input parameters
for the algorithm include a pixel to physical unit scaling, a maximum feature diameter to
be resolved, and a dimensional scaling factor. The bed-level signal extracted from the range
J. Mar. Sci. Eng. 2021,9, 413 10 of 23
sensor time series was used, along with the camera’s known ﬁeld of view speciﬁcations,
to establish the pixel to physical unit scale factor for each image. The bed level signal
was smoothed to eliminate short period changes in bed level attributable to individual
grain movements. The maximum feature diameter, deﬁned as the inverse ratio of the pixel
width to the width of the largest feature to be resolved, was also dynamically assigned
to maintain a maximum feature resolution of 56 mm—a value chosen to balance output
resolution at both small and large grain sizes. The dimensional scale factor was set as 0.8.
See Appendix Afor a discussion of the choice of dimensional scale factor and for more
detailed descriptions of the remaining input parameters.
Figure 6. Sample images processed using the wavelet-based digital grain sizing method. The mean
grain size (MGS) of each is indicated. The images were captured by array camera A during tide 27.
The ﬁelds of view at bed level are ca. 0.8
1.4 m. The left and right photos were captured at 14:26
and 14:45, respectively.
Though the algorithm is capable of returning a full grain size distribution, validation
of the output against distributions from both sieve and manual point count analyses
, or Appendix Afor a description of the point count method) indicated that
only the lowest moment of the grain size distribution (mean grain size) was captured with
satisfactory accuracy. We attribute the algorithm’s poor representation of the higher order
moments to the wide grain size distribution. See Appendix Afor further discussion of the
2.3.3. Cobble Tracking
Cobble trajectories were manually extracted from the video image sets captured by
the overhead camera. To mitigate the difﬁculties posed by the partial or full occlusion
of cobbles by bubbles and foam in the swash, pixels with high white content (red, green,
and blue channel intensity values all exceeding 175 out of 255) were subtracted from
each image, then each image was averaged with the 10 preceding images. The resulting
composite images showed a partially reconstructed bed, with more tracer cobbles being
visible than in the original images. Due to the regular occlusion of the cobbles by the swash,
the extracted trajectories are assumed to be accurate at swash forcing timescales (ca. 6 s),
i.e., any transport occurring while the cobbles were submerged was not captured. The
45–63 mm (yellow) size class was most easily identiﬁed in the images. Reduced visibility of
the other size classes meant that cobble identities could not be maintained with conﬁdence
between instances of occlusion. Thus, only trajectory data from the 45–63 mm size class is
presented in this paper. Tracking of each cobble began immediately after it was deposited
in the swash. Tracking was stopped when the cobble was buried or transported out of the
ﬁeld of view.
J. Mar. Sci. Eng. 2021,9, 413 11 of 23
3.1. Coevolution of Bed Level and Mean Grain Size
The frame bearing the array of range sensor and camera pairs was deployed during
ﬁve high tides over the course of the experiment, each characterised by low to moderate
energy forcing conditions (signiﬁcant wave heights less than ca. 0.5 m; see Figure 2).
The geometry of the array frame (i.e., the ca. 2 m cantilevered distance of the array elements
from the array frame base) meant that the use of the frame was limited to ‘fairweather’
conditions, during which the maximum swash runup distance was less than approximately
4 m. During tides 19 and 27, the array was favourably positioned relative to the high water
line (HWL) such that intermittent swash height and bed exposure could be observed for
periods longer than one hour without moving the frame. For these cases, time series of the
swash thickness, bed level, and image-derived mean grain size are available. During both of
tides 19 and 27, a pronounced berm developed near the HWL. The proﬁles and instrument
positions associated with tides 19 and 27 are shown in Figure 7.
Proﬁles of the upper beach for (
) tide 19 and (
) tide 27. Prior and post states at low tide
are indicated by the blue and black proﬁles, respectively. Positions of the range sensor and camera
array elements (A–D) are indicated by the blue dots. The four stations (S1–S4) occupied by the
overhead camera frame used for cobble tracking are indicated by the red dots (tide 19 only), where
each station’s coordinates were estimated using the average of three ground control points within
the overhead camera’s ﬁeld of view.
Applying the digital grain sizing algorithm to the images captured by the array
enabled the examination of coevolving bed level and mean grain size at the bed beneath
each array element. Figures 8and 9show time series of the bed level and mean grain
size during high tide for tides 19 and 27. The grain size data are inherently noisy, so the
individual data points are less valuable than the trends revealed by large numbers of data
points. In both cases, the morphological context was the formation—and for tide 27 the
J. Mar. Sci. Eng. 2021,9, 413 12 of 23
formation and shoreward translation—of a high tide berm. Visual inspection of the time
series indicates that bed level and mean grain size tend to co-vary.
Time series of (
) swash height, (
) bed level, and (
) mean grain size during high tide
for tide 19, from the data recorded by the range sensor and camera array elements (A–D), ori-
ented alongshore. The solid lines in (
) are locally-weighted (loess) regressions using a ca. 10 min
During tide 19, coarse material accumulated near the HWL, initially in a mound
directly beneath array element D (Figure 8). The mound initially resembled a developing
cusp horn, though its alongshore extent widened over the following tens of minutes,
becoming steeper in the offshore direction and more berm-like. An incipient topographic
low existed beneath array element A. By early ebb tide, a more longshore uniform berm
had formed. The berm beneath the array sloped downward alongshore to the south (note
the elevation differences between the array elements A and D), with a maximum elevation
increase of nearly 20 cm beneath the array element D. The grain size time series are noisy
and sparsely sampled, especially at high tide (i.e., between 11:30 and 12:00) due to the
more frequent swash events. However, common trends can be noted: namely, the upward
trend in mean grain size as the swash zone ﬁrst reached the sampling region (11:10–11:20),
which precedes the onset of the upward trend in the bed level time series. Fining of the
surﬁcial sediments under array element A following the initial coarsening trend is also
evident, and corresponds to a similar, but lagged, trend in the bed level time series.
J. Mar. Sci. Eng. 2021,9, 413 13 of 23
Time series of (
) swash height, (
) bed level, and (
) mean grain size during high tide
for tide 27, from the data recorded by the range sensor and camera array elements (A–D), ori-
ented alongshore. The solid lines in (
) are locally-weighted (loess) regressions using a ca. 10 min
During tide 27, a berm began to form seaward of the HWL (note the increase in
bed elevation in Figure 9, 13:50–14:10). As the swash zone migrated landward, coarse
material was pushed over the berm crest, leading to a shoreward migration of the berm
by roughly 2 m. The decrease in bed elevation between 14:10 and 14:30 is a result of this
berm translation. During early ebb tide, coarse material began to accrete on the seaward
face of the berm, leading to the bed elevation increase observed between 14:30 and 14:50.
The mean grain size was initially coarse (ca. 30 mm) in all three of the sampled locations,
but shows a downward trend in two of the three cases. Fining occurred in all cases after
the initiation of berm growth seen in the bed level time series. In all cases, the minimum
mean grain size occurred at or just after high tide, when the sampling location was near
the mid-swash zone, and also nearest the base of steep berm face. Bed surface coarsening
coincided with the increase in bed level on the seaward face of the berm during early ebb
tide. The absence of data from array element C in Figure 9is a result of damage to the SD
card used for data logging during demobilisation of the instruments.
A phenomenon that was often observed, both visually and in the grain size time series,
was the shoreward migration of a band of coarse material at the top of the swash zone
during late ﬂood tide (i.e., the ‘bumps’ in the mean grain size time series in
Figures 8and 9)
Similarly, a coarsening of the substrate was generally observed at the seaward edge of
the swash zone during early ebb tides. Surﬁcial ﬁning was generally observed nearer the
mid-swash zone. This ﬁning is apparent in both Figures 8and 9.
The distribution of bed level changes (Figure 10) shows that the majority of changes
between swash events were near zero. The larger changes—both positive and negative—
are loosely approximated by a Gaussian distribution, though with higher kurtosis values
J. Mar. Sci. Eng. 2021,9, 413 14 of 23
(kurtosis of 5.1 and 5.4 for tides 19 and 27, respectively, relative to a value of 3 for a Gaussian
distribution). This ﬁnding is consistent with similar analyses in the literature [
which have demonstrated that bed level change over the course of a tidal cycle is the
result of the cumulative effect of many instances of small accretion and erosion. The joint
probability distributions of the swash height and bed level change associated with each
swash event indicate that bed level change and swash height are largely uncorrelated.
Joint distributions of bed level change between swash events and swash height during
high tide for tide 19 (
) and tide 27 (
). Data from all four sensors are included. The grey
histograms indicate probability densities.
Figure 11 shows time series of swash height, bed elevation, and the change in bed
elevation during the high tide for tide 27. The magnitude of bed elevation change is largest
when bed elevation was higher (i.e., near the beginning and end of the time series). This
may be due to the larger mean grain sizes associated with the coarse lag at the leading
edge of the swash during ﬂood tide, and the accretion of coarse material on the seaward
face of the berm during ebb.
) Time series of swash height and bed level during tide 27 recorded by array element A,
and (b) the change in bed level between swash events over the period corresponding to (a).
J. Mar. Sci. Eng. 2021,9, 413 15 of 23
3.2. Cobble Dynamics
Cobble trajectory statistics were computed from data associated with tide 19. Video
datasets of cobble transport in the swash zone were collected at four locations in the
cross-shore (i.e., four distinct mean shoreline positions; see Figure 7) during high tide and
Station 1 (S1): at high tide, when the shoreline position was nearest to the HWL.
Here, the tracer cobbles were deployed atop the coarse berm material. The camera’s
cross-shore ﬁeld of view spanned
3.5 to 7 m in local cross-shore coordinates,
and contained almost entirely coarse berm material. Note that this is the station
associated with the images in Figure 4.
Station 2 (S2): 45 min after high tide. The shoreline and swash zone coincided with the
region immediately seaward of the coarse berm. Coarse berm material was present
in the landward one third of the camera’s ﬁeld of view, which spanned from
8.5 to 12 m (i.e., 5 m seaward of S1). The cobbles were deployed in the mid-swash,
over a combination of the coarse seaward face of the berm and the ﬁner material
Station 3 (S3): 75 min after high tide. The swash zone no longer coincided with any
coarse-grained berm material, and the substrate was predominantly ﬁne-grained and
uniform. The cobbles were deployed near mid-swash and mid-camera ﬁeld of view:
i.e., y≈12.5 to 16 m across-shore (9 m seaward of S1).
Station 4 (S4): 85 min after high tide, with the bed conditions and the cobble deploy-
ment being similar to those described for S3. The cross-shore ﬁeld of view of the
camera in this location was y≈15.5 to 19 m (12 m seaward of S1).
The net and cumulative transport statistics for the four stations are summarised in
Figure 12. The net cobble transport was shoreward at S1 and S2, where the substrate
consisted mostly of coarse-grained berm material. At S3 and S4, where the bed surface
was predominantly ﬁne-grained, the net transport was near zero, but with a high degree of
variation between individual cobbles. The cumulative transport of cobbles increased to
seaward (i.e., cobbles were more mobile where the mean shoreline position was farther
to seaward), corresponding to a decrease in coarse-grained material in the swash zone
substrate. Longshore transport was small in comparison to cross-shore transport at all
stations, consistent with previous observations at Advocate Beach .
Mean and standard deviation of the (
) net and (
) cumulative cobble transport. Positive
cross-shore transport is seaward.
J. Mar. Sci. Eng. 2021,9, 413 16 of 23
Closer inspection of the transport characteristics within each station reinforces the
ﬁnding of low cumulative transport and net onshore transport of cobbles in the presence
of the coarse-grained berm material. For example, data from S1 are shown in
At the more seaward stations, a trend of divergence of the cobbles away from the mid-
swash zone is observed: shoreward transport above the mid-swash level, and seaward
transport below. This was particularly the case at S2 and S3, for which the camera’s ﬁeld of
view was well-centred in the swash zone, and the surﬁcial sediments were predominantly
ﬁne-grained. Data from S3 illustrating this divergence are shown in Figure 14.
Cross-shore cobble transport trajectories and transport distances at station 1 (S1) during
tide 19. The bed composition was coarse-grained, leading to net onshore transport and low transport
) Time series of the cross-shore component of all the cobble trajectories. The grey line indicates
the time-varying position of the swash front. The colored lines represent individual cobbles. Cross-
shore positions are increasingly positive seaward. (
) Mean and standard deviation of the cross-shore
transport distance in each each of eight bins corresponding to the the cross-shore coordinates in (
The transport distance was assigned a bin based on its starting point. (
) Number of transport events
used in the calculations of the means and standard deviations in (b).
Cross-shore cobble transport trajectories and transport distances at station 3 (S3) during
tide 19. The bed composition was predominantly ﬁne-grained, leading to higher transport rates than
at other stations. (
) Time series of the cross-shore component of all the cobble trajectories. The grey
line indicates the time-varying position of the swash front. The colored lines represent individual
cobbles. Cross-shore positions are increasingly positive seaward. (
) Mean and standard deviation of
the cross-shore transport distance in each each of seven bins corresponding to the the cross-shore
coordinates in (
). The transport distance was assigned a bin based on its starting point. (
of transport events used in the calculations of the means and standard deviations in (b).
J. Mar. Sci. Eng. 2021,9, 413 17 of 23
The mean grain size data (Figures 8and 9) corroborate visual observations made
during the Advocate experiment, of coarse bands of sediments which tended to migrate
shoreward with the leading edge of the swash zone. This shoreward migration appeared
to precede any substantial changes in bed elevation during tides 19 and 27. This precursor
to berm formation has been reported in the literature [
], and has been attributed to the
temporary stranding of coarse material at the landward edge of the swash. At high tide,
the slowdown and arrest of the swash zone’s shoreward translation leads to continued
accretion at the leading edge. The berm crest migrates shoreward during periods of berm
overtopping, wherein the coarsest mobile fraction is saltated, or ‘thrown’, over the crest.
This is followed by accretion on the seaward face of the berm during the seaward regres-
sion of the shoreline during early ebb tide, leading to an increase in berm
The array data are consistent with this conceptual model. They indicate that the coarsest
sediments correspond to the berm crest, nascent or developed, with ﬁning occurring on
the seaward face of the berm.
The above results and interpretation of the swash zone bed level and mean grain size
signals are supported by the cobble tracer results. The divergence of the cobbles from
the mid-swash toward the seaward and shoreward edges of the swash zone is consistent
with the formation of a coarse deposit that migrates with the leading edge of the swash
zone, as well as with the frequently observed ﬁning of the surﬁcial material in the mid-
swash zone. Though not veriﬁable with the observations here, it is likely that seaward
transported coarse material accumulated in the beach step region associated with bore
collapse at the shore break, which also likely migrated with the cross-shore translating
swash zone. The beach step has been demonstrated elsewhere to play an important role
in controlling wave breaking on steep beaches, and has also been shown to migrate with
the translating swash zone [
]. The net shoreward transport of cobbles in the vicinity of
the berm (
, stations 1 and 2) suggests that the beach proﬁle at high tide was in
disequilibrium with the forcing in this case.
The cobble transport results highlight the inﬂuence of the substrate on the transport
dynamics of coarse particles in a mixed grain-size setting; cobble transport is favoured on a
ﬁne substrate, where low angles of pivot and greater exposure to lift and drag forces cause
the coarse particles to overpass the ﬁner ones. Transport is inhibited where the substrate is
coarse, due to higher angles of pivot required for mobilisation and decreased return ﬂow
velocities resulting from increased inﬁltration and hydraulic roughness.
The low-cost ultrasonic range sensors, despite their lower resolution compared to
similar sensors used in other studies, were capable of characterising bed level changes with
probability distributions that are comparable to those reported elsewhere [
at least one gravel beach [
]: namely, a quasi-Gaussian distribution that is indicative of an
inter-swash timescale for proﬁle evolution, where net changes to the proﬁle are a result of
time integration of small changes in bed elevation (both positive and negative) over many
swash cycles. The ultrasonic range sensors used in this study would be less suitable where
resolution ﬁner than
1 mm is required (e.g., in a pure sand setting where average grain
sizes are less than 1 mm).
The high kurtosis of the bed level change distributions (kurtosis of 5.1, 5.4 for tides 19
and 27, respectively) relative to a value of 3 for a Gaussian distribution may be attributable
to the ‘armouring’ effect of the coarse bed: low energy swash events with small runup and
low velocities may not have led to mobilisation or deposition in the range sensor sampling
region, resulting in a bed level change distribution more heavily weighted toward no
change. This is in contrast to a sandy bed, where some degree of bed level change might
be expected with each swash event due to the higher mobility of sand grains. Instances
of greater bed level change associated with the transport of gravel- or cobble-sized grains
into or out of the sampling region may also have contributed to a higher kurtosis value
through increased weighting of the tails of the bed level change distribution.
J. Mar. Sci. Eng. 2021,9, 413 18 of 23
The Raspberry Pi cameras were adequate for capturing images and video of the bed
for digital grain sizing and cobble tracking. The difﬁculties resolving higher order moments
of the grain size distribution (see Appendix A) can more likely be attributed to the wide
grain size distribution at Advocate Beach, which spans three orders of magnitude.
In future work, it would be of interest to make similar measurements with greater
spatial coverage, particularly in the cross-shore, in order to better resolve the ﬁne-scale
grain size and bed level changes associated with incipient berm formation at the leading
edge of the swash. More sensors in an across-shore conﬁguration would also allow for
the consideration of volume change in the swash region; e.g., is positive bed level change
at the berm balanced by erosion from the mid-swash, or must material be sourced from
the step region as well? The step has been shown in previous work to have an important
inﬂuence on swash processes via its control on wave breaking, and is likely to be an
important source of coarse material for swash zone morpho-sedimentary evolution in
MSG settings. However, the methods employed for this study are not capable of directly
observing processes at the step. To the knowledge of the authors, no non-intrusive methods
have been used to study the step in a ﬁeld setting.
Given the acknowledged inﬂuence of the full grain size distribution on mixed sed-
iment transport dynamics (e.g., the increased mobility of gravel-sized particles in the
presence of a large sand fraction [
]), quantifying higher order moments of the grain
size distribution would be of interest. It is possible that improvements upon the digital
grain sizing results presented in this study could be obtained using a calibration-based
]. Other properties of the grains, namely particle shape, have also been demon-
strated to play an important role in particle transport dynamics. The ability to digitally
quantify particle shape at wave forcing timescales would be valuable, particularly in the
context of coarse particle transport in swash ﬂows.
The morpho-sedimentary evolution of a mixed sand–gravel beach was investigated
at the swash scale through point observations of bed level and mean grain size using
collocated ultrasonic range sensors and optical cameras, with temporal resolution on the
order of seconds. The trajectories of painted tracer cobbles in the swash were tracked using
another optical camera. Data were collected near high tide during periods of fairweather
forcing characterised by low steepness wave incidence and berm building. The shoreline
position changed rapidly due to the large (ca. 10 m) tidal range.
We draw the following conclusions regarding processes in the swash zone at Advocate
Beach, relevant to conditions of fairweather forcing, and exclusive of the beach step:
• In general, increases in bed level correspond to increases in mean surﬁcial grain size.
The largest mean grain sizes occur at the leading edge of the swash front, during both
the ﬂooding and ebbing tide. The smallest mean grain sizes are associated with the
The magnitude of inter-swash-event bed level change is largest near the leading edge
of the swash zone.
• Bed level change and swash height are uncorrelated at inter-swash timescales.
The cumulative transport of cobbles in the swash is greater where the substrate
consists of ﬁner material. Cumulative transport is lower where the surﬁcial material
is coarser (i.e., of similar size to the cobble being trasported).
• Cobble transport tends to diverge shoreward or seaward from the mid-swash.
The divergence of cobble transport from the mid-swash results in a deposit of coarse-
grained material that migrates with the leading edge of the swash. The coarse-grained
depoist is stranded near the high water line, becoming a nascent berm. Accumulation
of coarse-grained material is also likely to occur at the beach step.
The low-cost, commercially available range sensors used in this study were successful
in resolving signals of morpho-sedimentary change in the subaerial swash zone. This
ﬁnding indicates potential of close-range remote sensing techniques for investigating the
J. Mar. Sci. Eng. 2021,9, 413 19 of 23
coevolution of bed level and grain size in response to swash processes, at least in macrotidal
mixed sand–gravel settings.
Conceptualisation, T.B.G. and A.E.H.; methodology, T.B.G. and A.E.H.;
software, T.B.G.; validation, T.B.G.; formal analysis, T.B.G.; investigation, T.B.G. and A.E.H.; resources,
A.E.H.; data curation, T.B.G.; writing—original draft preparation, T.B.G.; writing—review and
editing, T.B.G. and A.E.H.; visualisation, T.B.G.; supervision, A.E.H.; project administration, A.E.H.;
funding acquisition, T.B.G. and A.E.H. All authors have read and agreed to the published version of
This research was funded by the Natural Sciences and Engineering Research Council
of Canada (NSERC) Discovery Grant (RGPIN-2017-05157) to A.E.H. and a Nova Scotia Graduate
Scholarship awarded to T.B.G.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the
The authors acknowledge Richard Cheel’s invaluable assistance in preparing
for and carrying out the 2018 Advocate Beach ﬁeld study.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
Appendix A. Digital Grain Sizing Validation
digital grain sizing (DGS) method used in this study applies wavelet
analysis to space-series transects of greyscale pixel intensities in the image(s) being pro-
cessed. For the algorithm to function as intended, the images must contain only sediment,
and individual grains must be resolvable by eye (i.e., have minimum grain diameters of
3–4 pixels). The output is a distribution of grain diameters characterised by information
from the wavelet-derived power spectrum, i.e., using a statistical characterisation of each
pixel transect, rather than characterisations of individual grains. Unlike earlier statisti-
cal methods, the Buscombe
method does not require a site- or sediment population-
speciﬁc calibration. The method is therefore described as ‘transferable’. In comparison
to earlier methods, the transferable wavelet method is more applicable to poorly sorted
The DGS method requires a suite of input parameters: (1) a density parameter, which
determines the spacing between pixel rows in the input image to be processed; (2) a pixel to
physical unit scale factor; (3) a ﬁltering Boolean, which applies a Savitzki-Golay high-pass
‘ﬂattening’ ﬁlter if set to ‘True’; (4) a ‘notes’ parameter, which deﬁnes the number of notes
per octave to consider in the continuous wavelet transform; (5) an inverse pixel-to-image-
width ratio indicating the maximum diameter of grains to be resolved, in order to scale the
maximum width of the ‘mother’ Morlet wavelet; and (6) a conversion constant required to
enable comparability of the output with distributions obtained in a different dimensional
space. See Buscombe
or Cuttler et al.
for more detailed summaries of the parameters.
With the exception of the pixel to physical unit scaling parameter, the pixel-to-image-width
ratio, and the dimensional conversion constant, the default parameter values were used in
processing all images.
A validation analysis was carried out to ensure the most suitable parameter val-
ues were selected. Twenty-four surface sediment samples taken from the beach were
transported to the laboratory, where grain size distributions were computed by sieving,
a manual image-based point-counting approach, and the wavelet-based DGS method.
The mean sample mass was 1.28 kg. The samples were prepared and sieved following
the method of Ingram
to obtain volume-by-weight grain size distributions. The point
counting method is a standard validation technique for image-based grain sizing, in which
uniformly spaced grid (9
9, in the case of this study) is overlaid on the image,
J. Mar. Sci. Eng. 2021,9, 413 20 of 23
and the widths of the grains beneath each grid vertex manually extracted to produce a
grid-by-number type grain size distribution [12,32].
To implement the point-counting and wavelet methods, each sample was placed in a
tray and photographed using a tripod-mounted, downward-oriented Canon Powershot
Elph 190. 3–5 images were captured for each sample, with the sediments being redistributed
between each photograph. Each photograph was cropped so only sediment was visible in
the image. The cropped images were digitally ﬂatted in the process of implementing the
Since the output of the DGS algorithm is a distribution of line-by-number grain
diameters (see Kellerhals and Bray
, Church et al.
for descriptions of the types
particle size distributions), a conversion factor is needed in order for the DGS output to
be comparable to (i.e., dimensionally consistent with) output from a sieve-type analysis.
A commonly used conversion formula is [37,39,41]:
is the known proportion of the
th size fraction obtained using the input mea-
is the proportion of the
th size fraction in units consistent with the desired
is the grain diameter of the
th size fraction, and the exponent
a conversion constant whose value is empirically dependent upon the grain size distri-
is based on the voidless cube model from
Kellerhals and Bray 
The Kellerhals and Bray 
conversion is based on purely dimensional arguments, and
does not depend upon an idealisation of the material. Thus, though the parameter
can be theoretically deﬁned based only on knowledge of the input and output mea-
sures, it is best employed as an empirically deﬁned tuning parameter. For example,
Diplas and Sutherland 
suggested a value of
0.47 for converting from an area-
by-number to volume-by-number type sample using natural sediments with 33% porosity,
though the voidless cube model would indicate a conversion constant of
retically correct values of
for a given conversion can be found in Table 2 of Kellerhals
. The same exponent values can be deduced using dimensional arguments.
For example, converting from a grid-by-number type measure (
) to a volume-
by-number measure (O(D3)/O(D0)) requires a conversion factor of
For the output from the wavelet method to be theoretically comparable to output from
the sieve analysis, a conversion factor of
is required. Note that the same conversion
is used for comparing output from the wavelet method to output from the manual point
counting method, since the sieve method (volume-by-weight) and the point counting
method (grid-by-number) share an O(D0)equivalence.
For the validation analysis,
values in the range of 0.5 through 1.5 were tested. RMS
errors associated with all the
values tested are summarized in Table A1, and results for a
subset of the values are plotted in Figures A1 and A2 for the sieve and point count method
comparisons, respectively. The best result in a minimised root mean square error sense was
0.8 (RMSE = 3.35 mm). Though the higher values for
arguably lead to
a more linear (though positively offset) relationship (see
), this comes
at the expense of the ability to differentiate grain sizes in the low- to mid range—i.e., the
10–20 mm mean grain size range—which accounts for a large proportion of the grain
J. Mar. Sci. Eng. 2021,9, 413 21 of 23
Mean grain sizes (
) and sorting parameters (
) computed using the wavelet-based
DGS method, plotted against values obtained from sieve analysis, for values of the dimensional
scaling parameter xranging from 0.5 to 1.5.
Mean grain sizes (
) and sorting parameters (
) computed using the wavelet-based
DGS method, plotted against values obtained using the manual point counting method, for values of
the dimensional scaling parameter xranging from 0.5 to 1.5.
Root mean square errors (RMSE) of the DGS and sieve-derived mean grain size data for
the validation analysis.
xDGS-Sieve RMSE (mm) DGS-Point Count RMSE (mm)
0.5 4.11 4.63
0.7 3.43 4.36
0.8 3.35 4.39
0.9 3.48 4.55
1.0 3.81 4.83
1.2 4.90 5.71
1.3 5.71 6.27
1.5 7.08 7.56
Other parameter values were held constant. The inverse pixel-to-image-width ratio
was set as 5.3, for a maximum resolved feature scale of 56 mm, given a cropped image
with of 2453 pixels, and a pixel to metric scaling parameter value of 0.12. The inverse
J. Mar. Sci. Eng. 2021,9, 413 22 of 23
pixel-to-image-width ratio of 5.3 was chosen so the maximum feature scale was consistent
with the scale used to process the ﬁeld survey images, which were cropped to different
dimensions. Though this feature scale was not sufﬁcient to resolve the largest grains in
the distribution, it was deemed an acceptable compromise in the interest of optimising the
representation of both the small and large diameter grains.
Though an acceptable level of agreement was obtained between the mean grain sizes
computed using the DGS method and the validation methods, higher order moments of
the grain size distribution, namely, the grain size sorting parameter (i.e., the standard
deviation of the grain size distribution), the grain size skewness, and the kurtosis, were
not reproduced with the same quality. This was attributed to the broad and variable
grain size distribution within a given image, and throughout the image set. Consequently,
the measures of grain size other than the mean were omitted from any analyses.
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