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Sandy beaches in low-energy, non-tidal environments: Linking
morphological development to hydrodynamic forcing
Anne M. Ton
a,
⁎,Vincent Vuik
a,b
,Stefan G.J. Aarninkhof
a
a
Delft University of Technology, Civil Engineering and Geosciences, P.O. Box 5048, 2600 GA Delft, the Netherlands
b
HKV Consultants, P.O. Box 2120, 8203 AC Lelystad, the Netherlands
abstractarticle info
Article history:
Received 20 May 2020
Received in revised form 13 November 2020
Accepted 17 November 2020
Available online xxxx
Keywords:
Low-energy
Sandy lake beach
Morphodynamics
Depth of closure
The morphodynamic behaviour of low-energy beaches is poorly understood, compared to that of exposed coasts.
This study analyses the morphological development of sandy, low-energy beaches and the steering hydrodynamic
processes. Four densely-monitored study sites in the non-tidal lake Markermeer in the Netherlands offered a unique
opportunity to examine the relation between their hydraulic boundary conditions and morphodynamics. Regular
bathymetric surveys were executed at all locations. Furthermore, the wave climate was monitored at one of these
four sites. All four sites exhibit a commonly found low-energy beach morphology, with a narrow beach face and a
low-gradient, subaqueous platform. This platform reaches an equilibrium depth quickly and then stays relatively
stable. The stable elevation of the platform is located near Hallermeier's depth of closure. A sediment budget analysis
over time demonstrates that the beach faces at all study sites have eroded during more energetic periods, and sed-
iment accumulated offshore. During the monitoring periods of 2 to 4 years, the el evation of the platforms reached an
equilibrium, but other morphological dimensions are still developing. The new insights gained from this study en-
able the prediction of platform elevations along sandy beaches in low-energy, non-tidal environments, and have
contributed to our insight in the underlying processes driving the morphological evolution.
© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://
creativecommons.org/licenses/by/4.0/).
1. Introduction
Coastal regions near open coasts, estuaries and lakes are some of the
most densely populated regions of the world. Knowledge on
morphodynamics is crucial for protecting and managing these areas.
Most coastal research concerns high-energy or open coasts.
Low-energy or sheltered beaches are expected to have similar, but less
pronounced, morphodynamics compared to high-energy beaches. There-
fore, only few studies have focussed on low-energy coasts (Lorang et al.,
1993b;Nordstrom and Jackson, 2012;Eliot et al., 2006;Vila-Concejo
et al., 2020), implying that the knowledge on physical processes and
morphodynamics in this field lags behind that of exposed beaches. De-
spite the importance of low-energy beaches for coastal protection, recre-
ation, and ecology, morphodynamics remain poorly understood.
The terms low-energy, fetch-limited and sheltered are often used al-
ternately to describe similar environments, such as the beaches of
estuaries-, lakes, and reservoirs (Jackson et al., 2002;Nordstrom and
Jackson, 2012). The exact characteristics are poorly defined in the liter-
ature (Goodfellow and Stephenson, 2005;Nordstrom and Jackson,
2012). According to Jackson et al. (2002),definitions of low-energy
vary from very small prevailing significant wave height, H
s
< 0.10 m
(Nordstrom et al., 1996), to limited storm wave height, H
b
< 1.0 m
(Hegge et al., 1996). The influence of tides is not explicitly considered
in the definitions. In all definitions, it is agreed that morphological
changes are storm-driven, as prevailing wave conditions have limited
reshaping capacity (Jackson et al., 2002;Nordstrom and Jackson, 2012).
Jackson et al. (2002) found that low-energy tidal sandy beaches often
have a narrow, steep foreshore, with seaward a low gradient, subaqueous
terrace. This terrace is often referred to as a “low tide terrace”,“sub-tidal
terrace”or “platform”and may be vegetated (Travers et al., 2010). Several
sites with such low-energy conditions and morphology are described in
the literature (Eliot et al., 2006;Goodfellow and Stephenson, 2005;
Lorang et al., 1993b;Lowe and Kennedy, 2016;Mujal-Colilles et al.,
2019;Nordstrom et al., 1996;Vila-Concejo et al., 2010).
Besides describing and analysing low-energy sites, several scholars
have aimed to develop conceptual models describing the morphotype
of these beaches. These descriptions range from beach states applicable
to all energy levels (Wright and Short, 1984) to morphotypes for the
low-energy beach face only (Makaske and Augustinus, 1998). Although
all these models roughly point in the same direction, described in
Section 2, the morphotypes are based on varying indicators. Some are
based on wave energy and sediment characteristics, others just on one
of both, or even just on the location of the beach (for a review, see Vila-
Concejo et al. (2020)). Therefore, the morphodynamics of low-energy
beaches as well as their most important drivers are largely unknown.
Four study sites in lake Markermeer, the Netherlands, provide a unique
opportunity to study the morphology of low-energy, non-tidal, sandy
Geomorphology xxx (xxxx) xxx
⁎Corresponding author.
E-mail address: a.m.ton@tudelft.nl (A.M. Ton).
GEOMOR-107522; No of Pages 11
https://doi.org/10.1016/j.geomorph.2020.107522
0169-555X/© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
Geomorphology
journal homepage: www.elsevier.com/locate/geomorph
Please cite this article as: A.M. Ton, V. Vuik and S.G.J. Aarninkhof, Sandy beaches in low-energy, non-tidal environments: Linking morphological
development to hydrodynam..., Geomorphology, https://doi.org/10.1016/j.geomorph.2020.107522
beaches. These beaches are subject to low-energy waves and have the
commonly found steep foreshore and low-gradient platform.
The general profile shape of low-energy beaches is similar to profiles
found in laboratory experiments with constant waves on an initially
plane slope of sediment (Hallermeier, 1979). From these laboratory re-
sults, Hallermeier (1979) concluded that under controlled wave condi-
tions, commonly an equilibrium profile is reached with a platform,
which he called the submarine cut or wave cut with water depth d
c
(Fig. 1). According to Hallermeier (1979), the equilibrium depth of
this platform is at the depth where the surface waves reach the limit
of their erosive action.
Hallermeier (1980) developed a theoretical formulation to estimate
the depth of closure, the depth at which wave action has negligible ef-
fect on sediment transport (d
s
). It is calculated as follows:
ds¼2:28Hs;12h−68:5H2
s;12h
gT2
p;12h
;ð1Þ
where H
s,12h
(m) and T
p,12h
(s) are the nearshore significant wave
height that is exceeded for 12 h per year and its associated wave period,
and g is the gravitational acceleration (m/s
2
). Hallermeier (1980) vali-
dated this formula with measured values for d
c
from laboratory tests.
The laboratory experiments are representative for the hydrodynamic
conditions and morphological platform development at our study sites,
as is confirmed in Section 4.1.
This study aims to analyse the morphological development of sandy,
low-energy beaches and its relation to hydrodynamic forcing. Our cen-
tral hypothesis is that the platform elevation at the study sites is
governed by the depth of closure according to Hallermeier (1980).
The next section describes conceptual models regarding morphotypes
of low-energy beaches. Section 3 describes the field sites and methods.
Section 4 shows the bathymetric features of the study sites, a
quantification of hydrodynamic forcing and its relation to the cross-
shore profile. In Section 5 these results are discussed and lastly,
Section 6 gives the conclusions.
2. Low-energy beaches - morphotypes and classifications
Several researchers have pursued to classify the low-energy beach
and describe its shape in different morphotypes. Wright and Short
(1984) describe the beach state based on the dimensionless fall velocity,
given by Ω=H
b
/(w
s
*T
p
), where H
b
is significant breaking wave height
(m), w
s
is fall velocity (m/s) and T
p
is peak wave period (s). Beach states
ranging from reflective (Ω< 2) to intermediate (2 < Ω< 6) to dissipa-
tive (Ω>6) are described and linked to wave steepness and sediment
characteristics. A reflective morphology is expected for low-energy
beaches. Features of a reflective beach according to Wright and Short
(1984) are a steep, usually linear, beach face, with on the offshore side
a pronounced step, after which the bed slope decreases considerably.
Although beach states for a wide range of Ω(1 to >6) are described,
the method is derived from high-energy beaches. Therefore doubts
exist on whether low-energy beaches fall within the scope of this ap-
proach. Jackson et al. (2002) state that low-energy beaches can be clas-
sified as either reflective or dissipative if the nomenclature by Wright
and Short (1984) is followed, since rips and other 3D bed forms are
not observed at low-energy beaches. Hegge et al. (1996) consider
low-energy beaches to be described by the reflective beach state. How-
ever, the single reflective beach state cannot adequately describe the
wide range of profile slopes and concavities observed on low-energy
beaches. Therefore they identified four classifications from 52 low-
energy beach profiles, categorized by dimensions, slope curvature and
grain size. The morphotypes for low-energy shores, ordered from less
to more exposure are: (1) concave, (2) moderately concave, (3) moder-
ately steep, and (4) stepped, with the latter as exception since this type
does not fit in this order (Fig. 2). The beaches were ordered from fully
Fig. 1. Equilibrium profile with sub-marine cut or wave cut as found from laboratory experiments with constant waves on an initially plane slope (reused from Hallermeier, 1979).
Fig. 2. Low-energy cross-shore beach morphotypes by and adjusted from Hegge et al. (1996),Travers ( 2007) and Makaske and Augustinus (1998).
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
2
protected to fully exposed based on hydrographic charts, leaving hy-
draulic conditions unquantified.
Similar to the analysis by Hegge et al. (1996),Travers (2007) identi-
fied four low-energy beach types. She quantified the exposure with the
exposure factor E
f
= log(Fl/Ms), where Fl is the direct fetch length and
Ms is the marginal shoal width. The most protected sites have the low-
est exposure factor. From least to most exposed, the beach types are:
(1) exponential, (2) segmented, (3) concave-curvilinear and
(4) convex-curvilinear (Fig. 2).
Although the shapes by Travers (2007) are different from Hegge
et al. (1996), the general outline is quite similar.More sheltered beaches
show a more pronounced terrace, while more exposed shores have a
more or less plane slope.
Besides these state classifications, some conceptual models for the
beach face of low-energy beaches have been developed. Based on field
sites in estuaries in the U.S.A., Jackson and Nordstrom (1992) give a qual-
itative description of the morphodynamics. They found that sediment ex-
change is limited to a zone between the upper limit of swash at high
water and the break in slope separating the foreshore from the low-tide
terrace, since there is insufficient energy to mobilize sediment on the
low-tide terrace. During a typical storm, the upper foreshore would
erode and the sediment would be deposited on the lower foreshore. Par-
allel slope retreat of the foreshore can occur as a result of high-energy
events or prolonged periods of unidirectional longshore currents.
A second low-energy beach face model is developed by Makaske and
Augustinus (1998). They described the morphological changes of the
micro-tidal, low-wave beach face of the Rhone Delta in France, to ex-
tend the study by Wright and Short (1984). Cross-shore profiles were
measured during one spring-neap tide cycle, excluding storm condi-
tions from the results. Three types of “base profiles”were defined,
ordered from lower to higher wave energy: the straight profile (daily
H
b
< 0.25 m), the concave profile and the convex-concave profile
(daily H
b
>0.35m).
The different morphotype models coincide more than seems. Fig. 2
shows the conceptual models ordered from less (left) to more (right)
exposure. Similar profile shapes from different sources are aligned ver-
tically. For instance, the straight beach face coincides with the exponen-
tial/concave profile and a convex concave beach face is similar to the
concave-curvilinear and moderately concave profile.
In summary, the least exposed sites generally have the steepest and
narrowest beach face and the strongest breaks between the swash zone
and the terrace. The different models all point towards wave energy and
sediment characteristics as drivers for different morphotypes, but
quantification isdifferent per study or even absent. The physical relation
between hydrodynamics and morphology has at most been described in
general terms and morphological evolution over time has received even
less attention.
3. Study sites & methods
3.1. Study sites
As mentioned above, the four study sites are artificial beaches lo-
cated in lake Markermeer. Lake Markermeer is a shallow (⁓4 m deep)
inland fresh-water lake without tide in the Netherlands (Fig. 3). The
lake has regulated summer and winter water levels, respectively NAP
−0.2 m and −0.4 m, where NAP is the vertical reference datum in the
Netherlands, close to mean sea level. Since waves are fully determined
by local wind in this area, on average coming from the southwest,
there is a strong positive correlation between wave height and wind
set-up (Steetzel et al., 2017). Since the lake is shallow, waves are
depth-limited. The significant wave height does not exceed 1.5 m and
the peak wave period is typically between 2.5 and 3.5 s during storms.
Average and 95-percentile values of the significant wave height do not
differ much between the study sites (Table 1). Lake Markermeer is sep-
arated from Lake Ijsselmeer by a dam, the Houtribdijk, which is the
Fig. 3. Overview locationof thestudy sites, Pilot Houtribdijk and MarkerWadden beaches, in the Netherlands (NL), with considered transects within the white boxes. Right images from
Google Earth, Landsat/Copernicus.
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
3
location of the first study site, the Pilot Houtribdijk (Fig. 3). This was a
pilot study into dike reinforcement by sandy foreshores (Penning
et al., 2015). The 300 m long beach, closed off by a sheet pile wall at
the northwest side, was constructed and monitored from 2014 until it
merged into the sandy dike reinforcement in 2018. The other three
study sites are located at the Marker Wadden, constructed in 2016
(Fig. 3). This artificial archipelago consists of shallow marsh islands,
protected by three stretches of sandy beaches and dunes and is meant
to improve water quality and ecological habitats in this area. Pilot
Houtribdijk was constructed of sand with a D
50
of 270 μm and the
Marker Wadden beaches of sand with a D
50
of 350 μm.
3.2. Monitoring
At all sites, bathymetric data wascollected using a singlebeam (Pilot
Houtibdijk) or multibeam (Marker Wadden) echosounder, while shal-
low bathymetric data were measured by a moving RTK-GNSS-carrier
(Rijkswaterstaat and Stichting EcoShape, 2018). The GNSS carrier was
also used to monitor topography at Pilot Houtribdijk, while at the
Marker Wadden, topographic data was collected by aerial mapping
with a drone (structure-from-motion) (Natuurmonumenten, 2019).
The singlebeam and multibeam have a typical vertical accuracy of re-
spectively ±0.1 and ± 0.2 m, while the RTK-GNSS and aerial mapping
respectively have a typical vertical accuracy of ±0.03 m and ± 0.05 m.
At Pilot Houtribdijk, 43 transects with a spacing of 15 m were mon-
itored from September 2014 to March 2018 at 23 occasions, with inter-
vals ranging from 1 to 6 months (Table 2,Fig. 4). The measurements
from January 2018 onwards are not taken into account, since the Pilot
was excavated for other research purposes at that time. Longshore
transport was evident at this location, proven by the rotation of the
beach face due to varying wave angles. The platform elevation is similar
over all transects (Fig.4), so to limit the effect of the rotation in the anal-
ysis, only the transects in the centre of the area (transect 10–14) are
considered in this study. Morphological development of this 60 m
wide area is studied by averaging these 5 profiles. At all three study
sites on the Marker Wadden, 9 profiles with a spacing of 20 m were
monitored every 3 months, from July 2018 to September 2019, and
the same averaging method is followed (Fig. 4).
Incoming waves and flow velocities were recorded from October
2014 to March 2018 by an underwater frame with a Nortek Vector
ADV (8 Hz, velocity measurement point NAP-1.64 m, pressure gauge
NAP-1.44 m), 100 m offshore of Pilot Houtribdijk (Steetzel et al.,
2017). The measurements were done in bursts of 8 min per hour and
corrected for atmospheric pressure and pressure attenuation.
3.3. Depth of closure
To confirm that the morphological evolution of lake Markermeer
beaches aligns with the conditions considered by Hallermeier (1980),
we predict the depth of closure for Pilot Houtribdijk with Eq. (1).We
use the classic definition of the depth of closure, where wave induced
sediment transport is negligible, which should therefore be a proxy for
the platform elevation. To make an accurate approximation and analyse
the development over time, we predict the depth of closure for each
storm event. This classic approach is different from the method often
used nowadays, where the depth of closure is used to find the deepest
limit where sediment transport is negligible for (multi-year) time series
of coastal profile evolution, as for instance done by Hinton and Nicholls
(1998).Nicholls et al. (1998) demonstrated that Hallermeier's (1980)
approach defines robust estimates for the depth of closure, particularly
for individual erosional events.
The predicted depth of closure is compared to the level of the corre-
sponding platform from the bathymetry (see Section 3.5). The depth of
closure relative to datum (z
DoC
)isfoundbysubtractingd
s
from a repre-
sentative water level applicable during said storm event (Fig. 6).
3.4. Hydrodynamic analysis
To predict the depth of closure per storm event, information on
wave height, period and water level is needed. We executed a storm
analysis on the wave data from the offshore Vector ADV at Pilot
Houtribdijk. Storm events are determined through a peak analysis on
the spectral significant wave height, H
m0
, derived from the ADV data.
For each peak, the height, prominence and duration are calculated.
The peak prominence measures how much the peak stands out from
the surrounding baseline of the signal and is defined as the vertical dis-
tance between the peak and its lowest contour line. A peak in H
m0
is se-
lected if it fulfils the following three conditions (Fig. 5):
1. The peak height is higher than the threshold significant wave height
of 0.5 m;
2. The peak prominence is at least 0.3 m;
3. The peak duration at 45% (from the top) of the peak prominence is at
least 5 h
After selecting the peaks, the 12-hour exceeded wave height H
m0,12h
is calculated with a rolling window of 12 h, listing the minimum H
m0
.
Subsequently, the maximum value of H
m0,12h
for the period from 6 h be-
fore to 6 h after each peak moment is selected as the H
m0,12h
for that
storm. The 12-hour average peak wave period at the storm peak is
used for T
p,12h
.
For the representative water level needed to calculate z
DoC
,Nicholls
et al. (1998) suggest to use the Low Water Level or Mean Low Water.
But since the Lake Markermeer is non-tidal, we introduce another defi-
nition. We define the 12-hour exceeded water level during the storm,
h
12h
, as the vertical reference level to estimate the depth of closure
(Fig. 5). The 12-hour exceeded water level is calculated with a rolling
window of 12 h, listing the minimum water level. The maximum
value of h
12h
for the period from 6 h before to 6 h after each peak mo-
ment, as determined from H
m0
, is the 12-hour exceeded water level
for that storm. This calculation is identical to the method for H
m0,12h
,
Table 1
Significant wave height characteristics study sites.
Mean H
m0
[m] 95-percentile H
m0
[m] Period
Pilot Houtribdijk 0.20 0.54 Oct 2014 –Mar 2018
Noorderstrand 0.26 0.53 Apr 2019 –Sep 2019
Zuiderstrand/Recreatiestrand 0.27 0.63 Apr 2019 –Sep 2019
Table 2
Monitoring occasions Pilot Houtribdijk.
19-9-2014 27-5-2016
25-10-2014 23-8-2016
19-11-2014 23-11-2016
28-12-2014 6-3-2017
23-1-2015 17-5-2017
15-2-2015 1-9-2017
18-3-2015 19-10-2017
6-4-2015 1-12-2017
21-8-2015 22-12-2017
25-1-2016 6-1-2018
28-2-2016 20-2-2018
20-3-2018
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
4
but with the storm peak moments already determined from H
m0
. The
relative depth of closure is calculated as follows:
zDoC ¼h12h−ds:ð2Þ
To analyse the relation between hydrodynamics and morphological
development, the storm analysis is extended to two-weekly character-
istics, including cumulative wave energy. The wave energy is calculated,
assuming a Rayleigh distribution, as E¼1
16 ρgH2
m0. The cumulative wave
energy is equal to the sum of the wave energy at the peaks of all selected
storms within the two weeks.
3.5. Morphological quantification
We divided the cross-shore profile in three vertical sections to in-
clude the following morphological regions (Fig. 7):
I. the beach face above the yearly average water level (beach face
section),
II. the zone that includes the platform (platform section), and
III. the deeper part of the profile (offshore section).
These sections are separated by four vertical levels:
•above the beach face (NAP+0.95 m),
•at the annual average lake level (NAP-0.3 m),
•at the submerged slope, just below the platform (NAP-1.55 m),
•just below the lake bottom (Pilot Houtribdijk: NAP-2.8 m, Marker
Wadden: NAP-4.2 m).
The vertical limits of these sections are chosen starting from the yearly
average water level(NAP-0.3m).Fromthatlevel a distance is found that
upward includes the beach face and downward the platform for all four
locations, 1.25 m. The lowest limit is just below the flat lake bottom, off-
shore from the submerged slope below the platform. For Pilot Houtribdijk
all sections are of equal height, and for the Marker Wadden locations the
section height ratio for I:II:III is approximately 1:1:2. The upper vertical
limit at NAP+0.95 m is translated into a horizontal limit for the first mea-
surement in time per transect, to create a fixed onshore boundary and
more clearly demonstrate beach face erosion. The offshore boundary for
Pilot Houtribdijk is at 250 m, after which no bathymetric data is available.
For the Marker Wadden sites, this boundary lies at 150 m, since data avail-
ability is variable offshore from that point. This method of following vol-
ume change in vertical sections over time is similar to that of Steetzel
et al. (2017), but with a slightly adjusted volume definition, for a longer
time span and for more study sites.
The average platform height is the average height of the profile in
the platform section. The slopes of the beach face and the slope in the
offshore section are determined at respectively the yearly average
water level (NAP-0.3 m) and the transition between the platform sec-
tion and the offshore section (NAP-1.55 m). The local slope in each of
these two points is estimated from a 2 meter profile section centered
around these two locations of interest.
Fig. 4. Bathymetry of the four study sites, the white number sin the Houtribdijk plot represent the numbers of the transects. Pilot Houtribijk was surveyed in April 2015, andthe Marker
Wadden sites in July 2018.
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
5
4. Results
4.1. Bathymetric features
All four study sites in lake Markermeer display a similar profile
shape and a similar development over time (Fig. 8). At the Pilot
Houtribdijk site, where morphological development has been moni-
tored from construction onwards, a subaqueous platform evolved
within the first months at NAP-1.0 m, on average at 0.7 m below
water level (Fig. 8). The same is visible for the sites at the Marker
Wadden. The beaches at Noorderstrand and Recreatiestrand were con-
structed in late 2016, and reconstructed a few times between then and
March 2018. The beach at Zuiderstrand was constructed and recon-
structed between late 2017 and March 2018. Because of the number
of human interventions, it is not possible to give an as-built situation,
but below NAP+1 m the initial plane slope was approximately 1:20
for all the Marker Wadden beaches. At these sites, a platform is also
visible at NAP-1.0 m, but the initial development took place before the
first measurement (Fig. 8). The platforms vary in width from 30 to
almost 60 m, depending on the location and the time. The profiles
connect to the original lake bottom at NAP-2.8 m (Pilot Houtribdijk)
and −4.2 m (Marker Wadden) with a steeper slope.
All locations have a steep beach face, although at Noorderstrand it
has a slightly lower gradient (Table 3). Moreover, the Noorderstrand
beach face slope varies substantially over time. The beach face slopes
of the other three locations are very comparable. The average offshore
slope is similar for all four locations.
The bathymetric data show a retreat around the water line at all
sites. Because of erosion on the beach face, the platform widens over
time, growing in both onshore and offshore direction for all sites, except
for Recreatiestrand. There the slope below NAP-1.55 m is more or less
stable.
4.2. Depth of closure
The characteristic storm wave height H
m0,12h
,waveperiodT
p,12h
and
base water level h
b
are derived from the hydraulic data (Fig. 9). The 12-
hour exceeded H
m0
varies around 0.5 m, while the maximum storm
peak H
m0
is around 1.3 m (Fig. 9). The maximum storm wave height is
relatively stable, since the wave height is depth-limited in lake
Markermeer.
Per period of two weeks, the average, minimum and maximum
values of H
m0,12h
and T
p,12h
are used to calculate the average, minimum,
and maximum depth of closure. At times with more than two different
Fig. 5. Example from storm peak analysis of H
m0
, Pilot Houtribdijk. The wave height (H
m0
), with the identified storm peaks, and the corresponding 12-hour exceeded wave height
(H
m0,12h
), with its storm peak height. The water level (h) at the storm peak moment and the corresponding 12-hour exceeded water level (h
12h
), with its storm peak height.
Fig. 6. Visualisation definitions depth of closure (d
s
), depth of closure relative to datum (z
DoC
).
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
6
storms per two weeks, the minimum and maximum depth of closure
can differ up to almost a meter. The instantaneous z
DoC
per storm fluc-
tuates between z
DoC,min
and z
DoC,max
. Averaged over the whole period,
z
DoC,av
,z
DoC,min
and z
DoC,max
differ −0.07 m, 0.03 m and −0.18 m respec-
tively from the average platform height. For individual storms, z
DoC,max
can be up to 0.42 m lower than the average platform height. However,
the average z
DoC
(av. h
b
–av. d
s
) stays relatively stable over time,
and varies around NAP-1.0 m (standard deviation over all transects:
0.23 m). This accurately corresponds to the actual average platform
height at the Pilot Houtribdijk. At the study sites at the Marker Wadden
the platform height is also situated around NAP-1.0 m (Fig. 8). Unfortu-
nately no long time series of hydrodynamic data is available for these
sites. Analysis of short time series shows that the wave climate at the
Marker Wadden is similar to that of Pilot Houtribdijk (Table 1), as are
the sediment characteristics. Therefore, we can assume that the depth
of closure for the Marker Wadden sites is in the same order of
magnitude. The platform at these locations is also situated around
NAP-1.0 m (Fig. 8), which confirms the results at Pilot Houtribdijk.
4.3. Volume changes in time
To quantify morphological developments in time, cross-shore vol-
ume changes are calculated for different sections (Fig. 7). This analysis
reveals that the volume of the beach face decreases over time for all
four study sites (Figs. 10, 11). The volume around the platform steadily
decreases at Pilot Houtribdijk, while for the sites at the Marker Wadden,
the decrease in volume only occurs after a period of 6 months with sta-
ble or even increasing volumes. At Pilot Houtribdijk, Noorderstrand and
Zuiderstrand, the beach face and platform per location develop at a
comparable pace, while the offshore volume is gradually increasing. At
Recreatiestrand, the offshore volume change fluctuates around zero,
Fig. 7. Method of volume calculation at Pilot Houtribdijk, showing section I: beach face
section, section II: platform section and section III: offshore section. In dark grey the
volume corresponding to the profile at September 18, 2014.
Fig. 8. Development of the average cross-shore profile at the four study sites, with the as built profile at Pilot Houtribdijk (dashed line) and the as built angle at the Marker Wadden
locations (1:20) and thevertical section division for the morphological quantification.
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
7
and increases and decreases mostly simultaneously with the platform
volume, thus all sections develop in the same manner. The total volume
at the selected transects of Pilot Houtribdijk and Noorderstrand in-
creased over time, while at Recreatiestrand and Zuiderstrand, a nett de-
crease took place.
4.4. Relation between volume changes and wave conditions
The wave climate in 2015 is quite energetic year-round, whereas
and especially 2016 and 2017 are relatively more calm, as is visible in
the cumulative wave energy (Fig. 12). In general, no seasonality in the
wave climate is visible for these years, and both average wave height
(0.6 to 0.9 m) and maximum peak storm wave height (0.8 to 1.2 m)
are fairly constant throughout the year (Fig. 12).
The erosion or sedimentation rate varies over the period of observa-
tion, with slightly higher rates at the beginning of the monitoring period
(grey highlight) and a distinct deviation in April 2015 (Fig. 12). The
rapid changes in the first months after construction concern the initial
profile development. The sedimentation peak of the offshore section
in April 2015 does not coincide with a peak in wave energy event, the
cause is unknown. Note that the rate of volume change (in m
3
/m/day)
in the lower panel is influenced by the interval between bathymetric
surveys, with more frequent surveys, and therefore a more volatile
rate of change in the first months after construction. The energetic pe-
riods between May 2015 and February 2016 and between February
2017 and September 2017 (red highlight) coincide with erosion of the
beach face. Volume changes of theplatform section do not strictly corre-
spond with energetic periods, although erosion is slightly more com-
mon in periods with high wave energy. The offshore volume is
growing in energetic periods, but not exclusively in these periods. Dur-
ing the energetic period between September and December 2017
(yellow highlight) the beach face volume is increasing, contradictory
to the earlier trends. In this period, sedimentation on the top of the
beach face is observed (Fig. 8).
5. Discussion
The shape of low-energy beach profiles in lake Markermeer corre-
sponds to the general description by Jackson et al. (2002),witha
steep beach face and low-gradient platform. From the four considered
sites, only the relatively sheltered site Noorderstrand has a less steep
beach face and shows a less distinct break between the swash zone
and the platform, as would be expected from the conceptual models.
Fig. 9. Top frame:Maximum peak storm wave height per 14 days (Max. H
m0,peak
) and average peak storm wave heightper 14 days (Av. H
m0,12h
). Bottom frame: 12-hour exceeded water
level (h
12h
), subtracted by minimum (min.), average and maximum depth of closure (d
s
), compared to the average platform elevation.
Fig. 10. Volume change per section since September 2014, at Pilot Houtribdijk.
Table 3
Bathymetric features, averaged over time and transects.
Slope (1:x) Platform elevation (m NAP)
Beach face (μ±σ) Offshore (μ±σ)
Pilot Houtribdijk 9 ± 1 14 ± 2 −0.93
Noorderstrand 20 ± 7 14 ± 4 −1.11
Recreatiestrand 11 ± 3 13 ± 2 −0.89
Zuiderstrand 11 ± 2 14 ± 3 −1.00
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
8
The elevation of the characteristic platforms, at approximately NAP-1.0 m,
might be explained by applying the depth of closure formula by
Hallermeier (1980) (Eq. (1)). The laboratory conditions to which his for-
mula was validated, constant waves at a constant water level onto an
initially plane slope, correspond well to the conditions at the study
sites. Despite these similarities, some assumptions in the calculation
method are debatable. For non-stationary conditions, a time scale
should be chosen for events that determine the equilibrium limit or po-
tential depth of closure. In the analysis by Nicholls et al. (1998) for high-
energy coasts, the 12-hour exceeded H
m0
gave the best results for the
event dependent depth of closure compared to 6 h and 18 h. This dura-
tion has also been applied in the current study for low-energy beaches
in lake systems. However, the response of water levels and waves in a
lake like Markermeer is much quicker than in oceans and seas. As this
choice influences z
DoC
to a certain extent, a sensitivity analysis is
added here.
Since water levels and waves in lake Markermeer respond quicker to
wind variations than on open coasts, the 12-hour exceeded H
m0
covers a
large part ofthe storm, while on high-energy beaches, it only covers the
peak. The useof for instance the 6-hour exceeded H
m0
, would imply that
the relative depth of closure, z
DoC
, would be calculated relative to the 6-
hour exceeded water level. From the hydrodynamic data of Pilot
Houtribdijk, it follows that averaged over the full period, H
m0,6h
is higher
than H
m0,12h
,h
6h
is higher than h
12h
and z
DoC,6h
is deeper than z
DoC,12h
,
but the differences are small (Table 4). However, for individual storms
z
DoC,6h
can be up to 0.49 m deeper than z
DoC,12h
. Although the method
is sensitive for individual storms, it is robust when averaged over a
longer period, independently of the exceedance period. The observed
platform elevation is on average NAP-0.93 m and at the minimum
NAP-1.01 m, therefore with the current information the exceedance pe-
riod of 12 h gives the best result.
Although the time-averaged z
DoC,12h
fits very well with the observed
platform elevation, it varies considerably over time. For a high-energy
Fig. 11. Volume change per section since July 2018, at Marker Wadden.
Fig. 12. Hydro- and morphodynamics Pilot Houtribdijk. Top frame: Cumulative wave energy and average and maximum H
m0
per 14 days. Middle frame: Volume change per section
normalised to the first measurement. Bottom frame: Change to rate of volume change. Grey area: initial profile development after construction. Red areas: periods with energetic
wave climate. White area: periods with calm wave climate. Yellow area: period with energetic wave climate but aberrant morphological change.
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
9
event with z
DoC
significantly deeper that the platform elevation before
the event, it is not expected that the platform will lower with for in-
stance 0.42 m within 12 h or a similar period. However, a series of
events with a z
DoC
lower than the platform elevation could cause a low-
ering. With more frequent monitoring of the bathymetry compared to
Fig. 9, the timescale of these morphological developments could be
studied.
More elaborate monitoring on the depth of closure could also shed
more light on the optimal reference water level for non-tidal environ-
ment. Nicholls et al. (1998) stated that the best reference is Low
Water Level or Mean Low Water in tidal systems. The here used 12-
hour exceeded water level is a somewhat conservative choice, since it
basically represents the water level before and after the storm, while
there is a set-up during the storm. However, the results presented in
this paper clearly demonstrate that the platform elevation is controlled
by the depth of closure.
Development over time is described for our four study sites, but are
they underway to equilibrium? According to Jackson et al. (2002),low-
energy beaches do not reach an equilibrium state, but represent a storm
artefact or state. But, since morphotypes are based on hydrodynamic
conditions in more recent studies (Travers, 2007), we would expect
that for relatively constant hydrodynamic conditions, a dynamic mor-
phological equilibrium should be possible. After the short adaptation
time, the elevation of the platform of our four study sites reached an
equilibrium. Since lake level fluctuations are minimal in the non-tidal
lake Markermeer and wave height and surge are always positively cor-
related, this was expected and we can attribute the equilibrium eleva-
tion of the platform primarily to wave action. In other situations, most
likely both wave action and continued water level variations are respon-
sible for the platform elevation. The frequency and duration of these
fluctuations may influence the elevation of the platform (Eliot et al.,
2006), and may lead to variations over time.
Yet, the analysis of the morphology revealed that at none of the four
study sites the other morphological dimensions have reached equilib-
rium yet. For Pilot Houtribdijk, the rate of change slowed down over
time, but it did not fully stop after four years. At the Marker Wadden,
the morphology is still in full development after little over two years
of transformation. Physically, we would expect this process to find an
equilibrium once the platform is wide enough to bring the wave height
down so wave-induced sedimenttransport is negligible near the shore-
line. Since the platform has a very low gradient, a very wide platform
might be needed to meet this condition.
Longshore transport processes are not explicitly addressed in this
paper. As natural morphologies of low-energy beaches look similar to
laboratory results with only normally incident waves (Hallermeier,
1979), it is a fair assumption that the steering processes are alike and
that this typical shape develops due to cross-shore sediment transport.
This is also confirmed in field studies such as the study by Lorang et al.,
(1993a) at Flathead Lake in the United States, where morphology is said
to develop through cross-shore transport. However, when inspecting
the cross-shore development over time, the offshore-directed growth
does not seem to balance out the onshore erosion (Fig. 8). Moreover,
the total volume at the selected transects of Pilot Houtribdijk and
Noorderstrand increased over time, while at Recreatiestrand and
Zuiderstrand, a net decrease took place. This is inevitably linked to
longshore transport processes. At Pilot Houtribdijk, the total sediment
budget, over all transects, was kept in dynamic equilibrium due to the
presence of a sheet pile wall (Steetzel et al., 2017). The increase at the
middle transects was countered by a decrease at the off-centre tran-
sects. Noorderstrand, oriented under an angle compared to the common
wave incidence (SW),must be influenced by longshore transport. Since
Recreatiestrand and Zuiderstrand are constructed in such way that they
are oriented normally to the average angle of wave incidence, negligible
nett longshore transport was expected. The sediment budget was nega-
tive in September 2019, but perhaps the measurement period was too
short to conclude nett erosion.
To summarize the above, we haveattempted to introduce a concep-
tual model of the morphodynamic processes on the low-energy, non-
tidal beach (Fig. 13). The overall beach face erosion combined with si-
multaneous accretion lower in the profile suggests that sediment trans-
port in this area is primarily in cross-shore direction. This sediment
reaches the platform and most likely travels further in both cross-
shore and longshore direction, to meet the equilibrium depth. During
calm conditions the depth of closure is limited, causing sediment that
has previously been eroded from the beach face to accumulate on the
platform.Since the depth of closure is deeper during more energetic pe-
riods, erosion over the total platform occurs primarily in these periods.
Sediment that is transported “over the edge”of the platform will settle
and be deposited on the slope below the platform. In accordance with
the Hallermeier (1979) definition, no wave-driven transport can occur
in the region below the depth of closure. Therefore, these sediments
will not return shoreward causing profile changes in the region below
depth of closure. Model simulations can be used to further our insight
in the sensitivity and variability of these morphological processes.
6. Conclusions
The goal of this research was to understand the morphological de-
velopment and hydrodynamic forcing of low-energy, sandy beaches.
Through a literature analysis into morphotype classifications of these
environments, the general morphology in these environments was
characterized. Bathymetric developments were monitored at four
low-energy, non-tidal study sites in the shallow lake Markermeer in
the Netherlands. Here the typical low-energy morphology with a nar-
row beach face and low-gradient platform, as described by Jackson
et al. (2002), was observed.
Table 4
Sensitivity analysisof 12 h compared to 6 h exceedance valuesof significant wave height
(H
m0
), water level (h) and resulting depth of closure (z
DoC
).
12 h 6 h Difference
H
m0,xh
[m] 0.42 0.53 0.11
h
xh
[NAP + m] −0.21 −0.16 0.05
z
DoC
[NAP + m] −1.03 −1.17 −0.14
Fig. 13. Visual summary of conceptual model of morphodynamics on a low-energy, non-
tidal sandy beach during calm and st ormy periods. Re d: general erosion; blue: only
sedimentation; dotted arrows: possible sediment transpor t directions; grey: yearly
averaged water level.
A.M. Ton, V. Vuik and S.G.J. Aarninkhof Geomorphology xxx (xxxx) xxx
10
The sandy beaches at the study sites were all constructed in recent
years, showing a rapid initial profile adjustment during the first years
after implementation. Based on measurements of waves and water
levels, the depth of closure (Hallermeier, 1980) was calculated and
compared to the elevation of the platform. We conclude that the eleva-
tion of the platform is indeed located near this depth of closure, andthat
after reaching this depth, the platform elevation stays relatively stable.
The morphological development was quantified through calculating
the volumes of three vertical zones in the cross-shore profile: beach
face, platform, and offshore. Both longshore and cross-shore transport
are responsible for the development of platform. Results suggest that
erosion ofthe beach face is primarily by storm-driven cross-shore trans-
port, after which the sediment is most likely diffused both cross-shore
and longshore over the platform and offshore sections. Although the
depth of the platform is stable, the platform width did not reach an
equilibrium for the oldest study site (4 years) and the widening is still
in full development at the younger sites (2 years).
The typical low gradient platform of the low-energy, non-tidal sandy
beach develops at thedepth of closure. This insight is an importantstep
towards the prediction of morphology in low-energy environments and
contributes to the future prospect of implementing sandy beaches in
environments such aslakes, reservoirs and micro tidal seas for purposes
such as shoreline protection, wave energy dissipation for flood risk re-
duction or recreation.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Acknowledgements
This research is part of the LakeSIDE project, which is funded by
Rijkswaterstaat, The Netherlands.
The partnership for the project pilot Houtribdijk consists of
Rijkswaterstaat and an EcoShape consortium involving the research in-
stitutes Deltares and Wageningen Environmental Research, contractors
Boskalis and Van Oord and engineering companies Arcadis Nederland
BV, RoyalHaskoningDHV and HKV Consultants. Shore Monitoring is ac-
knowledged for carrying out the morphological surveys for this project.
The research at the Marker Wadden was supported by the Marker
Wadden Knowledge and Innovation Programme (KIMA), initiated by
Rijkswaterstaat, Deltares, EcoShape and Natuurmonumenten. See
https://kennismarkerwadden.nl/english/.
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