Introduction
Small-scale bedforms like ripples are ubiquitous morphological features in
sandy coastal and shelf sea environments. Their formation and dynamics are
controlled by waves and currents, while their equilibrium dimensions are
commonly described as being related to a characteristic sediment grain size.
The existence and evolution of ripples play important roles in the
interaction between the seabed and water column
. Hydraulic roughness and extraction of
momentum from the mean flow are enhanced beyond the effect of mere grain
roughness by orders of magnitude due to the presence of ripples
. Furthermore, the presence of ripples
influences turnover rates of nutrients and pollutants in the benthic
environment when compared to a flat seabed .
If the threshold of motion (expressed as the critical bed shear stress or the
dimensionless Shields parameter) for a characteristic grain size is exceeded,
sediment is transported and bedforms develop. As a fundamental understanding
of bedform development is still pending and deterministic prediction is not
yet possible, equilibrium ripple predictors based on extensive laboratory and
field datasets exist for waves e.g.,,
currents e.g., or for combined flows
e.g.,. A classification of the type of bedform and
corresponding dominant forcing can be made using the ratio of wave and
current shear stress. Wave ripples can be subdivided into orbital ripples
scaling with wave orbital diameter , anorbital ripples
scaling with grain size and intermediate forms
. The dimensions of current ripples are usually related to
grain size only . In contrast to dunes, ripple
dimensions are described as independent of the flow depth see the
classification in; however, by applying a virtual boundary
layer concept, recently demonstrated that water depth
may actually be a controlling factor along with grain size and flow velocity.
Under nonsteady forcing conditions, bedforms continuously adjust in shape and
eventually migrate. Equilibrium ripple predictors may not capture this
adaptation process, resulting in limited prediction of ripple dimensions
during morphodynamically active periods. Groundbreaking flume experiments on
the development and adaptation of current ripples in very fine sand have been
carried out by , introducing an exponential relaxation scheme
for the adaptation of ripple dimensions under changing flow conditions.
Time-evolving (nonsteady) ripple predictors have only recently been suggested
by and . These models also employ
an exponential relaxation with a given timescale and rate-of-change
coefficients during active conditions. This allows for smooth transitions of
bedform dimensions and also includes decay processes due to wash-out and
sheet flow based on additional critical shear stress levels as well as
bioturbation.
Understanding of the dynamics of in situ ripple fields may be impeded by
relict ripples, which are observed under conditions not related to their
formation. These may be inactive bedforms during low flow conditions (around
slack water in tidal environments, or after a storm).
A large number of empirical ripple predictors have been derived from data
acquired in flume studies. Hydrodynamic boundary conditions, local
sedimentology and (micro-)biological effects in the field however may be
different from flume experiments, e.g., in combined current and waves, in
tidal environments dominated by periodically changing flow conditions, or in
deep sea environments. This makes field data a necessary prerequisite for the
understanding, modeling, and assessment of bed conditions
.
Methods of ripple measurements in laboratory flumes and in the field make use
of optical and acoustical instrumentation. Among others, used
underwater cameras in combination with a scale bar to determine ripple wave
lengths. and later used rotary side scan
sonar images to describe the evolution of bedform wave lengths during storms.
used a sector scanning sonar to measure ripple wave
lengths while estimating the height of migrating ripples from the time series
of a point measurement of the bed level from an acoustic backscatter sensor.
developed a 3-D profiling sonar to measure the small-scale
bathymetry of rippled seabeds. Before that, the same authors employed a 2-D
scanning sonar to measure ripple dimensions along transects .
collected high-resolution bathymetry data using a laser
line in rectified camera images taken from a moving sledge. Commonly no
assessment of measured accuracy is reported in these studies, despite the
range of uncertainty in the technical setup, analysis, and derivation of
seabed properties.
In the literature, spatially averaged values of ripple dimensions are often
reported, while the geometric properties of individual bedforms or their
statistical distribution are not. However, show that even
under laboratory conditions with uniform sediment and stationary flow
conditions, bedform dimensions are far from uniform.
Bedform dimensions and shape can change drastically, when the nature of the
dominant forcing changes from current to strong wave dominance or vice versa
. This paper is focused on active ripples, i.e., bed
conditions in which the shape or dimensions of ripples change over the
observation time frame or in which they migrate without changing their
general shape or orientation. The time required for the adaptation is a
function of the sediment transport rate and thus related to the excess shear
stress induced by waves or currents and the sediment properties. For current
ripples, showed in a flume study that the
adaptation time is a function of the inverse power of flow velocity and
ranges from a few minutes to several days. Additionally, bedform heights were
shown to adapt faster than wave lengths. His dataset was used to calibrate
the empirical rate-of-change parameters in the time-evolving scheme by
with two expressions for height and length. For wave
induced bedforms, show that bedform heights adapt last
after wave lengths and orientations have almost reached a new stable
equilibrium. The adaptation timescale for wave ripples is related to the wave
period by and the rate-of-change parameter is related to
the wave mobility number. Recently, further highlighted
that bedform development can be significantly slowed down by low
concentrations (<1 %) of biologically cohesive extracellular polymeric
substances (EPS) in the sediment matrix.
The overall aims of this study are the following.
An assessment of the precision of different methods for the detection and measurement of small-scale bedforms from high-resolution sonar data in a shelf sea
environment
The comparison of the measurement precision to the dimensions of small-scale bedforms calculated by different wave and current ripple
predictors
In the following the bathymetry and sedimentary conditions at the study site
on a sandy shelf seabed in the North Sea are described. The setup and devices
used to measure the relevant data are shortly introduced. Processing steps
for different methods to extract bedform dimensions from raw sonar data are
detailed. The measured hydro- and morpho-dynamic data and ripple
characteristics collected over two tidal cycles are analyzed. The ranges and
error margins determined by the technical specifications of the sensors and
different methods employed to derive parameters from raw sensor data are
reported. The range of bedform dimensions as a result of a different
methodology is shown and evaluated. This range is related to the dimensions
derived from ripple predictors. Implications for the calculation of bedform
roughness from measured ripple dimensions are discussed.
Methods
Study site
Field data were acquired during cruises on RV Heincke to the German
Bight at station D (54.09118∘ N, 7.35881∘ E) of the NOAH
project (North Sea Observation and
Assessment of Habitats). An autonomous lander was deployed during cruise
HE441 (20–28 March 2015) over a period of around 36 h. The station was also
visited during cruise HE447 in June 2015, but the bedforms were inactive
then.
Station NOAH-D is located in the inner German Bight at a water depth of
35 m (Fig. ). Prior to deployment, a survey of the area
surrounding the deployment site by multibeam echosounder revealed a flat and
featureless bathymetry on the larger scale (500 m radius). The grain
size analysis of grab samples taken prior to deployment of the lander showed
bed sediments of fine sand with a median grain size d50=105 µm (Fig. ). Additional grab samples in the surrounding area
exhibit similar sedimentary conditions, which is supported by spatially
homogeneous backscatter intensity in the multibeam data (not shown).
Overview map with the location of station NOAH-D in the German Bight.
Grain size distribution and classification from Coulter laser diffractometer
analysis of the Shipek grab sample taken at the deployment site. Gray curves
in the background
from grab samples in the surrounding area are shown to indicate spatially homogeneous sedimentology.
Lander deployments
Intra-tidal hydro- and morpho-dynamics were observed by autonomous seafloor
observatory SedObs (Fig. a). The lander was developed as
part of the COSYNA
project
(Coastal Observing System for Northern and Arctic Seas) .
It consists of a steel frame with a 2×2 m grating platform
providing space for battery power supply and the installation of sensors. The
platform rests on four slim height-adjustable inclined legs to which
additional sensors can be attached close to the
seabed. Weighted foot plates provide a stable stand, prohibit subsidence and
reduce scouring around the legs. For the application described here, the
measurement platform was approximately 2 m above the seafloor to
minimize distortions of the near-bed velocity profile. The instrumentation
comprises optical and acoustic sensors for the measurement of hydrodynamics,
small-scale bathymetry and environmental conditions such as water
temperature, salinity and turbidity. The lander is deployed from shipboard
with the help of a launching frame and is recovered by acoustic release of
floating buoys.
(a) Deployment of autonomous seafloor observatory
SedObs. (b) Underwater photo showing the rippled seabed.
(c) Cropped sonar image with ripples and lander foot plates visible
in the small-scale bathymetry. Plane coordinates (x,y) are centered on the
sonar transducer and elevation z is given as a zero mean.
The position and field of view of the camera in (b) are indicated by a black dot and black lines.
Minimization of interference with the system under investigation was a key
factor in the design process of the lander as a benthic observatory. In
contrast to tripod frames, the four-legged structure allows free flow between
the legs. During the launch of the lander the heading is monitored to ensure
orientation in alignment with the dominant bottom current direction with the
help of a tail fin on the launching frame (Fig. a).
Bathymetry data were checked for the development of scour in the vicinity,
but such effects were not observed. Flow velocity and turbulence data were
evaluated for possible influence by the lander frame or by other devices and
removed if any influence was detected .
Devices and data
The devices used in this study are summarized in Table . An
acoustic Doppler current profiler (ADCP; Teledyne RDI Workhorse Rio Grande
1200 kHz) was used to record the near-bed velocity profile below the lander.
The along-beam resolution of the downward-looking ADCP was 0.1 m and
the instrument sampled at a frequency of 1 Hz. Additionally, two
acoustic Doppler velocimeters (Nortek Vector ADV) recorded point-wise
velocity data at two levels (0.12 and 0.45 m above the seabed) with a
sampling frequency of 32 Hz. In combination with the pressure signal
recorded, the velocity data were used to calculate wave parameters using the
PUV method e.g.,.
SedObs lander sensors, measured parameters and sampling rates.
Sensor
Parameter
Sampling rate
ADCP 1200 kHz (downward)
Flow velocity (profile) u(z)
1 Hz
2 × ADV
Flow velocity (point), wave parameters
32 Hz
3D-ARP
Bathymetry z(x,y)
1 in 12 min
CTD
Conductivity, temperature, pressure (C,T,P)
1 Hz
Digital camera
Underwater photos (first 90 min of deployment only)
0.1 Hz
The small-scale bathymetry below the lander was recorded by an 1 MHz 3-D
acoustic ripple profiler (3D-ARP; ).
Its pencil-beam sonar transducer with an effective beam width of 1.8∘
is mounted on a rotating and tilting mechanism in an oil-filled pressure
housing. In a step-wise procedure, the sonar is tilted through a preset arc
in 0.9∘ steps, recording along-beam echo intensities from the water
column for every ping (Fig. a). After completing one swath, the
transducer is rotated by 0.9∘ about the vertical axis and tilted to
the arc starting angle to record the next swath. For our applications, the
swath arc was limited to 120∘ because for grazing angles
γ<30∘ the energy backscattered to the sonar transducer rapidly
decreases and the bed echo cannot be detected reliably against background
noise. With the sensor installed 1.8 m above the seafloor, a circular
area of 6.2 m diameter is covered by the scans. With such settings a
full bathymetry scan can be acquired in 11:50 min; therefore, the scan
interval, i.e., the sampling rate of the sonar, was set to 12 min. The raw
echo intensity data were stored in camera raw format (rw2) with an ASCII
header containing sensor settings and metadata and a binary data section
listing echo intensity values of successive samples, pings and swaths.
(a) Definitions of sonar coordinates and beam footprints
on an average seafloor level at different grazing angles. (b) Estimation of maximum
error in ripple through depth due to picking of the highest elevation within
the sonar footprint. (c) Generation of a binary image from
bathymetry using half the standard deviation of the elevation as a cutoff
threshold.
In a morphodynamically active environment, the sampling rate of the
bathymetry must be faster than the rate of change of the morphology.
Furthermore, as the bathymetry scans are not instantaneous snapshots but
rather require a certain time to be recorded, consistency within the scanning
period needs to be guaranteed. Although not discussed here in detail, bedform
migration with displacement rates of up to 3 cmh-1 were
observed. At a sampling rate of five scans per hour, this results in a
maximum migration distance of 0.6 cm between two successive scans,
which is lower than the selected resolution of the gridded small-scale
bathymetries.
Bed detection methods
The raw 3D-ARP data are available as a 3-D matrix Si×j×k, containing the echo intensities for the number of i samples
along the beam, j pings along a swath and k swaths of a full scan. The
general form of the echo recorded in individual pings exhibits a high echo
level close to the sonar transducer due to ringing. This part of the signal
within the near range of the sonar is blanked before further processing. With
increasing range from the transducer, the backscattered echo level declines
due to signal losses to reverberation and scattering in the water column. At
bed range, a steep increase to a maximum level can be observed, followed by a
more gentle decline towards a constant background noise level. Averaged echo
shapes for variable grazing angles are illustrated in Fig. .
Echo intensities over the range derived from scan-averaged water
column echoes for different grazing angles.
To reduce noise, the raw echo signals are smoothed by a five-point moving
average in the along-beam direction. The resulting echo intensity profiles
are evaluated for the maximum echo, as the bed usually contributes the
strongest reflector. The simplest method of bed detection is therefore to
pick the maximum echo in the smoothed ping data. However, as marine life or
other instrumentation in the sonar beam may also contribute strong
reflectors, the water column echo was only evaluated within a certain depth
range around the expected bed level.
Threshold-level methods for bed detection in echo data acquired by similar
sonars have been implemented by and by
. These authors detect the bed level at the depth in
which a certain percentage of the maximum ping-wise echo intensity lmax
is exceeded: lp≥0.6lmax and
lp≥0.8lmax . These approaches
are extended to account for the widening of the along-beam target shape with
increasing grazing angles γ (see Fig. ). Therefore, a
threshold level as a function of the grazing angle is introduced:
lp=1-cosγlmax,
with values ranging from lp=0.7 at the outer swath beams to
lp=1.0 at the central vertical (nadir) beam.
Apart from the threshold level, further methods using the first and second
along-beam derivatives of the echo intensity, echo gradient and echo
curvature were tested. The maximum echo gradient is usually found midway
between background noise level and maximum echo intensity in the rising slope
of the signal, given that it is resolved by a sufficient number of samples.
The maximum in echo curvature represents the onset of the rising slope of the
echo intensity signal.
The last approach for bed detection tested was the cross-correlation with an
idealized bed echo model. The bed level is found at the along-beam range
where the cross-correlation of the recorded ping echo and the echo model is
maximized. designed a model of the bed echo (target)
represented by a sine wave accounting for the acoustic pulse length and the
incident angle between sonar lobe and seabed. The model echo is
cross-correlated with the echo profiles and the index of maximum correlation
denoting the best fit between echo model data determines the bed range. To
account for variable environmental conditions in the echo data at hand, 200
samples (180∘ in 0.9∘ steps) of echoes for every grazing
angle were taken into account for every scan. Averaging the individual pings
over all swath angles, a data derived echo model without the need to design
an idealized echo shape was obtained.
Coordinate conversion and gridding
The beam coordinates of the detected bed level are computed considering the
sound velocity and two-way travel time of the sonar signal yielding an
along-beam range. Together with the tilt and rotation angles for the
corresponding ping and swath, the bed level is described in spherical
coordinates (r,θ,φ) which then are transferred to Cartesian
coordinates (x,y,z) (see Fig. a).
The along-beam resolution can be estimated from the overall beam range and
the number of samples. Typical settings are a beam range of
rmax=4 m and ni=889 samples; the resulting vertical
resolution for the nadir beam is Δz=0.0045 m. The horizontal
resolution is controlled by the area of the sonar footprint as well as tilt
and rotation steps. With a beam angle of β=1.8∘ (±3 dB points conical, ) and a sonar
height of hs=1.8 m above the seabed, the nadir beam
ensonifies a circular area of wf=0.056 m diameter. At the maximum
grazing angle γmax=60∘, the total area ensonified over the
echo pulse length has a width wf,∥=0.226 m in the swath
plane. The along-swath beam spacing is set to Δβ∥=0.9∘ steps, resulting in an along-swath spacing of
Δs∥=0.028 m at nadir (γ=0∘),
Δs∥=0.057 m at γ=45∘ and Δs∥=0.116 m at the maximum grazing angle
(γ=60∘). The across-swath beam spacing is controlled by the
rotational step of Δβ⊥=0.9∘. With the intersection
of the outermost beam at γ=60∘ with the seafloor at
smax=tanγmax⋅hs=3.118 m it results
in a maximum step of Δs⊥=smax⋅tanΔβ⊥=0.049 m. With β=2⋅Δβ, the
across-swath footprint width is double the across-swath beam spacing.
As the acoustic pulse is most likely reflected by the highest elevation
within the sonar footprint, the depth of troughs may be underestimated
(Fig. b). Assuming a triangular bedform shape and a maximum slope
equal to the angle of repose of sand α=32∘, the maximum error
in underestimating through depths yields εmax=0.5⋅wf⋅tanα=0.017 m at nadir and
εmax=0.070 m at the outermost beam in our
configuration. As ripple troughs are usually more flat, the error is expected
to be less pronounced. With a typical aspect ratio (ripple height over
length) ψ=0.1 much lower than the angle of repose, the maximum error
reduces to εmax=0.003 m at nadir and
εmax=0.011 m for the outermost ping.
For comparability among successive scans, the scattered data points were
gridded resulting in digital elevation models (DEMs) with consistent grid
cells (Fig. c). With a minimum along-swath sonar step size of
0.028 m at nadir, a grid horizontal grid resolution of Δx=Δy=0.025 m was selected to maintain the high resolution in
the center of the recorded bathymetry even if the effective resolution
decreases with increasing beam footprint and spacing towards higher grazing
angles.
In the last processing step, the bathymetry is cropped to the central area of
2 m by 2 m for further evaluation of bedform characteristics.
This limitation is made because the area outward of the lander legs is
shadowed from the sonar's field of view and the maximum grazing angle for the
cropped area is limited to γ=30∘, reducing the effects of
increasing beam spacing and sonar footprint. To better distinguish local
ripple features, the global trend of the larger-scale surrounding bathymetry
is computed from the average bathymetry of all scans of a deployment and
removed. The resulting residual zero-mean bathymetry is evaluated by the
following methods.
Ripple geometry
Ripple geometry can be described by the orientation φ of crest lines
in the horizontal plane and the cross-sectional dimensions: height η,
wave length λ and aspect ratio ψ=η/λ. The dominant
forcing can be distinguished from ripple cross-sectional shapes: in contrast
to symmetric wave ripples, current ripples exhibit a steeper downstream (lee)
slope and a more gently inclined upstream (stoss) slope. A classification for
a number of transitional forms between pure wave and current ripples is given
by . The ratio of the stoss and lee slope lengths (symmetry
index) can be used to identify bedform orientation with regard to the
dominant forcing and indicate migration in this direction
.
(a) Small-scale bathymetry cropped to the central
2×2 m below the sonar. (b) Overlay of detected
objects in an 8-connected neighborhood on a binary image with a threshold of
0.5σz. Object centers and major axes are marked
in red. (c) Polar histogram of ripple crest-perpendicular orientation in degrees
from north with the percentage of the total number of objects on the radial
axis.
The geometry of the ripples is extracted from the gridded bathymetry
datasets. First, the crest-transverse orientation θ of the ripple
field is derived: the gridded datasets are transferred into binary image
matrices using a threshold equal to half the standard deviation of the global
elevation ztr=0.5σz (Fig. c). The binary
images are processed using 8-connected neighborhoods to identify crest areas
of individual bedforms. The detected objects are represented by ellipses of
equal area. Small and circular objects are removed by criteria for minimum
area and ratio of the ellipses' semi-axes. The average orientation of the
remaining objects is used as characteristic ripple orientation.
Figure shows an example of the cropped bathymetry, the binary
image with detected ripple orientation and the corresponding distribution of
crest-perpendicular orientation in the polar histogram. The precision in
orientation detection throughout successive scans, even for inactive
bedforms, is on the order of 10∘. To avoid abrupt changes in the
subsequent computation of bedform heights and lengths, the ensemble average
ripple orientation is computed for the complete deployment period, given that
it does not change significantly over time. Afterwards, the scans are rotated
using the average ripple orientation and re-interpolated to the original
Cartesian grid for extraction of ripple dimensions using the following three
methods.
Statistical method (ηm,s)The first is a statistical estimate using the distribution of bed elevations.
The standard deviation of elevation, multiplied by k=22, was used to
estimate bedform heights ηs by and .
This method is usually employed to compute root mean square wave height from water
level records and assumes sinusoidal bedform cross sections.
Image extrema method (ηm,i)The second method finds local extrema in the 3-D bathymetry as grid cells surrounded
by cells of lower (crest) or higher elevation (trough), similar to finding extreme
pixel values in raster images. The averaged ripple ηi height is computed from the range between crests and troughs.
Transect method (ηm,t, λm,t)For the third method, transects are defined perpendicular to the crest orientation
and evaluated for local extrema (crest and trough) between zero up- and down-crossings.
The computed bedform height ηt is the average range between the elevations
of detected maxima and minima per transect. Apart from height, bedform length λt
is also computed by the transect method as the average along-transect distance between two
successive crests. With the DEM spacing and cropping window size used, a total of 80 transects of 2 m length are evaluated.
Methods for the evaluation of bedform dimensions can be divided into
continuous and discrete approaches. While statistical methods evaluate the
continuum of the bathymetry, discrete or direct methods provide dimensions of
a limited number of features detected with a given threshold for height and,
in the case of the transect method, also length. As described by
, the disadvantage of discrete methods is the
sensitivity of measured dimensions to the thresholds selected. As an
alternative, ripple orientation and length can also be determined from
spectra obtained from the 2-D discrete Fourier transform (DFT) of the gridded
bathymetry or from 2-D
autocorrelation. However, these methods require a certain regularity of the
bedforms and were not applied here. Especially when primary and secondary
bedforms are present, a carefully calibrated direct approach may be more
useful than a statistical approach cf.. The
disadvantage of direct approaches is that the selection of thresholds and
filter window sizes introduces a certain subjectivity and influences the
resulting statistics of bedform dimensions. The advantage of direct methods
is that they capture a range of bedform dimensions and therefore yield not
only average values for the overall bathymetry, but also a distribution of
dimensions allowing for a statistical evaluation.
Predictors for ripple dimensions
A number of predictors for wave ripple geometry exist in the literature and
few for current ripples. A recent overview and evaluation of the performance
of wave ripple predictors with an extensive dataset from lab and field
experiments can be found in . present
a literature review of predictors for wave, current and combined ripples and
recently developed a combined, time-evolving predictor.
After determining the dominant forcing, two formulations for wave or current
ripples are employed to determine equilibrium heights which are then used in
an exponential relaxation in the time-stepping procedure .
In contrast to comparative studies such as, e.g., , we
choose a number of common predictors and compare their range to the range of
measured ripple dimensions by the different methods described above.
The following ripple predictors are applied with a given median grain size
and hydrodynamic data and compared to measured dimensions. The traditional
current ripple predictors of (Ya64, Ya85) for
length and (Fl88) and (Ba94) for ripple
height were selected as they are widely used. For mixed forcing conditions,
the recent wave and current ripple predictors of (So12w,
So12c) are used by defining the prevailing dominant forcing and selecting the
appropriate predictor.
Current ripples
Current generated ripple dimensions are usually described as independent of
hydrodynamic parameters but scaling with grain size and immersed weight only.
An early work by (Ya64) predicts current ripple length as
λc=1000⋅d50
and was later revised including additional data (Ya85) in the form
600⋅d50≤λc≤2000⋅d50,
while the ratio between bedform height and length may be derived using an
empirical relation with the best fit to a large dataset from laboratory and
field data by (Fl88),
ηc=0.0677⋅λc0.8098,
and the maximum bedform height as
ηc,max=0.16⋅λc0.84.
(Ba94) gives bedform height as
ηc=18.16⋅d50λc0.84.
Building on this work, (So12c) predict maximum dimensions of current ripples as follows. For height they obtain
ηc,max=d50⋅202⋅D∗-0.554
and length yields
λc,max=d50⋅(500+1881⋅D∗-1.5).
Equations () and () are valid in a range of
1.2<D∗<16, where D∗ is the dimensionless grain size
D∗=g(s-1)ν21/3d50
with the density ratio of sediment and water
s=ρs/ρw, gravitational acceleration g and
kinematic viscosity of water ν. These maximum ripple dimensions are
reduced during wash-out conditions and existing ripples are completely
eliminated by sheet flow. The different flow regimes are delineated by
respective critical Shields parameters. In the measurements presented here,
supercritical Shields parameters for bed load transport were found, but they
remained far below wash-out and sheet flow conditions; thus, only the maximum
ripple dimensions are used here.
Hydrodynamic conditions at station NOAH-D, 20–22 March 2015.
(a) Water level, (b) flow velocity at a height of 0.12 m
above the seafloor, (c) wind speed and direction, and
(d) significant wave height and peak period.
Wave ripples
Predicted wave ripple dimensions commonly scale with a dimensionless number
derived from wave parameters in relation to sediment grain size and immersed
weight. (So12w) found that the use of the ratio of wave
orbital amplitude and median grain size Δ=A/d50 as independent
variables gives the best representation of a large dataset of measured ripple
dimensions from flume and field studies. They use the following empirical
predictors for wave induced ripple wave length:
λw=1+1.87×10-3Δ(1-exp(-(2.0×10-4Δ)1.5))-1A
and height
ηw=0.15(1-exp(-(5000/Δ)3.5))λw.
Earlier works as cited in based on flume and field data predict wave ripple dimensions as follows.
(GM82) predict height as
ηw=0.22A(θw/θcr)-0.16
and length as
λw=6.25η(θw/θcr)0.04.
(Li96) give
ηw=0.101A(θw/θcr)-0.16
for height and
λw=3.6η(θw/θcr)0.04
for length. In Eqs. ()–(), θw is the
wave induced and θcr the critical Shields parameter.
Hydraulic roughness
When bedform dimensions are known, their effect on the flow can be assessed
as a hydraulic roughness length using empirical relations
. The impact of form roughness due to bedforms is
important for numerical models as it can exceed the effect of grain roughness
kg by orders of magnitude e.g.,. A widely
used (bed)form roughness predictor is defined by
ks,f=1.1⋅η⋅(1-e-25η/λ).
Another common form of roughness length derived from ripple dimensions is
kf=f(η2/λ), with height in a power of 2 over length see
the overview in with varying scaling factors.
presents it as follows:
z0,f=arη2λ (with scaling factor typically ar=1).
(a) Shields parameters for wave orbital velocities θw,
tidal current θc and critical Shields parameter θcr.
During supercritical conditions (θ>θcr), filled markers indicate
the dominant forcing. (b) Evolution of ripple height and (c) wave length
compared to predicted equilibrium dimension for wave and current forcing as given by
. Indices in the legends of (b) and
(c) indicate
p – predicted, m – measured, c – current, w – wave, t – transect, s – statistical and i – image extrema.
Results
Hydrodynamics and sediment mobility
Hydrodynamic and meteorological data from the measurement site for a period
of 36 h are displayed in Fig. . Over the tidal cycle, water
depths range from 34 m at low tide to 37 m at hight tide at
the position of the lander. Current velocities measured by the lower ADV
0.12 m above the seabed range from 0.1 to 0.3 ms-1. The
depth-averaged flow velocities measured by the downward-looking ADCP are
25 % higher. The wind direction changes from westerly winds with speeds of
up to 15 ms-1 during the first day of the deployment through the
northerly to easterly directions with speeds of 5–15 ms-1 on the
second day. Wave parameters were calculated using the velocity and pressure
data from the lower ADV. Significant wave heights range from below
0.5 m in the first half of the measurement up to 2.5 m in the
second half, with a peak period between 8 and 10 s.
To relate the hydrodynamic forcing to sediment mobility, Shields parameters
were computed for wave (θw) and current
(θc) forcing and the critical Shields parameter
(θcr) was defined for the given median grain size
(Fig. a). For the first 18 h of the deployment, conditions with
excess shear stress were observed only during peak flood and ebb currents.
Wave induced excess shear stress conditions are reached for a period of 4 h
starting around 15:00 LT on the second day, followed by a period with
current induced excess shear stress lasting for around 4 h during flood
current around 22:00 LT.
Roughness lengths for measured ripple dimensions using Eqs. () and ().
Method
Statistical
Image extrema
Transect
ks,f (–); Eq. ()
0.01861
0.01486
0.01115
Reduction with regard to stat. method
1.00
0.80
0.60
z0,f (m); Eq. ()
0.00168
0.00119
0.00079
Reduction with regard to stat. method
1.00
0.71
0.47
Bed detection
An inter-comparison of the different methods for bed detection shows that all
threshold level methods reproduce similar characteristics of the rippled
seabed (Fig. ). They mainly differ in the absolute level of
average depth. The maximum echo gradient, maximum echo curvature and 60 %
maximum echo method provide a median depth around
0.025 m higher than the median depth computed by the remaining
methods. Additionally, the 60 % max. method exhibits a slight dependence on
the grazing angle and returns a bowl-shaped bathymetry (see
Fig. b). The comparison of the different bed detection methods
revealed that picking the maximum amplitude of a smoothed echo within a
certain range of the expected bed level provides the most efficient approach.
Level threshold methods do not enhance the bathymetry DEMs and echo gradient
and curvature methods are less robust. Bed picking by cross-correlation with
an echo model is more computationally expensive than the level threshold
methods, but it accounts for the shape of the complete bed echo rather than
depending on a single value. However, the bed echo model approach is limited
to flat seabeds and a perfectly horizontal sonar with a nadir beam normal to
the bed, where only the grazing angle determines the incident angle between
sonar lobe and bed. For rippled seabeds, however, the exact morphology within
the sonar footprint needs to be known a priori to adapt the echo shape to the
true incident angle. Echo model methods may therefore rather serve as
enhancement of the bathymetry computed by a threshold level method in a first
run.
Comparison of bathymetries obtained from different bottom-picking methods.
(a) Maximum echo, (b) 60 % max. echo ,
(c) 80 % max. echo and (d) grazing
angle related coefficient of max. echo. Elevation z is given as a zero
mean.
Ripple dimensions
Ripples with a mean wave length of λm,t=0.215 m and
a mean height of ηm,t=0.013 m (aspect ratio
ψ=0.06) are measured using the transect method (Fig. b, c).
The largest measured bedform heights of 0.019 m are obtained by the
statistical method followed by 0.017 m by the image extrema methods,
whereas the evaluation of extrema in individual grid transects yields the
lowest absolute heights of 0.013 m (Fig. a). The
dimensions remain stable for the first 24 h of the deployment and the
bedforms are considered inactive during this period as
θc<θcr. Thus, the scatter of measured
dimensions is used to quantify the precision of the methods used for their
detection. With the increasing flood current velocities and wave action on
the seafloor from 24 h onwards, the ripple height decreases by
0.004 m over a period of 2 h and increases to the initial height
over the following 6 h with increasing tidal current velocity. No
significant changes in ripple wave length can be observed. In terms of height
evolution the trend of change of ripple height on the second day of the
deployment is captured by all three methods. The statistical method returns
the most robust results, resulting in less scatter between successive
measurements.
Box plots of the precision of measured dimensions during stationary
conditions and accuracy in comparison with predicted equilibrium dimension for
wave and current dominated conditions using Eqs. ()–().
(a) Bedform height, measured by 2-D transect-wise extrema, 3-D image
extrema and a statistical method. Markers indicate predicted ripple heights
using the expressions for currents from ,
and
and for waves from , and .
(b) Bedform wave length measured from 2-D transects. Markers indicate
predicted ripple length using the current expressions from
and and the wave expressions from ,
and . In the box plots, the red line denotes the median,
the blue box indicates the 25th and 75th percentiles and the dashed lines
extend to extreme values.
All methods of bedform detection produce values that fall within the range
between mean (0.011 m) and maximum (0.024 m) bedform height
as given by Fl88. Following Ba94, the predicted current ripple height equals
0.015 m. Predicted current ripple dimensions using Eqs. ()
and () from result in
ηp,c=0.015 m and
λp,c=0.124 m. Predicted wave ripple dimensions from
Eqs. () and () follow the evolution of wave orbital
velocities; however, waves are expected to be dominant only where
θw>θc (Fig. a: Day 2,
15:00–19:00). During this period, the maximum predicted wave ripple
dimensions are ηp,w=0.017 m and
λp,w=0.115 m. Wave ripple height predicted by Li96
results in 0.015 m, while the height of wave (orbital) ripples by
GM82 results in 0.032 m.
Bedform wave lengths derived based on the transect method amount to
λm,t=0.215 m (Fig. b). The mean length
for current ripples predicted by Ya64 results in 0.105 m and the
range predicted by the relations of Ya85 yields 0.063–0.210 m. Wave
ripple length predicted by GM82 yields 0.205 m, while the length
predicted by Li96 results in 0.054 m and lengths predicted by So12
amount to λp,c=0.124 m for currents and
λp,w=0.109 m for waves.
The discrete transect method allows a statistical evaluation of the
distribution of measured dimensions. The evolution of dimension histograms
along with statistical parameters for bedform height and length are displayed
in Fig. . Due to the relatively large gridding cell size of
0.025 m, the distribution of lengths is rather narrow and mostly
varying between two cells (Fig. b). The standard deviation of
ripple height increases from 0.005 to 0.007 m throughout the first
day and decreases again to 0.004 m with the wave event (18:00–21:00
on the second day). This may indicate that the bedforms become more regular
due to the pronounced dominance of waves in this period.
Evolution of histograms and statistics of bedform dimensions measured by
the transect method. (a) Bedform height and (b) bedform wave length.
Blue dot markers indicate the median, black squares indicate the standard
deviation and gray triangles indicate the 5th and 95th quantiles. Due to the
large cell size and
narrow distribution of bedform lengths, the latter are only displayed for heights.
Hydraulic roughness
Roughness lengths z0,f and Nikuradse's equivalent sand roughness
ks,f resulting from the different ripple heights and the length from the
transect method are summarized in Table along with reduction
factors with regard to the statistical method. Nikuradse's roughness
ks,f (Eq. ) returned using ripple dimensions from the image
extrema method is reduced by a factor of 0.8 and by a factor of 0.6 for the
transect method. Due to the squared ripple height in Eq. (), the
difference between the methods is even more pronounced for roughness height
z0,f, which returns reduction factors of 0.71 and 0.47 for image extrema
and transect methods, respectively.
Discussion and assessment
Methods for dimension measurement
Only one method is shown for the analysis of ripple orientation and length
from sonar data, but three methods can be compared for the calculation of
ripple heights. The statistical method e.g.,
assumes a 2-D sinusoidal ripple field and computes its root mean square
height. The second method picking regional extrema in the bathymetry only
measures the height of a limited number of features. The evaluation of
transects makes use of the complete scan at the grid resolution and averages
over a larger number of regional extrema along the transects.
If bedform dimensions are computed from transects perpendicular to bedform
crests, the result depends on the lateral position of the transect. As can be
seen in Fig. b, ripples found in the field often exhibit curved
crest lines of limited length rather than being purely 2-D features.
Furthermore, the instantaneously observed rippled seabed always holds a
history of varying dominant forcing drivers, magnitudes and directions.
Transitional states may comprise newly formed active ripples superimposed on
decaying relict ripples with different orientation. Within a 3-D field, any
selected transect will cut across individual ripples at an arbitrary position
with respect to its lateral elevation profile. The ripple height can only be
regarded as meaningful by statistically evaluating multiple transects. This
is underlined by , who state that bedforms are far from
regular features that can easily be described using mean values, even in
laboratory flume experiments with uniform sediment and stationary flow
conditions.
Precision of measurement
To assess the accuracy of the measurement, a priori known topography
under controlled laboratory conditions would be required. This cannot be
achieved under field conditions. However, the precision of the
different methods described here, i.e., the repeatability of a dimension
measurement, can be estimated from the inter-comparison of the different
methods and the temporal variability of the dimensions obtained from each
individual method during stationary, inactive periods.
The different methods for ripple height measurement yield different absolute
values, but the magnitude of the change in height is captured by all three
methods. For a better assessment of the precision of the methods, bedform
dimensions from the first 18 h of the deployment were summarized in box
plots exhibiting the distribution of ripple height and length during
stationary conditions. The results shown in Fig. indicate that
both ripple height and wave length can be measured with a precision smaller
than 10 % of their absolute dimensions, regardless of the method used. The
distributions of ripple height for all three methods are negative-skewed.
Judging from the 25th and 75th percentiles, the statistical method
provides the most narrow range of ripple height, while image and transect
extrema yield comparable ranges.
As for ripple length, both 2-D cross-correlation and DFT did not prove
robust; thus, the transect method remains. Its results fall into the wide
range of lengths predicted by , but are around 60 % larger
than lengths predicted by for wave ripples and still
about 40 % larger than the length predicted for current ripples scaling
with grain size only.
Form roughness
The overestimation of ripple height has a significant effect on the
calculation of hydraulic roughness due to the fact that height is used in a
power of 2 in common roughness predictors (see the list in
). While the range of predicted heights is
in good general agreement with measured average values, the So12 predictor
tends to represent maximum heights of individual ripples rather than an
along-crest average height given a certain three-dimensionality with varying
crest elevation. If ripple height measured as an average over individual
transects is compared to the results from the statistical method, it is found
that the latter gives values 40 % larger than the transect method. This
corresponds to a roughness height increase by a factor of 1.56 if the ripple
dimensions are used to predict form roughness using bedform roughness height
as given by Eq. () and an increase in roughness
height by a factor of 1.96 using the relation given by Eq. ()
.
Conclusions
An in situ setup for measuring ripple dimensions and dynamics was described,
as well as several methods for processing the measured data. While the
accuracy of the measured ripple dimensions cannot be determined
without an absolute reference value, both ripple heights and wave lengths can
be measured with a precision smaller than 10 % of their absolute
dimensions during inactive conditions. All data processing methods tested are
consistent with regard to the ripple dimensions computed. Observed relative
changes in height are on the order of several millimeters between successive
scans during active periods. The dynamics of ripple dimensions obtained by
any of the methods (i.e., their relative changes) can be reliably obtained
and linked to changes in the forcing hydrodynamics.
The overall range of current ripple height can be predicted using the
empirical relation by . The current ripple predictors
from and and the wave ripple predictors
from and fit measured heights more
closely. Measured ripple lengths compare best to the upper end of the wide
range given for current ripples by and wave ripples by
but are somewhat longer than lengths predicted for both
wave and current dominated ripples
. The measured lengths of the ripples are best
predicted by the upper end of the range for current ripples given by
and wave ripples by .
The performance of time-evolving predictors introduced by
and could not be evaluated. The
predictor of was developed for wave orbital ripples in
more energetic environments. Both predictors could not predict the small
range of dynamic evolution of ripple heights in the shelf sea area. This may
also be related to the migration of the ripples due to nonlinear interaction
of wave and current forcing, which is not covered by the predictors.
Additionally, the migration of bedforms observed may result in the opposed
trends in the development of ripple heights during the wave dominated
conditions (around 18:00 on the second day) (Fig. a).
The commonly used statistical estimation of ripple height yields heights
40 % larger than average heights obtained by the transect method. This
results in calculated form roughness height increasing by a factor of 2. To
account for the spatial variability of ripple heights, dimensions derived
from transects should be considered whenever spatial bathymetry data with
sufficient resolution are available.