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MODELLING TIDAL-INLET MORPHODYNAMICS ON
MEDIUM TIME SCALES.
EDWIN ELIAS1, ROY TESKE2, AD VAN DER SPEK2, MARIAN LAZAR3
1. Deltares USA, 8070 Georgia Avenue, Suite 303, Silver Spring, Maryland, USA.
edwin.elias@deltares-usa.us
2. Deltares, Department of Applied Morphodynamics, P.O. Box 177, 2600 MH Delft,
The Netherlands. Contact: ad.vanderspek@deltares.nl.
3. Rijkswaterstaat, Zee en Delta, P.O. Box 5014, 4330 KA Middelburg, The
Netherlands. marian.lazar@rws.nl.
Abstract: Improved knowledge on tidal-inlet systems is important for
sustainable long-term management of the Wadden Sea. Process-based models are
essential to obtain such knowledge, but require improvements to make them
capable of accurate predictions on the time-scales relevant for coastal maintenance
(5-25 years). In this paper, we show that the use of the Van-Rijn 2007 sediment
transport formulation provides stable main channels in long-term model
predictions for Ameland inlet. Channel stability can further be enhanced by using
a bedform-related roughness predictor, transverse bed-slope factor, and graded
sediments. In future simulations, the use of the Van-Rijn 2007 transport formula
allows us to account for the wave-driven transports, resolve both the bed-load and
suspended-load transports and, in combination with a bedform roughness predictor
and graded sediments, bring more physically-realistic parameter settings into the
model simulations. Such improved settings are an essential step to increase the
accuracy of morphodynamic model predictions on the meso timescale.
Introduction
The Wadden Sea is a unique coastal wetland, consisting of an uninterrupted
stretch of tidal flats and barrier islands that span a distance of nearly 500 km
along the northern coasts of the Netherlands and Germany and the North Sea
coast of Denmark. Recent studies (e.g. Elias et al. 2012) have shown that most
of the ebb-tidal deltas in the Dutch part of the Wadden Sea experience severe
erosion, mostly related to past large-scale human interventions in the (back-
barrier) system. Only the ebb-tidal delta of Ameland inlet remained fairly stable
in volume between 1926 and 2012 (see next section). An abundant amount of
available field data on water-levels, current velocities, waves and well-
documented bathymetric changes (see Fig. 1) make this inlet ideal for expanding
and improving our understanding of tidal-inlet morphodynamics. Improved
knowledge on tidal-inlet systems is essential for sustainable long-term
management of the Wadden Sea.
2
Fig. 1. Overview of Ameland inlet in the years 1926, 1971, 2005 and 2011 (including the location
of the main channels and shoals)
Evolution of Ameland inlet
Israël and Dunsbergen (1999) point to a cyclic evolution of the channels and
shoals on the ebb-tidal delta of Ameland inlet with a period of 50 to 60 years.
The stage within this channel-shoal development cycle determines whether
erosion or sedimentation occurs along the island tips at the two sides of the inlet.
At the Ameland coastline, as part of this morphological cycle, a bar (called
Bornrif strandhaak [4]) formed and attached to the coast between 1968 and
1998, temporary inducing substantial local erosion and accretion. Presently, a
marginal channel appears to have developed again at the former location of
Bornrif, while the Bornrif sediments are redistributed eastward by littoral drift
(Figure 1, [3]). Both the ebb-tidal delta and the basin are governed by sediment
deposition (34 and 55 million m3 between 1935 and 2005), however more
recently (1990-2012), the ebb-tidal delta volume decreased by 0,5 million
m3/year.
Modelling inlet dynamics
Making predictions on the future state of complex morphodynamic systems
such as the Wadden Sea is not a trivial task. Large-scale tidal-inlet systems
exhibit a range of morphodynamic features that act and interact on different time
and spatial scales. Figure 2 illustrates this statement for morphological elements
3
present at the present-day Ameland inlet. De Vriend (1991) explains the basics
of the morphodynamic scale cascade; Depending on the scale of interest, the
same phenomenom can be just noise, or a component in the morphodynamic
interaction of process, or an extrinsic condition. In other words, if you aim to
model the evolution of the inlet system (right panel in the scale cascade), the
sandwaves or saw-tooth bars formed along the edges (left panel) might not be
relevant and vice versa. Existing conceptual models and empirical relations
often used to describe the morphodynamic behavior on the larger scales, do not
seem to accurately capture the observed changes in the Dutch Wadden Sea
(Elias et al. 2006; Elias et al. 2012). Process-based models that actually describe
the underlying physics of the morphodynamic systems are therefore essential.
Studies by various researchers show that process-based model suites like
Delft3D have reached the stage that they can be used successfully to investigate
tidal-inlet processes and greatly improve our fundamental understanding of the
processes driving sediment transport and morhodynamic change (see e.g. Elias
2006; Lesser 2009; Van der Weegen 2009; Dastgheib 2012; Elias and Hansen
2012).
Fig. 2. An example of a scale cascade describing various morphological elements in Ameland tidal
inlet (the Netherlands).
Process-based models seem to perform particularly well at the end nodes of the
scale cascade. Both short-term, quasi-realtime models (Elias 2006; Elias and
Hansen 2012) and the long-term models (Van der Weegen 2009; Dastgheib
2012) seem to produce usefull results. Lesser (2009) demonstrated, through
4
agreement between modeled and measured morphodynamic behavior of Willapa
Bay (WA), that a process-based numerical model could reproduce the most
important physical processes in the coastal zone over medium-term (5 year)
timescales. Medium term predictions of the Ameland inlet morhodynamics were
less successful (De Fockert 2008). As part of a Dutch coastal research program
that, amongst other things, monitors the morphodynamic changes, investigations
have been made on how to improve the coastal modeling tools to enable
accurate predictions on the time-scales relevant for coastal maintenance (5-25
years). In this paper we present the results of an analysis of the sensitivity of
model predictions to specific parameter settings that determine the stability of
tidal-inlet channels.
Research Aproach, Challenges and Questions
Van der Weegen (2009), Dastgheib (2012), Lesser (2009) and Elias (2006)
demonstrate the usefulness of the Delft3D process-based model to study inlet
morphodynamics on a wide variety of time and spatial scales. Each of these
studies used a carefully selected research and model schematization strategy. By
using different assumptions and schematizations, simulations over the
appropriate spatial and temporal scales can be made. Models that simulate
dynamics from the lower left of the scale cascade, the quasi-realtime models
(e.g. Elias 2006; Elias and Hansen 2012) have typically a high resolution in grid
size and boundary forcing, and use the most complex sediment transport
equations to capture the dominant processes as accurately as possible. Models
that simulate the evolution in the upper right side of the spectrum, the long-term
models (e.g. Van der Weegen 2009; Dastgheib 2012) are constrained by
computational run time. Low-resolution grids, schematisations of boundary
conditions, and morphodynamic acceleration techniques such as “MorFac” (see
Lesser 2009 for a detailed explanation) are used to enable such simulations. For
meso-scale model simulations one can try to run the quasi-real time models over
longer periods, but unless super-computers are employed, such efforts are still
limited to one or at best a couple of years. To reach timescales of 5-25 years, it
seems necessary to adopt the long-term model strategy, to improve
understanding of the underlying concepts, and where possible reduce the
schematizations applied.
In the research presented in this paper, we particularly focus on channel stability
and the use of “advanced” sediment transport formula. Up until the present-day,
long-term simulations, without tuning, often exhibited an unrealistic incision of
the major tidal channels. This unrealistic incision was corrected in different
ways: Van der wegen (2009) increased the effects of transverse bedslope
transport; larger values of the bedslope coefficient promote wider and shallower
channels. Van der Wegen (2009) and Dissanayaka (2011) increased the dry-cell
erosion factor to stimulate bank erosion, and Dastgheib (2012) added graded
5
sediment beds. In addition, these studies mostly used the Engelund and Hanssen
(1967) sediment transport equation, which only gives the total-load
representation. This formulation does not include additional wave-driven
transports or suspended-transport related processes such as settling lag and scour
lag. The Van-Rijn sediment transport equations can be used to model waves and
suspended transport, but also resulted in deeply incised channels (Dissanayake
2011).
In the research presented in this paper we aim to explore whether and how the
more sophisticated sediment transport formula of Van Rijn 1993 and Van Rijn
2007 (see Deltares 2014 for details) can be used to create stable long-term
predictions. In this, we pose the following questions:
1. What is the difference in morphodynamic development using the Van-
Rijn 1993 and the Van-Rijn 2007 sediment-transport formulations?
2. What is the effect of using a homogenously (representative) single
sediment fraction bed versus the use of multiple sediment fractions on
the stability of the main tidal channels?
3. What is the effect using a fixed, homogenous roughness parameter
compared to a space-depended, bedform-based roughness value on the
long-term morphologic development?
By answering these questions, we may be able reduce the amount of model
schematisations used in medium-term models, and bring more physically-
realistic parameter settings into the model. Such settings are a first step
necessary to improve accuracy of the morphodynamic predictions on the meso
timescale.
Model, Model Settings and Sensitivity Analysis
Model
In this study we use the Delft3D model suite (www.oss.deltares.nl). This model
consists of the coupled Delft3D-Wave and the Delft3D-Flow modules that
include the formulations for sediment transport and morphological updating
(Lesser et al. 2004). Delft3D-Flow forms the core of the model system; it
simulates water motion due to tidal and meteorological forcing by solving the
unsteady shallow-water equations. Wave effects, such as enhanced bed shear
stresses and wave forcing due to breaking, are integrated in the flow simulation
by running the 3rd generation SWAN wave processor. Sediment transports are
computed through the implemented transport formulations. In this study the
6
equations for Van-Rijn 1993 (from here on referred to as TR93) and Van-Rijn
2007 (TR07) are used (see Deltares 2014, for implementation details). Complete
overviews of the basics, testing and validation of the Delft3D Online
Morphology with analytical solutions and laboratory data have been reported in
Lesser et al. (2004).
Model Settings
Fig. 3. Model grid and bathymetry (black line shows location of the inlet gorge cross-section and red
dot illustrates the Borndiep1 observation station)
A basic model domain was created covering Ameland inlet. Grid cell sizes vary
from 300x300m offshore, to 200x200m in the inlet. Schematized water-level
boundary conditions were based on Dissanayake (2011) and placed on the
seaward boundary. On the side boundaries (Fig. 3) corresponding water-level
gradients (Neuman boundaries) were imposed. In the back-barrier basin,
boundaries coincided with the tidal divides and were defined as closed. The
model bathymetry was based on the 2005 Vakloding dataset (see Fig. 1). Two
years of hydrodynamic simulations were performed with a morphological
acceleration factor of 50, to represent 100 years of morphodynamic change.
Unless mentioned otherwise, the default settings are used for sediment transport,
the bed roughness is prescribed with a constant Chézy value of 65 m0.5/s, and
the bed consists of a 25m layer of homogeneous sediment (d50= 300 µm). This
value is slightly higher than the actual mean sediment diameter present at
Ameland inlet, but yielded best (read most stable) results. All simulations were
run for tidal conditions only, providing us with computational efficient
simulations that enable extensive sensitivity testing of the main parameter
settings. Tide-only runs seem justified as the focus is on inlet-gorge channel
stability. Ongoing research focusses on the addition of waves, which is essential
for a more realistic representation of the ebb-tidal delta morphodynamics.
7
Sensitivity Analysis
In addition, to the default simulations with uniform roughness, the effect of
space- and time-varying roughness (so-called Trachytopes –Trt- roughness) was
investigated for the Van-Rijn 2007 implementation. In this Trt roughness
formulation the combined quadratic bedform height is determined for the
contributions of ripples, mega-ripples and dunes (here only the ripples and
megaripples were considered). Sensitivity testing revealed a limited effect of
using the Trt roughness compared to equivalent Chézy (C) and Manning
coefficients in the inlet gorge for short-term (2-year) simulations. However, in
long-term model simulations the parameter settings of the Trt roughness became
increasingly important (see model results).
The effect of grain size on the channel development was investigated using a
homogeneous bed and the TR93 formulation (Fig. 4 left-hand panel). Only for
the largest 1000 µm fraction the main inlet channel remained stable, all other
fractions show a deepening, with a maximum of -3m for the 200 µm case. On
the shallower side of the profile (0-3km) larger vertical changes of up to 5m
were observed. Replacing the sediment transport formulation with TR07 shows
its potential in reduction of bed level changes. The TR07 prediction of channel
incision for 300 µm is similar in response to TR93 using a 1000 µm fraction.
This indicates that the new TR07, used in combination with realistic settings for
the bed composition, should be able to maintain stable inlet channels. Note that
the reason we seek a stable inlet channel is based on the measurements. Between
1926 and 2011 (Fig. 1) the inlet morphology changed considerably but the
maximum depth of the main channel remained similair. The differences in
response between TR93 and TR07 are most likely the result of both (small)
changes in the actual formulations, and its implementation in Delft3D.
Fig. 4. Cross-sectional bed development of the inlet gorge after 2 years of simulation for grain sizes
ranging between 200 µm and 1000 µm (left), and (right) for the default TR93 and TR07 sediment
transport formula (roughness C 65 m0.5/s).
8
Fig. 5. Morphologic development after 10, 40 and 80 years (left to right) for simulations using a
uniform sediment fraction of 300 µm and (a) TR93 and uniform C 65 m0.5/s, (b) TR93 and Trt bed
roughness, (c) TR07 and uniform C 65 m0.5/s, (d) TR07 and Trt bed roughness and (e) TR07, Trt bed
roughness and a 25m bed with multi-fraction sediment distribution of 100, 200, 300 and 400 µm
(25% each).
9
Fig. 6. (a) Bed level of the inlet gorge for different years of simulation (corresponds to Fig. 5d), (b)
tide-averaged bedform roughness map (initial state), (c) bed evolution inlet gorge for AlfaBn values
1.5 to 25, (d) difference in bed evolution after 80 years of simulation for AlfaBn= 1 and AlfaBn = 25.
(e) Bed level inlet gorge for 3 fraction distributions, and (f) difference between fraction distribution
1 (100,200,300,400 µm) and 3 (100,200,300,1000 µm) .
10
Model Results
The use of TR93 results in a distinct deepening of the main channels (Fig. 5a).
After 80 years the inlet gorge has incised to depths of -50 m, and a distinct
secondary channel was formed along the left island tip. It should be noted that
the initial sediment layer thickness was 25 m, so locally the base of the sediment
bed was reached limiting further erosion. The eroded material was deposited in
the basin and on the unrealistically seaward outbuilding ebb-tidal delta. The
addition of the bedform roughness (Fig. 5b) introduces a space-varying
roughness term over the domain. Predicted ripple roughness height (RpC) was
0.01 m along the landward margin of the basin and increased towards the
channels, with a maximum value of 0.045 in the smaller channels. The gorge
and main tidal channel had lower values similar to the distal basin. Here mega-
ripples dominated with maximum values of 0.2 m in the gorge, and lower values
(0.08-0.12 m) seaward and landward. In the distal part of the basin, the intertidal
flats, the effect of the mega-ripples was fixed at 0.02 m (Fig. 6b). The predicted
roughness distribution had a pronounced dampening effect on the longterm
morphologic development (Fig. 5b).
The implementation of VR07 Trt roughness can be tuned by the parameters for
relaxation length (RpR and MrR) and height (RrC and MrC), wherein R and M
represent Ripples and Mega-ribbels. Sensitivity testing on the parameter settings
showed identical responses to the relaxation length values. Therefore default
values of 1 were used in the final simulation. An increase of MrC did not
correspond to an increase in the roughness height for values larger than MrC >
1. The maximum 0.2 m value was the main contributor to the combined
roughness for the lower range of the tuning parameter. The RpC displayed a
different trend and allowed RpC >1 coefficients. The ripple height increased in
magnitude for larger values of RpC; from 0.045 m for RpC is 1.0, and 1.0 m for
an RpC of 24.0. The increased ripple parameter altered the combined roughness
height contribution from mega-ripples to ripples. An increase in (combined)
roughness height reduced the sediment transport through the inlet gorge
considerably (Table 1). The response of the maximum velocity magnitude in the
gorge, of the Borndiep1 observation point, to a combined roughness height is
given in Table 1. The low range of the bedform roughness predicted velocity
values similar to Chézy and Manning simulations of 1.0 m/s. The response to
larger tuning values consisted of an overall maximum velocity reduction for
11
increased RpC values. The instantaneous discharge through the inlet reduced
from 30*103 to 23*103 m3 for the roughest (RpC 24) environment.
Table 1. Relation between Roughness height, bedform height, velocity maxima at the Borndiep1
station, and total summed sediment transport through the inlet gorge (for a 80 year simulation).
RpC
MrC
kr
kmr
ks
Umax
(m/s)
Stot
(103 m3)
0.5
1.0
2.0
3.0
6.0
9.0
12.0
0.5
1.0
2.0
3.0
6.0
9.0
12.0
0.022
0.045
0.090
0.110
0.130
0.400
0.500
0.16
0.20
0.20
0.20
0.20
0.20
0.20
0.16
0.21
0.23
0.23
0.25
0.45
0.55
0.95
0.88
0.82
0.82
0.82
0.78
0.75
-
-420
-
-320
-220
-
-140
The introduction of the TR07 transport equation results in a distinct reduction of
the morphodynamic change compared to the TR93 simulation (compare Fig. 5a
and Fig. 5c). Morphologic development based on TR07 shows a stability of the
main channel in the inlet gorge, although the maximum channel depth does
increase in towards the basin. The reduced morphodynamic activity is reflected
in the sediment budget. In the basin, both the gross and net volume change
reduces from 350 to 285 million m3, and from -50 to -35 million m3
respectively. On the ebb-tidal delta, the gross volume change reduces from 190
to 123 million m3 and the net change reduces from +30 to -22 million m3.
During the first 40 years of simulation the inlet channel retained stability, but
the increasing scour of a secondary channel (Boschgat) started to influence the
morphologic evolution from then on (see cross-section Fig. 6a).
Morphodynamic change is further reduced with the introduction of Trt
roughness (Fig. 5d). The gross morphodynamic changes in the basin and ebb-
tidal delta reduce to 200 and 118 million m3, a roughly 40% reduction compared
to the initial TR93 simulation (Fig. 5a). Most likely related to the smaller
morphodynamic response, the ebb-tidal delta retains more of a realistic
characteristic, with a main delta platform that is intersected by smaller channels;
a configuration found in historic (tide-dominated) Wadden Sea ebb-tidal deltas.
Introduction of graded sediments to the simulation introduces a wide range of
additional tuning parameters. From a uniformly well-mixed bed the sediment
sorting took 25 years to complete for a 1.0 m active layer, afterwards the
fraction distribution remained stable. Figure 5e shows the bed evolution for a
simulation with an 1 m active layer and 4 equally distributed fractions of 100,
12
200, 300 and 400 µm sand (in total 25 m bed thickness). The addition of the
finer sediment fractions results in a strong seaward outbuilding of the ebb-tidal
delta in the first 20 years. This outbuilding continued and led to the
development of a large shallow ebb-tidal delta with the main inlet channel
curving to the west. The central channel incised to -28 m in the gorge and -40 m
in the basin. The initial fraction distribution largely controlled the morphologic
developments. The large scour of the channels could be minimized by
substituting either the 100 µm or the 400 µm with a larger fraction of 1000 µm
(Fig. 6e). This also reduces the ebb-tidal delta outbuilding as availability of the
fine sediments decreased (Fig. 6f). The effectiveness of the transverse bed-slope
parameter (AlfaBn in Delft3d) for reducing channel incision was already shown
in previous studies (e.g. Van der wegen (2009). The morphology of the ebb-tidal
delta did not vary significantly for the low range of AlfaBn values (1.5-5).
However, the model showed large response to an AlfaBn value of 25 as the inlet
widened and reduced the depth of the main channel (Fig. 6e,f).
Conclusions
This strict coupling of scale-cascades seems to work well at the end nodes of the
matrix. Both short-term (quasi-realtime models) and the very long-term
(schematized) models seem to produce very reasonable results. In this paper we
resolve a small part of the puzzle on how to improve medium term and meso-
scale model predictions. We show that the use of the Van-Rijn 2007 (TR07)
sediment transport formulation improves of the morphologic development of the
model regardless of the roughness definition and transverse bed-slope factor. By
using TR07 (default settings) incision of the main channel was greatly reduced
compared to TR93. An additional reduction of channel scour was achieved by
using a bedform-related roughness (Trt) predictor. Models using Trt roughness
displayed stable channels in the first 40 years of simulation. Channel deepening
after 40 years was likely related to the morphologic changes and feedback into
the simulation of these. The Trt roughness shows a large variation over the inlet
domain that cannot be captured by a constant Chézy or Manning coefficient.
Even with a single, homogenous sediment fraction of 200 µm or 300 µm stable
channels were found with the combined use of TR07 in combination with Trt
roughness. In these models, the transverse bed-slope (AlfaBn) coefficient is still
an effective parameter to fine-tune the channel development, but to retain
representative cross-sections AlfaBn should not exceed 25. Stable channels can
13
also be obtained by using multiple sediment fractions. However, using a realistic
fraction distribution did not improve channel stability compared to the
homogenous bed as the fine sediments are eroded from the system rapidly and
deposited on the ebb-tidal delta. Adding a coarser sediment fraction (or starting
from an initial equilibrium fraction distribution) tends to stabilize the runs
efficiently. For realistic simulations of the complete inlet system, graded
sediments are likely essential due to the increased, more genuine, morphological
response in both energetic and non-energetic areas.
Discussion and future research
Previous long-term modeling studies often use the Engelund and Hansen (1967)
transport formulation, which only gives a total load representation and does not
include additional wave-driven transports. By using TR07, we can include such
additional wave-driven transports, which are essential to improve predictions of
the ebb-tidal delta evolution (ongoing research). All model results presented in
this study showed a dominance of the suspended-load transports in the inlet
gorge, even for the medium to coarse sand fractions. Typically, model input
schematizations focus on the tidal residual and tidal asymmetry-related flow and
transports. These net transports dominate the bed-load transports, but may be
insufficient to characterize the net suspended transports in which additional
mechanisms such as settling lag and scour lag may occur. To accurately capture
the dominant sediment transport mechanism in complex tidal inlet systems,
additional research using both models and field measurements is essential.
Acknowledgements
The analysis presented in this paper is a result of the research programme KPP
Beheer en Onderhoud Kust (Research for Coastal Management and
Maintenance) which is executed jointly by Rijkswaterstaat – Waterdienst and
Deltares. The work presented here was part of the internship of Roy Teske at
Deltares. We would like to thank especially Ankie Bruens of Deltares and
Quirijn Lodder of Rijkswaterstaat for stimulating us to present these results.
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