Morphodynamics of ebb-tidal deltas: a model approach
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ARTICLE IN PRESS
Estuarine, Coastal and Shelf Science 57 (2003) 1–9
Morphodynamics of ebb-tidal deltas: a model approach
S.M. van Leeuwen*, M. van der Vegt, H.E. de Swart
Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Princetonplein 5, 3508 TA, Utrecht, The Netherlands
Received 17 December 2001; accepted 25 November 2002
Abstract
The results of 2DH numerical models of the Frisian Inlet (located in the Dutch Wadden Sea) are discussed to gain further
knowledge about the physical mechanisms causing the presence of both ebb-tidal deltas and of channels and shoals in tide-
dominated inlet systems. A hydrodynamic model, extended with sediment transport formulations, was used to verify earlier
conceptual models that deal with ebb-tidal delta characteristics. The model does not confirm their hypothesis concerning the
observed spatial asymmetry of ebb-tidal deltas and suggests that long-term morphological simulations are needed to understand this
aspect. Furthermore, the model indicates that the initial formation of the ebb-tidal delta is mainly due to convergence of the tidally
averaged sediment flux related to residual currents, whilst the net sediment transport in the basin is mainly caused by tidal
asymmetry. A second model (accounting for feedbacks between tidal motion and the erodible bottom) was used to simulate the
long-term bathymetric evolution of the Frisian Inlet under fair weather conditions. This model reproduces the gross characteristics
of the observed morphology: the presence of a double-inlet system with two distinct ebb-tidal deltas having different sizes and the
presence of channels and shoals. The role of the ÔEngelsmanplaatÕ, a consolidated shoal in the middle of the Frisian Inlet, was not
found to be crucial for the morphodynamic stability of this inlet system.
Ó 2003 Elsevier Science B.V. All rights reserved.
Keywords: tidal inlets; ebb-tidal delta; sediment transport; erosion; deposition; Wadden Sea; Frisian Inlet
1. Introduction respect to the direction of tidal propagation in the outer
sea (Sha, 1989).
It has been noted by Davis (1996), Hubbard, Oertel, Ebb-tidal deltas play an important role in the ex-
and Nummedal (1979) and others that significant parts change of water and sediment between the backbarrier
of the world’s coastal system consist of series of barrier basin and the coastal zone (cf. Fenster & Dolan, 1996).
islands separated by inlet systems. The behaviour of This observation motivated the main objective of the
water motion and morphology in these areas is strongly present study, i.e. to identify and understand the phys-
controlled by offshore wave and tidal forcing. The ical mechanisms causing the presence of an ebb-tidal
present study focuses on a specific class of inlet systems: delta on the seaward side of a tide-dominated inlet and
those characterised by both strong shore-parallel tidal why channels on this delta often have a preferred up-
currents and strong currents in the strait. Such systems stream orientation.
are found in the Dutch Wadden Sea (Ehlers, 1988). They A conceptual model to explain the observed asym-
have a complex bathymetry, consisting of an ebb-tidal metry of ebb-tidal deltas of tide-dominated inlet systems
delta and a network of channels and shoals. Typical was formulated by Sha (1989). He attributed this prop-
tidal velocity amplitudes in the channels are of the order erty to the interaction between shore-parallel tidal cur-
of 1 m s1. Most of the channels on the ebb-tidal delta of rents and tidal currents in the strait. This would cause
tide-dominated inlets have an upstream orientation with an overshoot of the tidal flow on the downstream side
of the inlet, resulting in weaker and more eccentric tidal
currents than on the upstream side. A definition of tidal
* Corresponding author. eccentricity is given in Pugh (1987). As a result, sediment
E-mail address: s.m.vanleeuwen@phys.uu.nl (S.M. van Leeuwen). deposition (and thus shoal formation) would take place
0272-7714/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0272-7714(02)00420-1ARTICLE IN PRESS
2 S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9
on the downstream side of the inlet, thereby forcing the the seaward side of a prototype tide-dominated inlet, the
main channels on ebb-tidal deltas to have an upstream Frisian Inlet. In order to study the long-term morpho-
orientation. Shoals forming in this area would then logical evolution of tidal inlets, the feedback from the
migrate under the influence of waves and aeolian changing bottom to the water motion has to be taken
processes. This model is simple and transparent, but it into account. As this facility is not yet available for
is based on conceptual ideas rather than physical anal- the simplified model, such simulations are carried out
ysis. It is therefore important to test these ideas with with a full morphodynamic model, called Delft3D. The
process-oriented models, based on physical laws for the latter has already been successfully used by Wang et al.
water motion, sediment transport and bottom changes. (1992, 1995) to model water motion and morphological
Such quasi-realistic models for tidal inlets are nowadays evolution of the Frisian Inlet on timescales of several
available (see Cayocca, 2001; Ranasinghe, Pattiaratchi, years. In this paper, results of longer time periods are
& Masselink, 1999; Wang, De Vriend, & Louters, 1992; presented which reveal the development of an ebb-tidal
Wang, Louters, & De Vriend, 1995). Up to now, such delta.
models have not been used to test the conceptual ideas In the following section, the characteristics of the
of Sha (1989). Moreover, these models are so complex Frisian Inlet system are presented, followed by a
that it is difficult to gain fundamental knowledge about description of the numerical models and the results with
the physical processes involved. regard to the initial formation of channels and shoals.
This motivates the use of less complex models in which Next, the long-term evolution of the bathymetry is
highly schematised tidal inlet systems and simplified investigated with the Delft3D model, followed by a
equations of motion are used. In order to test the concepts discussion of the results and the conclusions.
discussed above, such a model should at least be able to
describe the eccentricity of horizontal tidal currents. Van
Leeuwen and De Swart (2002) analysed tidal properties 2. Material and methods
and patterns of sediment erosion–deposition for idealised
inlet geometries, using the HAMSOM model developed 2.1. The Frisian Inlet
by Backhaus (1985), which they extended with sediment
transport routines. They found indications that the The Frisian Inlet is located in the Dutch Wadden
mechanism of Sha (1989) is not fully supported by their Sea, between the barrier islands Ameland and Schier-
numerical experiments, but did not consider to what monnikoog (Fig. 1). It consists of a wide basin (now-
extent their findings were representative of realistic tidal adays its length and width are approximately 10 and
inlets. Besides, they neither investigated the possible 20 km, respectively). Most of the bottom material is
formation of an ebb-tidal delta nor that of channels and fine sand (mean grain size of 200 lm). In the inlet, a
shoals in this area. supra-tidal shoal (called the Engelsmanplaat) is located.
Therefore, in this paper, a similar simplified model as It consists of consolidated sediment that is much more
that discussed by Van Leeuwen and De Swart (2002) is resistant to erosive forces than sand. Therefore, the
analysed, but with emphasis on understanding tidal Engelsmanplaat causes a rather effective separation of
properties and net erosion–deposition of sediment on two sub-inlet systems called the Pinkegat (on the west)
Fig. 1. Location and detailed map of the Frisian Inlet, the prototype tide-dominated inlet that is used in the present study.ARTICLE IN PRESS
S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9 3
and the Zoutkamperlaag (on the east). Both subsystems The extended HAMSOM model was applied to a
have their own ebb-tidal delta: the size of the delta of highly schematised tidal inlet system, consisting of a
Pinkegat (with a seaward extension of about 3 km) is rectangular inner basin that is connected by a strait to
about half that of Zoutkamperlaag. Horizontal water the adjacent sea. Fig. 2 shows the default geometry and
motion in this area is mainly driven by tides, with the default depth profile. The geometric (and other param-
semi-diurnal M2 constituent being the dominant com- eter) values are representative for the Frisian Inlet
ponent. Characteristic sea surface amplitudes are about system and were obtained from the data presented by
1 m and maximum tidal currents are of the order of Oost and De Boer (1994). Note that the central axis of
1 m s1; the tidal wave propagates along the coast from the strait does not coincide with that of the inner basin.
west to east at about 15 m s1. Significant wave heights The default bottom neither contains an ebb-tidal delta,
in this area are about 1 m. This system is a mixed-energy nor any channels and shoals: the depth is constant in the
tide-dominated inlet system according to the classifica- basin (2 m) and increases linearly in the outer sea in the
tion of Gibeaut and Davis (1993) and Hubbard et al. offshore direction. The motivation for this choice was to
(1979). investigate whether the interaction between tidal cur-
Presently, on both ebb-tidal deltas and in the inner rents and this initial bathymetry (to be expected after a
basin, a complex pattern of channels and shoals is ob- storm-induced flooding of the backbarrier area) would
served. Recent field data of the water motion at various result in the formation of features like an ebb-tidal delta
locations in the Frisian Inlet were discussed by Van de and channels and shoals. The water motion was forced
Kreeke and Dunsbergen (2000). They reported small by prescribing an eastward propagating semi-diurnal
(positive and negative) values of the eccentricity of tidal (M2) tidal wave, with a constant amplitude of 1 m, at the
currents in the basin. Only one station was situated on open boundaries (the dashed lines in Fig. 2). Tidal
the ebb-tidal delta, so that the spatial distribution of residual currents and overtides are generated internally
eccentricity in this area cannot be reconstructed from by nonlinear shallow water terms and bottom friction.
data. Forcing by waves is not included. For numerical details,
see Stronach, Backhaus, and Murty (1993).
2.2. The HAMSOM model with added sediment
transport routines 2.3. The Delft3D-MOR model
Experiments with a fixed bathymetry were carried out The morphodynamic model that was used in the
with the HAMSOM model (HAMburg Shelf Ocean second part of this study is Delft3D, a process-oriented
Model), extended with routines to compute sediment numerical model developed by WLjDelft Hydraulics.
fluxes and erosion–deposition of sediment at the bed. The water motion is calculated by solving the shallow
The HAMSOM model, developed by Backhaus (1985), water equations: here, the depth-averaged version was
calculates the water motion by solving the shallow water used. A staggered grid is used and the alternating direc-
equations. Here, the depth-averaged version of the model tion implicit (ADI) technique is applied in the numerical
was used. scheme (Stelling & Leendertse, 1992). Bed level changes
For the sediment transport, a suspended load pa- are calculated from the divergence and convergence of
rameterisation is used which contains advective and
diffusive contributions and explicitly accounts for
settling lag effects. For further details, see Van Leeuwen
and De Swart (2002). The erosion–deposition is given by
the divergence of this flux. As the interest here is in
bottom changes on a morphological timescale (order of
years), which is much longer than the tidal period, it
suffices to compute the divergence of the tidally
averaged flux (denoted by brackets hi). Mass conserva-
tion of sediment then implies that
~ h~ qzb
r Fi ¼ ; ð1Þ
qt
where ~F is the volumetric sediment flux vector per unit
width, zb the bed level with respect to the undisturbed
Fig. 2. The geometry and depth profiles used in the HAMSOM model
water level z ¼ 0 and t the time. Hence if the left-hand simulations. Topview (left) and depth profile along central axis (right).
side is positive (negative), there will be local erosion The dashed lines in the topview plot represent open boundaries where
(deposition) of sediment. free surface elevation is prescribed.ARTICLE IN PRESS
4 S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9
the tidally averaged sediment flux h~ F i; as denoted by Eq. stream side of the inlet than on the upstream side. This
(1). The formulation for the volumetric sediment flux was tested with the extended HAMSOM model by
per unit width, ~F ; is discussed later on. computing the long axis and eccentricity of the M2 tidal
The geometry used resembles that of the Frisian Inlet. current ellipses. The results, shown in Fig. 3, indicate
The conditions at the open boundaries were taken from that large tidal currents occur at the transition basin–
a larger scale model that simulates the entire Dutch outer sea with local maxima in the vicinity of the two
Wadden Sea (Hibma, personal communication). Only barrier islands. Nearly circular tides are found at the
M2 elevations were used, which had an amplitude of downstream side of the inlet, but their amplitudes are
1.14 m. Forcing due to wind and waves was neglected. not much smaller than those of the currents on the
upstream side. The results obtained with the process-
oriented model thus confirm some aspects of the con-
3. Results ceptual model.
The last aspect of the water motion that is discussed
3.1. Initial patterns: water motion concerns the residual flow. The motivation for doing
this is that it is one of the important factors that cause
The concepts of Sha (1989) were tested by carry- net sediment transport. Within the context of the
ing out numerical experiments with the extended adopted (suspended load) sediment flux formulation,
HAMSOM model. The simulations covered a period the other important factors are tidal asymmetry (joint
of several tidal cycles. At each gridpoint, a Fourier action of M2 and M4 tidal currents), settling lag effects
analysis was made of the tidal velocity components of (sediment concentration lags tidal currents because par-
the last two tidal periods (representing non-transient ticles have a finite settling time) and diffusive processes.
behaviour). From this, the characteristics of the M2 tidal The physical concepts of these transport mechanisms
ellipse (long axis, eccentricity, orientation and phase) are discussed in Ridderinkhof (1997), Van de Kreeke
and the residual current were computed. and Robaczewska (1993) and references therein. In
The first aspect of the hypothesis of Sha (1989) to be Fig. 4, the residual currents are shown. In the strait,
verified with the process-oriented HAMSOM model is these currents are found to be directed to the open sea.
that during flood an overshoot of the tidal current The residual flow in the outer sea is in the direction of
occurs on the downstream side of the inlet, due to phase tidal wave propagation.
differences between shore-parallel tidal currents and The results of Fig. 4 can be understood from the fact
currents in the strait. The model results (not shown) that the tide in the strait is a partially standing wave,
indeed reveal such phase differences, but no overshoot hence the phase difference between tidal elevations and
of the tidal current on the downstream side of the inlet is tidal velocities is less than 90 , in particular near the in-
found. These results are consistent with those of Van let. The tidal wave transports mass into the basin (the so-
Leeuwen and De Swart (2002) who used a different inlet called Stokes drift) and mass conservation implies that
geometry and a different bathymetry. there must be a residual current in the opposite direc-
The second statement of Sha (1989) is that tidal tion to compensate for this mass flux. Seaward of the
currents are weaker and more eccentric on the down- strait, the residual current directed along bathymetric
Fig. 3. Contour plots of the M2 long axis (maximum tidal current, in m s1) (left) and of the M2 eccentricity (right) computed with the extended
HAMSOM model.ARTICLE IN PRESS
S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9 5
to form an ebb-tidal delta. Initial adjustments of the
bathymetry also occur in the basin.
Fig. 5(b) shows that in the strait net erosion occurs,
particularly on the sides. This indicates the tendency to
form two channels. On the seaward side of the inlet and
near the basin boundaries, net deposition of sediment is
observed, with the most significant changes occurring
near the downstream island. The model results do not
clearly confirm the idea of Sha (1989), that on the down-
stream side of the inlet preferred deposition occurs. In
particular, in the area where tidal eccentricity is large
(Fig. 3(b)) erosion, rather than deposition, is found. The
initial pattern of erosion–deposition does not show that
channels tend to develop with a preferred upstream
orientation.
To test the sensitivity of the model results to the
Fig. 4. Residual depth-averaged currents calculated with the extended
sediment flux formulation used, additional model runs
HAMSOM model.
were performed with the following expression for the
volumetric sediment transport per unit width:
contours is caused by tide–topography interaction (see uj ~
0:05j~ u
4
Zhang, Boyer, Pérenne, & Renouard, 1996). ~
F ¼ pffiffiffi ð2Þ
gCz ðs 1Þ2 d50
3
3.2. Initial patterns: sediment fluxes and This is the total-load formulation of Engelund and
erosion–deposition Hansen (1972), with ~u being the depth-averaged velocity
vector, Cz the Chezy coefficient, g the acceleration due to
The net sediment flux was computed with the gravity, s 2:65 the ratio between grain density and
extended HAMSOM model by using the suspended fluid density and d50 the mean diameter of the grains.
load formulation. The sediment erosion–deposition was Compared with the suspended load sediment flux, the
obtained from the divergence of this flux. Fig. 5 shows Engelund–Hansen flux does not account for settling
the resulting net volumetric sediment flux per unit width lag effects and has no diffusive components. Results
(left) and erosion–deposition of sediment at the bed obtained with the Engelund–Hansen formulation (not
(right). Noticeable are the landward-directed flux in the shown) agree well with those found with the suspended
basin and the seaward-directed flux in the strait and load flux. Thus the model results are robust with respect
nearby outer sea. A net transport of sediment from the to changes in the sediment transport formulation. The
strait to the open sea is found, as well as a tendency presence of an area near the strait where divergence of
Fig. 5. Net volumetric sediment flux per unit width (left) and erosion–deposition of sediment at the bed (right) computed with the extended
HAMSOM model. Dashed lines represent negative contour lines and refer to erosion, drawn lines represent deposition. Grey areas are land.ARTICLE IN PRESS
6 S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9
the sediment flux occurs (Fig. 5(b)) is a common feature 3.3. Long-term simulations
in tidal inlets; this area is called a bedload parting zone
(Harris, Pattiaratchi, Collins, & Dalrymple, 1996). The long-term development of bottom patterns in a
The results mentioned above also imply that settling tidal inlet system was studied with the Delft3D model.
lag effects and diffusive processes are not dominant The initial bathymetry and all parameter values were
factors in forcing net sediment fluxes. Thus, the two the same as those used in the previous section. The
possible mechanisms that remain are: the joint action of Engelund–Hansen formulation (2) was used to compute
stirring by tides and subsequent transport by residual the volumetric sediment flux per unit width.
currents, and tidal asymmetry. The relative contribu- First, the initial patterns of the water motion,
tions of both mechanisms to the total net transport can sediment fluxes and erosion–deposition were computed
be quantified by the dominance index ID (Van der with the Delft3D model (not shown) and compared with
Molen & De Swart, 2001), those of the extended HAMSOM model (Section 3.2).
The two models yielded similar results, thereby con-
j~
F res j j~
F asym j firming the validity and versatility of the extended
ID ¼ : ð3Þ
~ ~
jF res j þ jF asym j HAMSOM model. The subplots in Fig. 7 show the
evolution of the bathymetry from the initial stage up
Here j~ F res j and j~
F asym j are the magnitudes of the to 500 years. At first, there is no ebb-tidal delta but
transport related to residual currents and tidal asym- the results of the previous section already showed that
metry, respectively (Van de Kreeke & Robaczewska, sediment is deposited in the area seaward of the inlet.
1993). Note that ID can attain values between 1 and After 100 years, depths have clearly decreased here, so
þ1; positive (negative) values imply that sediment an ebb-tidal delta does indeed develop. At this stage, its
transport related to residual currents (tidal asymmetry) spatial pattern is still rather symmetrical and two
prevails. A contour plot of this dominance index is channels are forming in the inlet, near the tips of the
shown in Fig. 6. It reveals the importance of combined two barrier islands.
tidal stirring and transport by the residual current on the After 200 years, it becomes clear that two distinct
seaward side of the inlet and the dominance of tidal ebb-tidal deltas develop. The channels in the inlet are
asymmetry in the basin. still deepening and protruding further into the basin.
The model results presented here indicate the ten- Besides, a clear asymmetrical pattern develops: the east-
dency of the inlet system to form an ebb-tidal delta. The ern channel in the neighbourhood of Schiermonnikoog
underlying process is that sediment, being mainly eroded is becoming larger and deeper than the western chan-
in the strait, is transported (by the joint action of tidal nel. With the deepening of the channels, the ebb-tidal
stirring and residual currents) towards the outer sea and delta is extended, the eastern delta becoming larger than
is deposited seaward of the strait. Besides, part of the the western one. The orientation of the ebb-tidal deltas
sediment that is eroded in the strait is transported into is changing as well. The delta of the eastern tidal inlet
the basin (by tidal asymmetry) and is deposited on the system becomes upstream-oriented, whilst the other one
landward side of the barrier islands. becomes downstream-oriented. Thus, the entire system
becomes asymmetrical. After 300 years, this degree of
asymmetry further increases and even channel branch-
ing can be observed in the eastern part of the basin.
After 400 years, the seaward extension of the ebb-tidal
delta slows down and after 500 years, a kind of large-
scale morphodynamic equilibrium is reached.
The asymmetrical patterns only appear after a long
time. This suggests that the evolution of the asym-
metry of the ebb-tidal delta is a long-term, non-linear
process that involves the feedback between tidal motion
and the erodible bottom. In these simulations, the
ÔEngelsmanplaatÕ, a consolidated shoal in the middle of
the Frisian Inlet, was not incorporated. Nevertheless,
a clear double-inlet system develops. Apparently, the
Engelsmanplaat does not play a crucial role in the
stability of the Frisian Inlet.
A comparison of the results of the long-term model
Fig. 6. Contour plot of the dominance index ID defined in Eq. (3).
simulation after 500 years (Fig. 7) with the observed
Dashed lines represent negative contour lines. The step between bathymetry of the Frisian Inlet system, as shown in
contour lines is 0.2. Fig. 1, reveals some remarkable similarities. Both theARTICLE IN PRESS
S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9 7
Fig. 7. Bathymetry, computed with the Delft3D model, at time t ¼ 0 and after 100, 200, 300, 400 and 500 years. Initially, the depth in the basin is 2 m
and it increases linearly in the outer sea. The black lines represent the coastal boundaries. The forcing consists of tides only, waves and storm events
are not accounted for.
model and the field data show the presence of two 4. Conclusions
separated subsystems, the Pinkegat on the west and the
Zoutkamperlaag on the east. The model also yields an In this paper, results have been presented of
eastern ebb-tidal delta, which is larger than the one numerical experiments with process-oriented models
located more to the west. The orientations of these applied to tidal inlet systems. The first objective was to
deltas correspond with those observed in the Frisian verify a conceptual model, formulated by Sha (1989),
Inlet: an upstream-oriented Zoutkamperlaag and a stating that the formation and spatial asymmetry of ebb-
downstream-oriented Pinkegat (although the orienta- tidal deltas in tide-dominated inlet systems is due to the
tion of the Pinkegat varies with time). Also the interaction between shore-parallel tidal currents and
branching of the main ebb channel in the eastern inlet currents in the strait. The second objective was to
is reproduced by the model. On the other hand, many identify the dominant physical mechanisms causing the
features that are present in the original Frisian Inlet initial formation and long-term behaviour of the ebb-
system are not captured by the model. The Zoutkam- tidal deltas and channels and shoals in a prototype tide-
perlaag shows a sequence of channels branching into dominated inlet system, the Frisian Inlet, located in the
smaller and shallower channels towards the land, which Dutch Wadden Sea.
is not seen in the model results. This is not surprising The results indicate that tidal currents are slightly
as their extents are smaller than the grid size (about weaker and more eccentric on the downstream side of
200 m) of the numerical model. Furthermore, towards the inlet than on the upstream side, which is consistent
the end of the simulation, the model shows a ten- with the conceptual model of Sha (1989). No overshoot
dency to form multiple channels on the ebb-tidal of the tidal current is observed during flood and no clear
delta, which is not realistic. It should also be noted tendency for preferred sediment deposition on the
that storm events were not included in the long-term downstream side of the inlet is found. The conclusion
simulation. is that the concepts of Sha (1989) are only partlyARTICLE IN PRESS
8 S.M. van Leeuwen et al. / Estuarine, Coastal and Shelf Science 57 (2003) 1–9
confirmed by the model results. The precise formulation This research was supported by NWO-grant no. 750-
of the sediment transport is not a key issue: both a 19-707.
suspended-load and total-load formulation yielded al-
most the same results. The two important mechanisms
controlling the net transport in this case are the
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