MODELLING WAVE ATTENUATION DUE TO SALT MARSH VEGETATION USING A
MODIFIED SWAN MODEL
Elizabeth K Christie1 , Iris Möller1 , Tom Spencer 1 , Marissa Yates2
Vegetated shorelines have been increasingly recognized for their contribution to natural coastal protection due to their
ability to dissipate wave energy. Within the UK, salt marshes are beginning to be included in flood defence schemes.
Predicting wave dissipation over vegetation requires accurate representation of salt marsh canopies and the feedback
relationship between vegetation and wave conditions. We present a modification to the SWAN vegetation model,
which includes a variable drag coefficient and a spatially varying vegetation height. Its application is demonstrated by
modelling wave propagation over UK salt marshes. The third generation wave model, SWAN includes a vegetation
module for calculation of wave attenuation over vegetation. Wave dissipation is determined based on the vegetation
properties and a drag coefficient. This drag coefficient, C D , is used to calibrate the model, and a fixed value is used per
model run. Empirically the drag coefficient has been found to vary with ambient wave conditions. Typically the drag
coefficients are defined empirically as a function of either the stem Reynolds number, Rev , or the Keulegan-Carpenter
number, KC . The parameter values have been shown to vary with vegetation type. In this paper, we modify the SWAN
vegetation module to include a temporally varying C D . This allows the drag coefficient to vary with ambient wave
parameters, which gives an improved prediction under time varying wave conditions (e.g. passage of a storm) and
includes the change in wave conditions as they travel through the vegetation. We also incorporate spatially varying
vegetation height into the model to further improve the representation of the complexity of vegetated shorelines. Using
the new formulation we find improved prediction of wave dissipation over both idealized laboratory and field salt marsh
vegetation.
Keywords: salt marsh; vegetation; wave dissipation; SWAN; wave modelling
INTRODUCTION
Recent years have seen the increasing recognition of wave dissipation by vegetation in aquatic and
coastal environments. This realization stems from growing field evidence of wave attenuation, both in salt
marshes (Möller et al., 1999, 2001) and other types of vegetation (Kobayashi et al., 1993; Méndez et al.,
1999; Paul and Amos, 2011; Bouma et al., 2014). The ability of vegetation particularly salt marsh to dissipate waves provides an important coastal protection function during storms. It has widely been argued that
the restoration of new coastal wetlands can, alongside existing coastal defences, increase coastal resilience
to climate change (Temmerman et al., 2013; Spalding et al., 2014). For incorporation into coastal management and planning, the prediction of wave dissipation due to vegetated wetlands must be rigorously studied
under a range of conditions to ensure accurate prediction of the impacts of the vegetation.
Wave dissipation due to coastal wetland vegetation is typically calculated based on the Morison equation, which assumes that the vegetation can be represented as a cylinder. The Morison equation describes
the force of a wave on a cylinder to calculate the energy dissipation due to the cylinder. This equation has
been adapted for use in vegetated wetlands by Dalrymple et al. (1984) and Mendez and Losada (2004),
where the energy dissipation is calculated based on the properties of the plants including the plant height,
plant diameter, number of plants and a drag coefficient. The drag coefficient, C D , is a simple method for
parameterizing the approximations and physical processes not explicitly calculated.
Predicting the wave dissipation due to vegetation relies on accurate representation of marsh vegetation
canopies within existing shallow water wave models. One of the difficulties in doing so arises from the
complex nature of these vegetation canopies. Salt marsh vegetation often consists of mixed plant canopies
with a mosaic of plant assemblages controlled by surface elevation and the related parameters of inundation
frequency/duration (hydroperiod) and salinity gradients. In addition, canopies are often characterized by
vegetation clumps forming spatially varied (on scales of metres) canopy characteristics, and are occupied,
at least in the higher elevation zones of more mature marshes by often complex (woody/shrubby) vegetation types (such as Atriplex spp). Existing studies have shown that submergence ratio, i.e. the ratio between
water depth and plant height, is critical in determining wave dissipation over salt marshes (Mendez and
Losada, 2004; Möller et al., 2001). Vegetation height is thus a critical parameter.
1 Department
2 Laboratoire
of Geography, University of Cambridge, UK
d’Hydraulique Saint-Venant, Cerema, France
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The drag coefficient is typically given a fixed value and used to calibrate models of waves across coastal
wetlands, and is dependent on the plant species. However, empirically the drag coefficient has been shown
to vary with the ambient wave conditions (Kobayashi et al., 1993; Méndez et al., 1999; Mendez and Losada,
2004; Möller et al., 2014). The empirical drag coefficient for various types of vegetation has been shown to
vary with the vegetation Reynolds number (Rev ) and the Keulegan-Carpenter number (Kc ), defined as:
Rev = Um
D
v
ν
(1)
where Dv is the vegetation diameter and ν is the kinematic viscosity defined as ν = 1 × 10−6 m2 s−1
KC =
Um T
Dv
(2)
where T is the wave period. Figure 1 presents empirical relationships found for different vegetation types
between the drag coefficient and Rev and KC . Kobayashi et al. (1993), Méndez et al. (1999), and Paul and
Amos (2011) found an empirical relationship between the drag coefficient and the Rev number for kelp,
seaweed, and seagrass, respectively. Mendez and Losada (2004) and Jadhav et al. (2013) determined an
empirical relationship between the drag coefficient and KC number for kelp and salt marsh, respectively.
Augustin et al. (2009) compared empirical relationships between Rev and KC over a salt marsh, finding
that the drag coefficient showed greater correlation with the Rev number under emergent conditions, whilst
under near-emergent conditions the drag coefficient had a better correlation with KC . Bradley and Houser
(2009) found the drag coefficient is better described by the Rev in low energy conditions for seagrass. Whilst
Sánchez-González et al. (2011) showed the drag coefficient correlates closer to KC than Rev over a seagrass
meadow.
Figure 1: Relationship between C D and a) vegetation Reynolds number (Rev ) and b) the KeuleganCarpenter number (KC ) for empirical studies of wave dissipation over a range of vegetation types.
In this paper we improve the calculation of wave dissipation over vegetated wetlands by introducing a
temporally varying drag coefficient. Additionally, we extend the representation of coastal wetlands in the
SWAN wave model by introducing a spatially varying vegetation height.
METHODOLOGY
Current SWAN Vegetation module
SWAN is a third generation wave model (Booij et al., 1999) based on the wave action balance equation and includes source and sink terms for energy generation, dissipation and non-linear interactions. The
dissipation due to vegetation, S ds,veg , is calculated within a vegetation module, SWAN-Veg. The current
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formulation for vegetation dissipation (Suzuki et al., 2012) uses a modified version of the Dalrymple et al.
(1984) wave dissipation formula by Mendez and Losada (2004).
Mendez and Losada (2004) determined the energy dissipation based on the properties of the vegetation.
The vegetation characteristics include plant height (Hv ), plant diameter (Dv ), number of plants per m2 (Nv )
and the drag coefficient (C D ). The mean rate of energy dissipation due to vegetation per unit horizontal area
(Mendez and Losada, 2004) is expressed as:
!3
gk sinh3 kHv + 3 sinh kHv 3
1
Hrms
(3)
hǫi = √ ρC D Dv Nv
2σ
3k cosh3 kh
2 Π
where ρ is the water density, C D is the drag coefficient, k is the mean wave number, σ is the mean wave
frequency, h is the water depth, and Hrms is the root mean square wave height. As such the drag coefficient
is commonly used to calibrate the wave model.
The SWAN vegetation module can differentiate between emergent and submergent vegetation, if emergent the height of the plant is specified as the water depth. The vegetation characteristics can be varied
vertically, by dividing the vegetation into layers and specifying different vegetation characteristics for each
layer. This allows the module to be used for vegetation which varies significantly with height, such as
mangrove trees. In this case the energy dissipation for a layer i is defined. All the vegetation parameters
(Dv , Nv and C D ) can be varied vertically. The vegetation density can be varied spatially, which allows the
plant diameter to also vary spatially, however, the vegetation height is fixed spatially.
Modifications to the SWAN Vegetation Module
We modified the SWAN-Veg module to introduce a temporally varying C D and a spatially varying Hv .
This allows the vegetation height to be input as a grid over the model domain in an ascii format. We extended
the wave dissipation to include a new formulation where the drag coefficient is calculated internally based
on the vegetation Reynolds number (Eq.1), instead of the fixed user input parameter. This formulation
requires knowledge of the relationship between C D ∼ Rev , which, as shown earlier, is dependent on the
vegetation properties and will vary by vegetation type. The relationship between the drag coefficient and
Reynolds number is usually expressed (Kobayashi et al., 1993; Méndez et al., 1999; Bradley and Houser,
2009; Paul and Amos, 2011; Möller et al., 2014) in the form :
!c
b
(4)
CD = a +
Rev
where a, b, and c are empirically derived constants, which, are user defined in the SWAN steering file.
We use the empirical work of Möller et al. (2014) to define the C D ∼ Rev relationship for a typical North
West European salt marsh. Möller et al. (2014) used the Hydralab Large Wave Flume, GWK Hannover, to
observe waves over a ∼ 40 m long test section of transplanted salt marsh in a 300 m long, 5 m wide flume
under 2 m water depth. They found a relationship between C D & Rev for irregular waves with:
!1.615
227.3
C D = 0.159 +
(5)
Rev
This equation is based on the Rev at the front of the marsh section. For inclusion in the new module in
SWAN, the calculation of vegetation Reynolds must be completed at each grid cell, therefore, the C D ∼ Rev
calculation needs to take into account the change in Rev over the salt marsh surface. We instead modify
the relationship of Möller et al. (2014) and calculate the drag coefficient based on the median vegetation
Reynolds number (i.e. ((Rev,0 − Rev,n )/2) + Rev,n ), where 0 indicates the front of the marsh section and n is
the end of the transect). Using the large wave flume data we calculated the new relationship as:
!1.922
170.489
C D = 0.174 +
(6)
Rev,med
Figure 2 presents the relationship between C D and Rev using data from the flume study showing the
relationship for the Rev,0 calculated by Möller et al. (2014) (Figure 2a) and the relationship for the median
vegetation Reynolds number Rev,med (Figure 2b). The fit to the data is good, with r2 = 0.99 for both cases.
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(a)
(b)
Figure 2: Relationship between C D and a) Rev calculated from the maximum wave orbital velocity at the
front the salt marsh transect of Möller et al. (2014), and b) the Rev,med calculated from the median maximum
wave orbital velocity.
MODEL VALIDATION AND RESULTS
Validation: Wave Flume Data
We validated the new SWAN-Veg module using the empirical data of Möller et al. (2014). The SWAN
model was run in 1D mode with waves from a JONSWAP spectrum, wave setup and wave breaking were
included with default parameters. The model input conditions were calibrated to reproduce the wave conditions at the initial wave gauge. The model was run for both the fixed drag coefficient, with C D calculated
for each test condition determined by Eq. 5, and for the temporally varying drag coefficient using the relationship between C D and Rev determined by Eq. 6. The vegetation used in the experiment is typical of
upper intertidal zone North West European salt marsh, consisting of Elymus athericus, Puccinellia maritima, and Atriplex prostrata. The relevant plant characteristics, as mean values for the marsh section were,
Dv = 0.00125 m, Hv = 0.7 m, Nv = 1225. The model was run for 11 wave conditions, with a water depth
of 2 m and irregular waves with H s = 0.111-0.909 m and T p = 1.44-6.26 s.
The measured and predicted significant wave height reduction for the different wave conditions are
presented in Figure 3. The measured experimental values show the significant wave height reduction increases with increasing initial wave height. The wave height reduction predicted by the original SWAN-Veg
module, with a fixed C D , shows a good fit to the measured data at low initial wave heights (6 0.3 m), but
underestimates the wave dissipation over the higher initial wave heights. Whereas the new SWAN-Veg
module, with varying C D , overestimates the wave dissipation for the small values of H s,0 (6 0.3 m), and
agrees well with the measured data for the high initial significant wave heights representing storm waves.
Overall, RMSE errors are 0.027 m, and 0.022 m for the fixed and temporally varying C D , respectively,
giving a slightly better fit with the new formulation.
Validation: Field Data
We validated the new SWAN-Veg formulation using the wave dissipation field measurements of Möller
et al. (1999), providing a dataset for a natural salt marsh setting. Möller et al. (1999) measured the wave
conditions at the seaward margin and at the end of a 197 m salt marsh transect at Stiffkey, North Norfolk, UK. Along the transect the marsh surface is characterised by the halophytes Limonium vulgare, Aster
tripolium, Atriplex portulacoides, Salicornia spp. and Spartina spp. At the landward end the same species
occur alongside Suaeda maritima, Plantago maritima and Puccinellia maritima.
Only experimental data with onshore winds within 45◦ of the transect orientation were used for the validation test; wind conditions were taken from the Weybourne station, 12 km east of the study site (BADC
MIDAS wind database). A spatially invariant vegetation height was used, derived from side-on photography
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Figure 3: Observed and modelled wave height reduction over a 40 m long section of transplanted salt marsh
in a 300 m wave flume (Möller et al., 2014). Modelled data compares calculation of wave dissipation using
a fixed C D and temporally varying C D .
Run
Water Depth
(m)
1
2
3
4
5
6
0.77
0.76
0.74
0.96
0.98
1.19
Significant
wave height
(m)
0.29
0.28
0.27
0.30
0.45
0.52
Peak Period
(s)
Mean wind
direction (◦ )
Mean wind
speed (ms−1 )
6.83
5.39
1.86
2.73
2.73
4.18
60
60
60
90
80
70
15
15
15
14
22
25
Table 1: Experimental conditions of wave dissipation measurements over a salt marsh transect at Stiffkey,
North Norfolk, UK (Möller et al., 1999)
of the canopy (Möller et al., 1999), where Hv = 0.11 m. Plant diameter was assumed to be Dv = 0.00125
m (representative of North West European salt marsh (Möller et al., 2014)) and plant density, Nv = 1061
stems/m2 (similar to marsh vegetation at Tillingham, Essex, UK (Möller, 2006)).
We set the 1D transect up with an elevational slope of 0.00196. The model was forced with 6 individual
wave bursts (using a JONSWAP spectrum) with a fixed water depth. The model conditions are presented in
Table 1 and cover water depths ranging from h = 0.74−1.19 m, significant wave heights of H s = 0.27−0.52
m, and peak periods of T p = 1.86−6.83 s. The measured significant wave height reduction is compared with
the predicted wave height reduction by the new SWAN-Veg module in Figure 4. The field observations for
these 6 wave bursts suggest that the wave height reduction is fairly constant over the range of initial wave
heights, this pattern is also shown in the modelled results. The predicted wave height reduction by the
new SWAN-Veg model shows a very good agreement with the measured results (RMS E = 0.0274 m), the
agreement is best under the larger waves.
Sensitivity Testing
We ran a series of sensitivity tests to investigate the impact of the new SWAN-Veg formulations on
the modelled wave dissipation over vegetation. All sensitivity tests were run using a hypothetical salt
marsh wave flume experiment, we used a 1-D transect, with an initial water depth of 1 m. Wave setup and
wave breaking were included, using default parameters, and bottom friction was included using the Collins
6
COASTAL ENGINEERING 2018
Figure 4: Observed and modelled wave height reduction over a 197 m long section of salt marsh at Stiffkey,
North Norfolk, UK (Möller et al., 1999)
formula (friction coefficient = 0.015). In all cases wave conditions were input as parameters and calculated
using the JONSWAP spectrum.
A synthetic storm event is used to test the temporally varying C D over a 200 m salt marsh transect. A
28 hr synthetic storm event was generated with water level range of 1.80 − 4.0 m and maximum significant
wave height of 2.77 m . The vegetation parameters were defined as Hv = 0.4 m, Dv = 0.00125 m and
Nv = 1061 stems/m2 , giving vegetation parameters typical of UK East coast salt marshes in and around the
Tillingham, Essex marsh location.
The synthetic storm conditions are presented in Figure 5a. The timeseries of normalised wave height
reduction for both a fixed C D , calculated using the maximum wave orbital velocity during the storm, and
the new temporally varying C D are presented in Figure 5b. At the peak wave heights the normalised wave
height reduction is the same for both the fixed and temporally varying C D , for all other wave conditions the
fixed C D predicts a lower wave height dissipation than the temporally varying C D .
Figure 5: Modified SWAN-Veg formulation sensitivity testing for a storm event on a 100 m section of salt
marsh. a) Storm water level and significant wave height, b) normalised wave height reduction for a fixed
C D and a temporally varying C D
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Sensitivity to the spatially varying vegetation height was tested across four 100 m salt marsh transects
with different vegetation patterns in hypothetical wave tank experiments. The model vegetation patterns are
displayed in Figure 6 and include a constant plant height (6a), gradually increasing plant height (6b), a
stepped plant height (low-high) (6c) and tufts of plants (6d). In all cases the mean vegetation height is
Hv = 0.25 m, plant diameter is Dv = 0.0045 m, and plant density is Nv = 1061 stems/m2 . The model is
forced with a significant wave height of H s = 0.5 m and peak period of T p = 4 s.
Figure 6: Modified SWAN-Veg formulation sensitivity testing for spatially varying vegetation height. Significant wave height variation over a) constant plant height, b) gradually increasing plant height, c) stepped
plant height, d) tufted plants.
As shown in Figure 6, the spatially varying plant height does not influence the wave height reduction
seen at the end of the 100 m transect. However, the significant wave height is clearly reduced at a faster
rate as the wave travels over larger plants generating differences in the spatial pattern of wave height over
the 100 m distance between the four cases.
DISCUSSION AND CONCLUSIONS
In this paper we present modifications to the SWAN-Veg module to better incorporate the complex hydrodynamics and varied vegetation structure across coastal vegetated wetlands. Firstly, the spatially varying
vegetation height was added to the SWAN-Veg module. The sensitivity of wave dissipation over a 100 m
long salt marsh was tested under a range of different vegetation structures. Whilst the different heights do
not impact the final wave height over a transect they do impact at other points over the marsh. The spatially
varying vegetation is difficult to validate as there are limited studies that have measured the required vegetation characteristics, due to labour intensive techniques required for this in the field. Current advances in
8
COASTAL ENGINEERING 2018
sensors mounted on unmanned aerial vehicles (UAVs) and in methods for extracting vegetation community
type information from remotely sensed imagery, however, may offer ways to acquire such information with
greater ease in the future. Our new formulation will have the most impact in a 2D rather than a 1D case, and
we plan future work to compare the results presented here to 2D empirical data of wave dissipation over
vegetation.
Secondly, the module was extended to include a temporally varying drag coefficient, which, when used
to compute wave dissipation has shown a good agreement with experimental data on salt marsh vegetation
from a wave flume under simulated storm conditions and in the field. The new formulation has the advantage over the fixed C D as the user does not have to either change the drag coefficient for each wave condition
or use C D as a calibration parameter to get the best fit of wave energy dissipation due to vegetation over
all conditions. The new module can be used for modelling situations over longer periods of time where the
wave conditions are likely to vary significantly, such as during storms. Additionally, it can be used for other
types of vegetation using empirically derived constants from the literature.
The new wave dissipation calculation fit to empirical data was shown to be better for larger waves. This
is due to two reasons i) the empirical data of Möller et al. (2014) used to derive the C D ∼ Rev relationship
was acquired for simulated extreme storm events, therefore, includes predominantly large waves, and ii)
the vegetation Reynolds numbers have a large range, and particularly high values at low wave heights.
Therefore, the drag coefficient is particularly sensitive to small wave heights. To improve the formulation
future work will test the model against further empirical data sets both in wave flumes and in the field.
Additionally we will investigate the effect of including an additional SWAN-Veg formulation based on the
relationship between C D ∼ KC . For the prediction of the coastal protection function provided by salt marsh,
however, we are mostly interested in wave dissipation under storm waves. The fact that the best model fit
is achieved at higher water depths and for more energetic wave conditions thus makes our results highly
relevant to the needs of coastal managers and engineers.
ACKNOWLEDGEMENTS
This work was supported by the NERC BLUECoast project (NE/N015878/1) and the EU FP7 RISCKIT project (grant no. 603458). The flume observations were acquired during an experiment supported by
the European Community’s 7th Framework Programme through the grant to the budget of the Integrating
Activity HYDRALAB IV, Contract no. 261529 and a grant from The Isaac Newton Trust, Trinity College,
Cambridge (11.35(s)).
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