SWAN and its recent developments

SWAN

Marcel Zijlema, Gerbrant van Vledder, Leo Holthuijsen, James Salmon, Pieter Smit

Simulating WAves Nearshore

Environmental Fluid Mechanics Section
Faculty of Civil Engineering and Geosciences

Abstract
The SWAN model is a third-generation spectral wave prediction
model developed by Delft University of Technology. Since its initial
release in 1998 this model has become a widely used and reliable
tool for offshore and near shore wave predictions. Its main field of
application is the coastal zone where, by virtue of its implicit
numerical scheme, it can be considered as a very efficient tool forhigh resolution coastal applications. Besides this field of application itis also appropriate for open ocean conditions.
The source code of SWAN is published, well documented and webserved (www.swan.tudelft.nl). Delft University continuously develops
and improves SWAN with the support of U.S. Office of Naval
Research and Dutch Ministry of Public Works. New features andimproved physics are regularly added. This poster provides anoverview.

The main conclusion is that there is no prevailing dissipation modelwith default settings for the best performance of SWAN underarbitrary bathymetries. Next, a scaling for the well-known BattjesJanssen model has been developed based on a joint dependency on
local bottom slope  and local water depth normalized by wave
length kd (Figure 3). In addition, this scaling is extended with theeffect of directional spreading. This extended -kd scaling is shown toresolve the observed problem of overestimating wave heights over a
horizontal bottom and underestimating waves generated by a local
wind in idealized 1D shallow lakes. The inclusion of directional
spreading has been shown to improve the model for predicting
short-crested waves propagating over the horizontal tidal flats.

Figure 5. Bathymetry and flexible mesh of the Dutch Wadden Sea.

Physics and model features
Wind drag and bottom friction
An alternative to the well-known Wu (1982) wind dragparameterization is added. It is based on a review of a large numberof more recent observations, and will gives lower drag values for
relatively high wind speeds; see Figure 1. This parameterization has
been published in Zijlema et al. (2012). In addition, we recommend
the use of the lower value of the bottom friction coefficient based on
the JONSWAP formulation for both wind seas and swell waves,
Cf=0.038 m2s-3, provided the new wind drag parameterization isapplied. Using this lower value has also improved the estimates ofwave growth in shallow water and of low-frequency wave decay in a
tidal inlet, independent of the wind drag.

Figure 3. The calibrated  used in the -kd scaling and  = 0.73 for reference.

Triad wave-wave interactions
A number of formulations from the literature (Becq-Girard et al.,1999, Booij et al., 2009, and Toledo and Agnon, 2012) have been
implemented to assess their feasibility for operational use in SWAN
and to model higher harmonics and the equilibrium spectral tailmore accurately compared to the default Lumped Triad
Approximation (LTA) of Eldeberky (1999). Some preliminary results
are given in Figure 4. We see improvements over the LTA.

SWAN and SWASH
SWASH is a time domain, non-hydrostatic wave-flow model thatsimulates the wave phenomena of interest in coastal regions,
including wave breaking, runup, wave-induced currents, wavecurrent interactions and generation of bound long waves in a realistic
wave climate (Zijlema et al., 2011). This model has been coupled to
SWAN in order to seamlessly propagate wind waves from oceans tocoastal waters including sandy beaches, reefs and harbors. A PhD
project has been started recently to implement an efficient
numerical method in SWASH for nesting moored floating bodies (e.g.
ships) for the purpose of studying detailed wave interaction withthose objects in harbors and waterways based on a realistic wave
climate (Rijnsdorp and Zijlema, 2013).
Other functionalities
An extra source term for wave dissipation by aquatic vegetation hasbeen added based on the work of Suzuki et al. (2012).
Recently, a functionality has been implemented in SWAN thatenables to generate block and spectral output files in the netCDF
format. This may be useful for any kind of operational use, e.g. realtime wave forecasting.

Figure 1. Observed values of the wind drag coefficient from various studies and theweighted best-fit 2nd and 4thorder polynomial (n is the number of independent data
points per study).

White capping
It has been known for a long time that SWAN underestimates
structurally the peak and mean wave periods. Investigations ofRogers et al. (2003) showed that adjusting a specific parameter in thewhite capping term of WAM Cycle III (i.e. exponent of the mean wave
number) leads to an improved prediction of the wave energy atlower frequencies which, in turn, improved the wave periods. Thisadjustment has led to a new default value in SWAN.
Depth-induced wave breaking
To improve model performance of wave breaking in the depthlimited regions, including bottom slopes, reefs and horizontal flats, aliterature study was carried out. This is summarized in Figure 2.
Scatter index#BJ'78

TG'83

0.73

Mad'76 Ting'01+ T&M'02

S&Hol'85 S&How'89 Lipp'96+

vdW'09

FA'12

Bald'98

DDD'85

Rue'03

R&S'03/07

Slopes

J&B'07

Wallingford*

49

0.06

0.10

0.11

0.18

0.08

0.13

0.16

0.07

0.06

0.07

0.08

0.06

Katsardi*
Smith*

18
31

0.13
0.08

0.14
0.08

0.23
0.13

0.34
0.26

0.16
0.14

0.22
0.22

0.24
0.28

0.15
0.08

0.10
0.11

0.16
0.10

0.17
0.10

0.12
0.09

Boers*

30.05

0.07

0.15

0.41

0.19

0.31

0.36

0.06

0.13

0.11

0.08

0.10

B-J*

2

0.05

0.13

0.15

0.34

0.13

0.24

0.32

0.06

0.07

0.07

0.07

0.10

Petten**

8

0.15

0.17

0.19

0.57

0.45

0.53

0.55

0.15

0.23

0.15

0.13

0.15

Wallingford*

49

0.07

0.07

0.10

0.29

0.11

0.13

0.13

0.08

0.07

0.07

0.07

0.06

Katsardi*

5

0.10

0.10

0.11

0.40

0.19

0.26

0.27

0.10

0.03

0.11

0.11

0.10

Jensen*

45

0.21

0.21

0.37

0.30

0.11

0.14

0.14

0.27

0.21

0.24

0.260.26

AZG**

3

0.16

0.15

0.10

0.58

0.47

0.53

0.55

0.10

0.24

0.15

0.14

0.20

Lakes**

50.16

0.17

0.08

0.64

0.66

0.71

0.71

0.10

0.27

0.02

0.02

0.11

Guam**

4

0.38

0.29

0.52

0.79

0.41

0.45

0.48

0.56

0.47

0.39

0.29

0.44

Haringvliet**

3

0.16

0.16

0.35

0.51

0.32

0.56

0.60

0.19

0.11

0.20

0.21

0.13

slopes

111

0.09

0.12

0.16

0.35

0.19

0.27

0.32

0.10

0.12

0.11

0.10

0.10

horizontal

114

0.18

0.16

0.23

0.50

0.32

0.40

0.410.20

0.20

0.17

0.16

0.18

laboratory*

202

0.09

0.11

0.17

0.32

0.14

0.20

0.24

0.11

0.10

0.12

0.12

0.11

field**

23

0.20

0.19

0.25

0.62

0.46

0.55

0.58

0.22

0.27

0.18

0.16

0.20

overall

225

0.13

0.14

0.20

0.43

0.26

0.33

0.37

0.15

0.16

0.14

0.13

0.14

# 1-7

# 8-12

Horizontal

Figure 4. The evolution of the spectrum (stations 1, 2, 5 and 7 in the upper panel),computed with the LTA (Eldeberky, 1996), DCTA (Booij et al., 2009) and SPB (BecqGirard et al., 1999) and Toledo and Agnon (2012) triad source terms over a 1:30 flatbed, compared with the spectra observed by Smith (2004). Note that the vertical scale issuch that a k 4/3 tail, as observed in the surf zone, would appear as a horizontal line.

Unstructured grids
For many coastal applications the use of unstructured grids provides
a huge modeling flexibility to have high resolution where needed.
Mesh spacings are varied within the application domain using asingle, unstructured mesh. This approach is economical, but it cancause accuracy errors in regions where the bathymetry is underresolved. In particular, excessive directional turning can occur oncoarsely-resolved mesh. CFL-limiters have been proposed for thespectral propagation velocities in SWAN (Dietrich et al., 2012b).
These limiters are not required for model stability, but they improveaccuracy by reducing local errors that would otherwise spreadthroughout the domain.

Averagess.i.< 0.10
BJ'78
= Battjes & Janssen [1978]
TG'83 = Thornton & Guza [1983]
Bald'98 = Baldock et al. [1998]
DDD'85 = Dally et al. [1985]
J&B'07= Janssen & Battjes [2007]

0.10<s.i.<0.20

0.20<s.i.<0.40

s.i.>0.40

0.73 = fixed in third-generation models
Mad'76= Madsen [1976]
Ting'01+ = Ting [2001, present authors]
T&M'02= Tajima & Madsen [2002]
S&Hol'85 = Sallenger & Holman [1985]
S&How'89 = Sallenger & Howd [1989]

Lipp'96+ = Lippmann et al. [1996, presentauthors]
FA'12= Filipot & Ardhuin [2012]
vdW'09= van der Westhuysen [2009]
Rue'03= Ruessink et al. [2003]
R&S'03/'07 = Rattanapitikon et al. [2003]+ Rattanapitikon [2007]

Figure 2. Scatter index of the 12 models based on 13 data sets containing 225 cases oflaboratory observations (*) and field observations (**). The highlight colors indicate thetwo ranges of performance (green and blank) and four ranges of scatter index (fromblank to orange).

SWAN-ADCIRC coupling
At present, coupling spectral wave models with circulation models isfeasible and is of vital importance for (wave) climate studies and realtime forecasting of waves and storm surge. The tightly-coupled
SWAN-ADCIRC model has become a mature tool for realistic highresolution wave-current predictions in basin scale and inlet scale
systems. The combined codes use identical grids and are highly
scalable on petascale computers (Dietrich et al., 2012a). At DelftUniversity we shall apply this model to the North Sea and Dutch
Wadden Sea under extreme storm conditions for the near future. An
example is depicted in Figure 5.

Future developments
In the framework of the NOPP project (Tolman et al., 2013) new
parameterizations were developed for the source terms. Deep water
source terms have been implemented in the WaveWatch III model,
whereas shallow water source terms have been utilized in SWAN.
Progress will be made to implement the new source terms ofWaveWatch III in SWAN to enhance consistency between thesemodels. Additional developments are related to the efficient andaccurate computation of quadruplets using the GMD (Tolman, 2013)
and the drag coefficient for very short fetches and under extreme
wind speeds (U10 > 30 m/s). In the near future, the SWAN model will
be extended with a spectral partitioning scheme to enable wave field
tracking in large ocean basins to help synoptic wave forecasters.
References
Becq-Girard, F., P. Forget and M. Benoit (1999). Non-linear propagation of unidirectional wave
fields over varying topography, Coastal Engineering, 38, 91-113.
Booij, N., L. H. Holthuijsen and M. Benit (2009). A distributed colinear triad approximation inSWAN, Proc. Conf. Coastal Dynamics 2009.
Dietrich, J.C., S. Tanaka, J.J. Westerink, C.N. Dawson, R.A. Luettich, M. Zijlema, L.H. Holthuijsen,
J.M. Smith, L.G. Westerink and H.J. Westerink (2012a). Performance of the unstructured-mesh,
SWAN+ADCIRC model in computing hurricane waves and surge, Journal of Scientific
Computing, 52, 468-497.
Dietrich, J.C., M. Zijlema, P.-E. Allier, L.H. Holthuijsen, N. Booij, J.D. Meixner, J.K. Proft, C.N.
Dawson, C.J. Bender, A. Naimaster, J.M. Smith and J.J. Westerink (2012b). Limiters for spectral
propagation velocities in SWAN, Ocean Modelling, 70, 85-102.
Eldeberky, Y. (1996). Nonlinear transformation of wave spectra in the nearshore zone, Ph.D.
thesis, Delft University of Technology, The Netherlands.
Rijnsdorp, D.P. and M. Zijlema (2013). Numerical modelling of interactions between nonhydrostatic free-surface flows and a non-moving floating body, Proceedings of 2013 IAHR WorldCongress.
Rogers, W.E., P.A. Hwang and D.W. Wang (2003). Investigation of wave growth and decay in
the SWAN model: three regional-scale applications, J. Physical Oceanography, 33, 366-389.
Smith, J.M. (2004). Shallow-water spectral shapes, 29th Int. Conf. Coast. Engng, 206-217.
Suzuki, T., M. Zijlema, B. Burger, M.C. Meijer and S. Narayan (2012). Wave dissipation byvegetation with layer schematization in SWAN, Coastal Engineering, 59, 64-71.
Toledo, Y. and Y. Agnon (2012). Stochastic evolution equations with localized nonlinear
shoaling coefficients, European Journal of Mechanics B-Fluids, 34, 13-18.
Tolman, H.L. (2013) A Generalized Multiple Discrete Interaction Approximation for resonant
four-wave nonlinear interactions in wind wave models with arbitrary depth. Ocean Modelling,70, 11-24.
Tolman, H.L., M.L. Banner and J.M. Kaihatu (2013). The NOPP operational wave model
improvement project , Ocean Modelling, 70, 2-10.
Wu, J. (1982). Wind-stress coefficients over sea surface from breeze to hurricane, Journal ofGeophysical Research, 87, C12, 9704-9706 .
Zijlema, M., G.S. Stelling and P.B. Smit (2011). SWASH: An operational public domain code forsimulating wave fields and rapidly varied flows in coastal waters, Coastal Engineering, 58, 9921012.
Zijlema, M., G.Ph. van Vledder and L.H. Holthuijsen (2012). Bottom friction and wind drag forspectral wave models, Coastal Engineering, 65, 19-26.

Acknowledgements: The authors would like to thank the Office of Naval Research for their support research grants N00014-10-1-0453 and N00014-12-1-0534. Also support from Rijkswaterstaat and Deltares is greatly acknowledged.