Application of UnSWAN for wave hindcasting

in the Dutch Wadden Sea

Marcel Zijlema‡

Environmental Fluid Mechanics Section

Faculty of Civil Engineering and Geosciences

Delft University of Technology

P.O. Box 5048

2600 GA Delft, The Netherlands

1 Introduction

While spectral wave models (WAM, WAVE-WATCH III and SWAN) mainly focus on large-scale wind-wave and wave-wave interactions, wavefeatures on small scale associated with irregularbathymetry, e.g. surf breaking, triad and wave-current interactions, are critical to understandingwave dynamics and assessing impacts of engineer-ing activities. This is particularly important in thesurf zones. An example is a tidal inlet, which is thefocus of the present paper.

The Dutch Wadden Sea in the northern part ofthe Netherlands is a tidal inlet system that ispartly sheltered from the North Sea by islands;see Fig. 1. Waves entering a tidal inlet from theopen sea and subsequently propagating over tidalshoals vary substantially in length scales. In addi-tion, the Wadden Sea is a particularly challengingarea due to its complex bathymetry and the occur-rence of many physical processes, such as depth-induced wave breaking, local wave generation andwave-current interaction. All these processes canbe characterised as spectral evolution of the windwaves and swells.

Although the quality of the wave height predic-tion in a tidal inlet is quite good, the predictionof the wave periods and of the spectra is gener-ally poor. As a result, the SBW (Strength andLoads on Water Defenses) project is being carriedout for the Dutch goverment (Groeneweg et al.,2009; Van Vledder et al., 2009). In Groeneweg etal. (2009), recently obtained measured data havebeen used in extensive hindcasts of the tidal in-let of the island Ameland in the Wadden Sea for

‡E-mail: m.zijlema@tudelft.nl

a variety of storms. These hindcasts were carriedout using SWAN (Booij et al., 1999) and provideduseful insight in the performance of SWAN and inthe relevant processes in the Wadden Sea. For in-stance, the penetration of low-frequency wave en-ergy over the ebb-tidal delta appears to be sig-nificantly underestimated, whereas the computedwave heights in the shallow interior with a nearlyhorizontal bathymetry are too low compared to themeasured ones. Therefore, there is a strong needfor accurate and efficient spectral wave simulationsto better understand and analyse the interactionsbetween wind, waves and currents in tidal inlets.

2 Use of unstructured grids in

terascale environment

The SWAN simulations of Groeneweg et al. (2009)were performed on two curvi-linear grids. The firstis a coarse grid covering a large part of the WaddenSea. The second grid is a detailed one covering thetidal inlet of Ameland and was obtained from refin-ing a part of the larger grid. The resolution in thisinlet is about 30 to 50m. See Fig. 2. As reportedin Van Vledder et al. (2009), the resulted detailedgrid is not optimal, as it is still unnecessarily finein some areas in the computational domain. Off-shore wave boundary conditions for the fine gridwere obtained from the coarse grid computationcombined with some measured spectra; see Fig. 2.This amounts to the application of an interpola-tion procedure from coarse to fine grids. Althoughinterpolation is not conceptually difficult, it is adisadvantage because it is costly to perform. Thenested mesh is also detrimental because it intro-duces additional boundaries. Problems often occur

1

Figure 1: Map of the Dutch Wadden Sea located in the north of the Netherlands, with the inlet ofAmeland (source: Google Maps).

Figure 2: Curvi-linear grid (every fourth grid cell is shown) and outline of the detailed grid, coveringthe tidal inlet of Ameland (courtesy of Deltares, The Netherlands). The triangles indicate the locationswhere boundary conditions are imposed, the circles some buoy locations.

2

near model boundaries, due to mismatches in nu-merics and/or physics. Different accuracy proper-ties or abruptly local changes in physics can makeit difficult to apply the solution from one (coarse)grid as a boundary condition in another (fine) grid.

This static, one-way nested refinement approach isan example of a classic trade-off that is experiencedin coastal environmental problems. Better physicsrequire better resolution, but that resolution canbe costly. Hence, one must choose a level of reso-lution that captures the important physics withoutsacrificing computational efficiency.

Unstructured meshes with variable resolution pro-vide the capability to simultaneously capture scalesranging many orders of magnitude, e.g. from hun-dreds of kilometers to tens of meters. These meshesconcentrate computational effort where it is mostneeded. Moreover, they offer a very large geomet-rical flexibility. The application of unstructuredgrids to the study of wave dynamics in oceanic andcoastal areas is a new and powerful technique. Fora structured-grid wave model to yield results of thesame accuracy, there is no doubt that the compu-tational cost would be much higher.

Recently, an unstructured-mesh version of SWANhas been developed, called UnSWAN (Zijlema,2009). UnSWAN maintains the structured-gridSWAN versions feature of being unconditionallystable. This is accomplished through the im-plementation of the unstructured-mesh analog tothe four-direction Gauss-Seidel iteration techniquethat is employed in the structured-grid version.The UnSWAN model orders the mesh vertices insuch a way that it can sweep through them and up-date the action density using updated informationfrom neighboring vertices. It then sweeps throughthe mesh in opposite directions until the wave en-ergy has propagated sufficiently through geograph-ical space. Thus, this model retains the physics andnumerics and the code structure of the structured-grid SWAN model, but is able to run on unstruc-tured meshes. UnSWAN has been verified andvalidated through its application in many bench-mark cases of the so-called ONR testbed (Ris etal., 2002).

In order to efficiently carry out high-resolution sim-ulations with UnSWAN, a parallel code is buildusing message passing paradigm and tested ona commodity computer cluster. In parallelizingUnSWAN, we employ the same paradigms for high-performance computing as applied in the circula-tion model ADCIRC (Westerink et al., 2008). Inthis way, UnSWAN takes advantage of the same

scalability as ADCIRC, which remains efficient tothousands of computational processors.

Gains in efficiency create opportunities for rapidbenefits in accuracy. Thus, once the set up of themodel for the Wadden Sea has proven to be effi-cient and scalable, the next step will be verifica-tion. We will need to learn how best to employ theparameterizations for the source terms to simulatestorm waves. Finally, when we are confident thatthe model is running efficiently and correctly, thenwe can proceed to validation studies. The workpresented here builds on the study of Groeneweget al. (2009) and seeks to achieve higher accuracy.

3 Model set up

This section presents the set up of the model, in-cluding the optimal mesh, the storm instants stud-ied, the hydrodynamic and boundary conditionsand the SWAN source term settings.

3.1 Mesh

The first ingredient of the numerical calculationsis the design of the unstructured mesh. The tidalinlet and the inner-tidal area require a fine meshwhereas in the open sea in the north a coarse gridis sufficient. This highly variable resolution is re-flected by a typically sudden and large change inwave height due to surf breaking on the ebb-tidaldelta and regeneration by wind over the inner shoalsin front of the mainland. We use the BatTri pack-age (Bilgili and Smith, 2003) to generate the ap-propriate mesh for the present simulations. Thisfinal mesh is depicted in Fig. 3. The mesh is madeup of triangles only. As a result, the finest grid res-olution is about 15m in between the islands Ter-schelling (left) and Ameland (right) whereas thecoarsest part is about 1,000m. The total numberof mesh nodes is 140,703 with many of them lo-cated in the tidal inlet and behind the islands.

In order to take advantage of parallel computing,the global mesh is partitioned into local meshes at-tributed to each of the processors of a distributed-memory machine. For this, the METIS domain-decomposition algorithm has been applied (Karypisand Kumar, 1998). An example of the partitionof the mesh on 16 processors is shown in Fig. 3.The local meshes are shown in separate colors, andthe processors communicate via the so-called halolayer of overlapping cells that connect these localmeshes. The parallel implementation of UnSWANrequires communication only at the nodes of thehalo layer along the boundaries of the local meshes.

3

Figure 3: Load-balanced partitioned unstructured mesh of 279,845 triangles of sizes comprized between15m and 1km.

Figure 4: Measured speedups of parallel, unstructured SWAN for the Wadden Sea case on Huygensmachine.

4

The mesh partitioning is designed to uniformly dis-tribute the computational load, i.e. local mesheswith a similar number of nodes, and minimise thecommunications. Note how the local meshes de-crease in geographical area as their average meshsize is decreased.

The speedup is defined as the ratio of the comput-ing time for the model running on one processor tothe time needed to carry out a run on several pro-cessors. With the obtained partition, the speedupis equal to or larger than the number of processors,as illustrated in Fig. 4.

3.2 Selection of storm instants

Three severe westerly storms (wind speeds of 8 to24ms−1) were observed in the inlet of Amelandduring the 2006-2007 winter storm season, namelyon 11-12 January 2007, 18-19 January 2007 and18-19 March 2007. During these events, two ar-rays of wave buoys were located along transectsthrough the tidal inlet, starting seaward of the ebb-tidal delta and ending well into the shallow inte-rior. The eastern transect follows the main channel(buoys AZB12-AZB62), whereas the western tran-sect crosses the tidal flats (buoys AZB11-AZB61);see Fig. 5.

The travel time of the waves through the consid-ered model area is small compared to the time scaleof atmospheric and hydrodynamic conditions, sothe simulations were carried out in the stationarymode. A selection of 5 representative time instantswas made, around the peak of the storms: 1) Jan-uary 11, 13h00 (local time), 2) January 11, 22h40,3) January 18, 14h00, 4) March 18, 10h00 and 5)March 18, 14h40. These cases feature high windspeeds (on average 20ms−1) and very small depthsin the Wadden Sea interior (on average 2m). Thewind directions of the selected instants remain inthe directional sector 230o

−280o (Nautical conven-tion). The selected cases provide the opportunityto study both penetration of the North Sea wavesin the tidal inlet of Ameland and finite depth wavegrowth over the shallow Wadden Sea interior.

3.3 Bathymetry, water level, current

and wind

The bathymetry (Fig. 5) was obtained from de-tailed measured bathymetric information and in-terpolated to the employed computational grid.

For each of the selected storm instants, water leveland current fields were computed with a circulation

model that includes tidal, wind and wave forcing;for details, see Groeneweg et al. (2009). These out-puts are interpolated on the unstructured mesh aswell.

Spatially uniform winds were applied over the modeldomain, computed as the average of the wind ob-servations at three stations HBG, TSW and LWOin the Wadden Sea region (Fig. 5).

3.4 Boundary forcing

As westerly wind prevailed over the Wadden Searegion, the wave energy spectrum measured at theoffshore station ELD (located west of Wadden Seain the North Sea) is imposed at the offshore bound-ary running along west and north side of the modeldomain.

3.5 Source term settings

In default mode, UnSWAN uses the wind input andwhitecapping expressions of Komen et al. (1984),with wind input based on Snyder et al. (1981)and whitecapping based on Hasselmann (1974), to-gether with the Discrete Interaction Approxima-tion (DIA) for quadruplet nonlinear interactions(Hasselmann et al., 1985). Concerning the shallowsource terms, the so-called LTA approach of El-deberky (1996) for modelling triad wave-wave in-teraction is employed, depth-induced breaking ismodelled according to Battjes and Janssen (1978)and bottom friction is based on the JONSWAP for-mulation (Hasselmann et al., 1973).

It is well-known that physical processes in spectralwave models have definite limitations. Rogers etal. (2003) and Van der Westhuysen et al. (2007)pointed out a number of deficiencies of some sourceterms of SWAN in simulating wind-sea and swellsin ocean and coastal regions. Overall, the waveheight is well reproduced by SWAN, but the waveperiods, e.g. Tm01 and Tm02, are consistently un-derestimated. Moreover, SWAN wave spectra showsignificant deviations from the observed ones.

The use of mean wave number in the default white-capping formulation of Hasselmann (1974) oftenresults in too high and too low dissipation ratesat the lower and higher frequencies, respectively.Consequently, the spectrum is underestimated atthe lower frequencies and overestimated at the high-er frequencies. This explains the consistent un-derestimation of the wave periods. Rogers et al.(2003) altered the weight of the relative wave num-ber in the default whitecapping formulation, suchthat the lower frequencies are more evolved, i.e.

5

less dissipation rates at those frequencies, and thehigher frequencies are less overestimated. Theyreported significantly better reproduction of thewave periods.

Alternatively, Van der Westhuysen et al. (2007)proposed a saturation-based whitecapping expres-sion based on that of Alves and Banner (2003) inconjunction with a wind input term based on thatof Yan (1987). It is demonstrated that this alterna-tive setting yields improved agreement with fetch-and depth-limited growth curves. Also, contraryto the model of Komen et al. (1984), it correctlypredicts the wind-sea part of the spectrum undercombined swell-sea conditions.

The simulations of Groeneweg et al. (2009) wereconducted using the physical settings of Van derWesthuysen et al. (2007) and the DIA for quadru-plets. The shallow water source terms have beenapplied with their default formulations and the cor-responding parameter values: bottom friction withcoefficient Cb = 0.067m2s−3, surf breaking withbreaker index γBJ = 0.73, and triad interactionswith coefficient αEB = 0.05. In the present study,these settings are regarded as default.

4 Revision of source term set-

tings

Groeneweg et al. (2009) have indicated three mainobserved inaccuracies in their SWAN hindcasts,two of which will be discussed in the present paper,namely, 1) inaccurate estimation of low-frequencywind-generated wave components in the region ofthe ebb-tidal delta and 2) underestimation of waveheights and periods under finite depth wave growthconditions in the near-horizontal Wadden Sea in-terior.

Possible sources of inaccuracies and alternative pa-rameterizations found in the literature for improv-ing the model skill will be discussed in the next twosections. This is followed by summarizing the op-timal model settings. No attempt has been madein this study to carry out a calibration process.

4.1 Penetration of North Sea waves

It was shown that most North Sea waves do notpenetrate to the main coast in tidal inlets but dopenetrate in the more exposed areas. Moreover, itappears that SWAN underestimates the amountof low-frequency peak energy of wind-generatedwaves that penetrates to the mainland coast. Groe-

neweg et al. (2009) suggest that this is due to theapplication of only linear refraction as a propaga-tion mechanism predicting most of the wave energyis trapped on the tidal flats, whereas a small frac-tion of the energy is propagated across the maintidal channel. However, we believe that the ori-gin of the observed underestimation of the low-frequency wind-sea peak on the ebb-tidal delta can-not be associated with any propagation phenomenonand that the cause must be sought in the SWANsource term settings. Sensitivity analysis showedthat the source term of bottom friction has a sig-nificant effect on the primary peak of the spectrum.

The default JONSWAP formulation of Hasselmannet al. (1973) models energy dissipation by bot-tom friction using a tunable friction parameter Cb.Hasselmann et al. (1973) found Cb = 0.038m2s−3

which is in agreement with the JONSWAP resultfor swell dissipation. However, Bouws and Komen(1983) suggest a value of Cb = 0.067m2s−3 fordepth-limited wind-sea conditions in the North Sea.This value is derived from revisiting the energy bal-ance equation employing an alternative deep waterdissipation deviated from the one used in SWAN.Since this is the default value used in SWAN, itbecomes questionable.

Generally, short waves are much less affected bythe bottom friction than long waves. So, it isexpected that bottom friction dissipates most ofthe energy at relative low frequencies. In this pa-per, we reuse Cb = 0.038m2s−3 which is foundto be appropriate for swell conditions. We as-sume, however, that this might also be the casefor relative low frequencies in the wind-sea spec-trum as well. Hence, we believe that the defaultSWAN value Cb = 0.067m2s−3 is erroneous andwill dissipate too much energy at the lower frequen-cies. Lowering the value of Cb (from 0.067m2s−3

to 0.038m2s−3) will dissipate less energy at relativelow frequencies in both swell and wind-sea parts.

4.2 Finite-depth wave growth

Because of the dominance of locally generated wavesin the Wadden Sea interior, the inaccuracy of finitedepth wave growth in SWAN affects the reliabilityof computed wave conditions along the mainlandcoast of the Netherlands. This inaccuracy can beexpressed as a systematic underestimation of thedimensionless ratio Hm0/d, with Hm0 the signif-icant wave height and d the local water depth.The default setting of the source term for depth-induced breaking in SWAN is found to be strongin finite depth growth situations (Groeneweg et al.,

6

2009; Van der Westhuysen, 2009).

The depth-induced breaking expression of Battjesand Janssen (1978) developed for surf zones andused in SWAN, has proved to be successful in awide range of situations. Usually, this formulationis studied for the case of waves from deep waterbreaking on a beach. However, its role in finitedepth wave growth has received relatively little at-tention (Van der Westhuysen, 2009). The maincalibration parameter in the formulation of Battjesand Janssen (1978) is the breaker index γBJ. Sev-eral studies proposed dependencies of γBJ on somelocal wave characteristics. For example, Ruessinket al. (2003) proposed a dependency of γBJ onthe dimensionless depth kp d, where kp is the peakwave number of the wave spectrum,

γBJ = 0.76 kp d + 0.29 . (1)

This breaker index parameterization is derived forsloping bed surf zones situations. However, Vander Westhuysen (2009) shows that this parameter-ization also yields optimal values of γBJ for finitedepth wave growth over near-horizontal bottoms,including those found in the Wadden Sea interior.

Given the promising results of the Ruessink et al.(2003) parameterization found in the aformentionedstudy, this formulation is considered suitable forpractical application in its present form and willbe employed in the present study.

4.3 Optimal model settings

Based on the considerations as outlined in the pre-vious sections, the obtained optimal model set-tings, to be applied in the present study, are givenas follows.

• For the effect of growth and decay of wave en-ergy, the default formulations of Komen et al.(1984) with the modified whitecapping expres-sion of Rogers et al. (2003), so-called n2.0 set-ting, are adopted. This setting will eliminateproblems associated with non-physical depen-dence of the whitecapping term on mean wavenumber.

• Four-wave interactions are modelled using theDIA approach of Hasselmann et al. (1985).

• Bottom friction is specified using the JON-SWAP formulation with friction parameterCb = 0.038m2s−3, thus enhancing the predic-tive ability with respect to the low-frequencypart of the wind-sea spectrum.

• The breaker index parameterization of Ruessinket al. (2003) is employed as it will improve fi-nite depth results with Battjes and Janssen(1978) surf breaking significantly.

• The triad wave-wave interaction is omitted fortwo reasons. Firstly, it is well-known that theLTA approach leads to a significant overesti-mation of the energy transfer to super-harmonicfrequencies, and consequently to a consider-able underestimation of the energy level at theprimary peak. Secondly, based on an analy-sis with a newly developed three-wave inter-action approximation (Holthuijsen, 2009, pri-vate communication), there is an indicationthat this physical process has a relative mi-nor contribution to the wave dynamics in theshallow parts of the Wadden Sea region.

5 Validation and performance

The simulations for the selected instants were car-ried out by applying the default source term set-tings as employed in the hindcast study of Groe-neweg et al. (2009) and given in Section 3.5. Thiswas repeated for the optimal model settings asgiven in Section 4.3. The frequencies ranged from0.03Hz to 1.0Hz and are distributed on a logarith-mic scale into 37 bins, while the directions are di-vided into 36 sectors of each 10o. The stationarysimulations are solved iteratively and the conver-gence criteria are based on the so-called curvature-based criteria proposed by Zijlema and Van derWesthuysen (2005). All the simulations were per-formed using 128 processors on an IBM Power6cluster (max. 60 Teraflops), Huygens, a new Dutchnational supercomputer at the supercomputing cen-ter SARA at Amsterdam. Each simulation con-sumes roughly 5 minutes wall-clock time.

Computed frequency spectra were compared againstmeasurements at all buoy locations. The effect ofboth default and optimal model settings on spec-tra were evaluated. Some of these results are high-lighted in this paper. Fig. 6 displays a comparisonbetween the predicted and measured wave spectraat buoys AZB21 (Jan. 11, 13h00), AZB31 (Jan.11, 13h00 and Mar. 18, 10h00) and AZB32 (Mar.18, 10h00). These buoys are located on the ebb-tidal delta. The systematic underprediction of thewave energy at the primary peak by the defaultmodel settings can clearly be observed. This isalso reported by Groeneweg et al. (2009). Further-more, by employing the optimal model settings,the spectra at the lower frequencies are better re-produced. In particular, the energy around the

7

Figure 5: Bathymetry and the locations of the wave buoys in the tidal inlet of Ameland (courtesy ofDeltares, The Netherlands).

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

1.2

E(f

) (m

2 /Hz)

AZB21 (Jan. 11, 13h00)

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

1

1.2AZB31 (Jan. 11, 13h00)

0 0.2 0.4 0.60

1

2

3

4

f (Hz)

E(f

) (m

2 /Hz)

AZB31 (Mar. 18, 10h00)

observeddefault settingsoptimal settings

0 0.2 0.4 0.60

0.5

1

1.5

2

f (Hz)

AZB32 (Mar. 18, 10h00)

Figure 6: Comparison of simulated and measured spectra at some buoy locations on ebb-tidal delta ofAmeland.

8

lowest peak frequency is significantly improved. Sen-sitivity analysis showed that this is mainly due tothe application of the lowered friction parameterCb in the JONSWAP formulation. Note the varia-tion in scale for the two time instants showed (Jan.11, 13h00 and Mar. 18, 10h00) at location AZB31.

The predictive skill of the source term settings dis-cussed here was determined by measuring the biasand the scatter index SI. These are given by

bias =1

N

N∑

i=1

(

φicomp − φi

obs

)

(2)

and

SI =

√

1N

∑N

i=1

(

φicomp − φi

obs

)2

1N

∑N

i=1 φiobs

(3)

where φobs is the observed wave parameter, φcomp

is the corresponding value computed by UnSWANand N is the total number of data points in agiven data set. These statistical measures were de-termined for the significant wave height Hm0, thepeak period Tp and the spectral periods Tm−10,Tm01 and Tm02, and were computed for all consid-ered storm instants and available data. The scatterplots and statistical scores are presented in Figs. 7and 8.

Clearly, the periods computed by the default modelsettings are systematically lower than the measuredvalues. By contrast, almost no hindcast bias wascomputed with the optimal model settings for waveperiods (Fig. 8). This can be explained to a largeextent by the fact that the spectra located at buoysin ebb-tidal delta have relatively more grown atthe lower frequencies than at the higher frequen-cies. As seen earlier, this is a consequence of theuse of the lowered parameter Cb in the formulationfor bottom friction. Both figures also reveal thatUnSWAN predicted the wave height very well, nomatter what model options were employed.

The scatter indices computed by the optimal set-tings for Tp, Tm01 and Tm02 are slightly larger thanthose computed by the default ones. However, theopposite is observed for the period Tm−10. On theother hand, there is no difference in the scatter in-dex computed by both employed model settings forthe wave height. Hence, we may conclude that thereliability of the optimal settings used for the pre-diction of wave height and periods is very similarto that of default options. In so far, the statisticalscores clearly justify the superiority of applicationof the optimal model settings for the prediction ofwave height and periods.

The statistical results for the wave height presentedabove suggest no improvement of the model out-comes regardless of the model options used. Con-cerning the finite depth wave growth in the Wad-den Sea interior, the buoys AZB41, AZB51, AZB61and AZB62 were considered separately. Fig. 9 com-pares the scatter plot results between model andobservations for this subset obtained with the de-fault and optimal model settings, respectively. Itcan be seen that the optimal model options yielda significant improvement in Hm0/d ratio over thedefault ones. Accordingly, the Battjes and Janssensurf breaking source term with the breaker indexof Ruessink et al. (2003) improves the predictionof wave heights over nearly horizontal beds. Thisis also reflected in the wave spectrum as demon-strated in Fig. 10, showing the computed and mea-sured spectra at locations AZB61 (Jan. 18, 14h00)and AZB62 (Jan. 11, 13h00).

6 Summary and conclusion

In this paper, we have presented the set-up, opti-mization and validation of a highly-resolved, un-structured-mesh SWAN (UnSWAN) model for theDutch Wadden Sea. Although the present workhas to be considered as a first attempt towards ahigh-resolution model of the Wadden Sea, it nowappears possible to broaden the range of scales sim-ulated by a single model.

Performance of UnSWAN was investigated usingthe wave measurements during three severe stormsof 2007 in the tidal inlet of Ameland. Using theoptimal model settings discussed in this paper,UnSWAN is skillful in predicting the variations ofwave height and periods in the tidal inlet, over theebb-tidal delta and over the shallow Wadden Seainterior.

Our experiences to date with simulating storm eventsin the Wadden Sea indicate that improvements inspectral wave modeling, including optimization ofthe UnSWAN source term settings, and in domaindefinition and mesh resolution, significantly increasesthe accuracy and reliability of SWAN. Moreover,high-performance computing with unstructuredmeshes opens the possibility to simulating stormsat unprecedented fidelity and gives rise to a num-ber of modeling challenges.

9

1 2 3 4 5

1

2

3

4

5bias = −0.032m, SI = 0.186

Hm0

(m) measured

Hm

0 (m

)

com

pute

d

4 6 8 10

4

6

8

10

bias = −0.37s, SI = 0.163

Tp (s) measured

Tp (

s)

com

pute

d

4 6 8

3

4

5

6

7

8

bias = −0.49s, SI = 0.147

Tm−1,0

(s) measured

Tm

−1,

0 (s)

com

pute

d2 4 6

2

3

4

5

6

7

bias = −0.46s, SI = 0.148

Tm0,1

(s) measured

Tm

0,1 (

s) c

ompu

ted

2 4 62

3

4

5

6

bias = −0.51s, SI = 0.167

Tm0,2

(s) measured

Tm

0,2 (

s) c

ompu

ted

Figure 7: Scatter plots of computed and observed wave parameters with default model settings.

1 2 3 4 5

1

2

3

4

5

bias = 0.032m, SI = 0.183

Hm0

(m) measured

Hm

0 (m

)

com

pute

d

4 6 8 10

4

6

8

10

bias = 0.012s, SI = 0.184

Tp (s) measured

Tp (

s)

com

pute

d

4 6 8

4

6

8

bias = −0.081s, SI = 0.12

Tm−1,0

(s) measured

Tm

−1,

0 (s)

com

pute

d

2 4 6 82

4

6

8bias = −0.048s, SI = 0.158

Tm0,1

(s) measured

Tm

0,1 (

s) c

ompu

ted

2 4 62

3

4

5

6

7

bias = −0.089s, SI = 0.176

Tm0,2

(s) measured

Tm

0,2 (

s) c

ompu

ted

Figure 8: Scatter plots of computed and observed wave parameters with optimal model settings.

10

0.2 0.3 0.4 0.50.2

0.25

0.3

0.35

0.4

0.45

0.5bias = −0.048, SI = 0.155

Hm0

/d (−) measured

Hm

0/d (

−)

SW

AN

(de

faul

t)

0.2 0.3 0.4 0.50.2

0.25

0.3

0.35

0.4

0.45

0.5bias = 0.012, SI = 0.100

Hm0

/d (−) measured

Hm

0/d (

−)

SW

AN

(op

timal

)

Figure 9: Scatter plots of computed and observed Hm0/d ratio at locations AZB41, AZB51, AZB61 andAZB62 with default (left panel) and optimal (right panel) model settings.

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

f (Hz)

E(f

) (m

2 /Hz)

AZB61 (Jan. 18, 14h00)

observed defaultoptimal

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

f (Hz)

AZB62 (Jan. 11, 13h00)

Figure 10: Comparison of simulated and measured spectra at locations AZB61 and AZB62 on tidal flats.

11

Acknowledgements

Part of this work was sponsored by the NationalComputing Facilities Foundation (NCF) for the useof supercomputer facilities, with financial supportfrom the Netherlands Organization for ScientificResearch (NWO). Gerbrant van Vledder, Andrevan der Westhuysen, Ivo Wenneker and Jacco Groe-neweg are acknowledged for their input.

References

Alves, J.H.G.M. and M.L. Banner, 2003: Perfor-mance of a saturation-based dissipation-rate sourceterm in modelling the fetch-limited evolution ofwind waves. Journal of Physical Oceanography,33, 1274–1298.

Battjes, J.A. and J.P.F.M. Janssen, 1978: Energyloss and set-up due to breaking of random waves.Proceedings 16th International Conference on Coast-

al Engineering, pp. 569–587.

Bilgili, A. and K.W. Smith, 2003: BatTri: a 2-D finite element grid generator, version 11.11.03.Available from: <http://www-nml.dartmouth.edu/Publications/internal reports/NML-03-15/>.

Booij, N., R.C. Ris and L.H. Holthuijsen, 1999: Athird-generation wave model for coastal regions, 1.Model description and validation. Journal of Geo-

physical Research, 104, C4, 7649–7666.

Bouws, E. and G.J. Komen, 1983: On the bal-ance between growth and dissipation in an extremedepth-limited wind-sea in the southern North Sea.Journal of Physical Oceanography, 13, 1653–1658.

Eldeberky, Y., 1996: Nonlinear transformation ofwave spectra in the nearshore zone. Ph.D. thesis,Delft University of Technology, Delft, The Nether-lands.

Groeneweg, J., A. van der Westhuysen, G. vanVledder, S. Jacobse, J. Lansen and A. van Don-geren, 2009: Wave modelling in a tidal inlet: per-formance of SWAN in the Wadden Sea. Proceed-

ings 31th International Conference on Coastal En-

gineering, pp. 411–423.

Hasselmann, K., T.P. Barnett, E. Bouws, H. Carl-son, D.E. Cartwright, K. Enke, J.A. Ewing, H.Gienapp, D.E. Hasselmann, P. Kruseman, A. Meer-burg, O. Muller, D.J. Olbers, K. Richter, W. Selland H. Walden, 1973: Measurements of wind-wavegrowth and swell decay during the Joint North SeaWave Project (JONSWAP). Dtsch. Hydrogr. Z.,

Suppl. 12, A8, 95 pp.

Hasselmann, K., 1974: On the spectral dissipationof ocean waves due to white capping. Boundary-

Layer Meteorology, 6, 107–127.

Hasselmann, S., K. Hasselmann, J.H. Allender andT.P. Barnett, 1985: Computations and parameter-izations of the nonlinear energy transfer in a grav-ity wave spectrum. Part II: parameterizations ofthe nonlinear transfer for application in wave mod-els. Journal of Physical Oceanography, 15, 1378–1391.

Karypis, G. and V. Kumar, 1998: METIS: fam-ily of multilevel partitioning algorithms. Availablefrom: <http://glaros.dtc.umn.edu/gkhome/views/metis>.

Komen, G.J., S. Hasselmann and K. Hasselmann1984: On the existence of a fully developed wind-sea spectrum. Journal of Physical Oceanography,14, 1271–1285.

Ris, R.C., L.H. Holthuijsen, J.M. Smith, N. Booijand A.R. van Dongeren, 2002: The ONR TestBed for coastal and oceanic wave models. Pro-

ceedings 28th International Conference on Coastal

Engineering, pp. 380–391.

Rogers, W.E., P.A. Hwang and D.W. Wang, 2003:Investigation of wave growth and decay in the SWANmodel: three regional-scale applications. Journal

of Physical Oceanography, 33, 366–389.

Ruessink, B.G., D.J.R. Walstra and H.N. South-gate, 2003: Calibration and verification of a para-metric wave model on barred beaches. Coastal En-

gineering, 48, 139–149.

Snyder, R.L., F.W. Dobson, J.A. Elliott and R.B.Long, 1981: Array measurements of atmosphericpressure fluctuations above surface gravity waves.Journal of Fluid Mechanics, 102, 1–59.

Van Vledder, G.P., J. Groeneweg and A.J. van derWesthuysen, 2009: Numerical and physical aspectsof wave modelling in a tidal inlet. Proceedings 31th

International Conference on Coastal Engineering,pp. 424–436.

Van der Westhuysen, A.J., M. Zijlema and J.A.Battjes, 2007: Nonlinear saturation-based white-capping dissipation in SWAN for deep and shallowwater. Coastal Engineering, 54, 151–170.

Van der Westhuysen, A.J., 2009: Modelling of depth-induced wave breaking under finite-depth wave growth

12

conditions. Journal of Geophysical Research, in re-view.

Westerink, J.J., R.A. Luettich, J.C. Feyen, J.H.Atkinson, C. Dawson, H.J. Roberts, M.D. Pow-ell, J.P. Dunion, E.J. Kubatko and H. Pourtaheri,2008: A basin to channel scale unstructured gridhurricane storm surge model applied to SouthernLouisiana. Monthly Weather Review, 136, 833–864.

Yan, L., 1987: An improved wind input sourceterm for third generation ocean wave modelling.Rep. 87-8, Royal Dutch Meteor. Inst., 20 pp.

Zijlema, M. and A.J. van der Westhuysen, 2005:On convergence behaviour and numerical accuracyin stationary SWAN simulations of nearshore windwave spectra. Coastal Engineering, 52, 237–256.

Zijlema, M., 2009: Parallel, unstructured mesh im-plementation for SWAN. Proceedings 31th Inter-

national Conference on Coastal Engineering, pp.470–482.

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