Effects of the deep-water wave breaking dissipation on the wind-wave modelling in the Irish Sea

s 67 (2007) 59–72www.elsevier.com/locate/jmarsys

Journal of Marine System

Effects of the deep-water wave breaking dissipation on thewind-wave modelling in the Irish Sea

Pedro Osuna, Alejandro J. Souza, Judith Wolf ⁎

Proudman Oceanographic Laboratory, Joseph Proudman building, 6 Brownlow Street, Liverpool L3 5DA, United Kigdom

Received 15 February 2006; received in revised form 20 July 2006; accepted 5 September 2006Available online 11 October 2006

Abstract

A numerical study of the effect of the deep-water wave breaking on the simulation of wind-waves in the Irish Sea region duringsome North Hemisphere winter months (January–February 2003) was carried out. A new formulation that takes into account thenonlinear effect of wave groups on the onset of wave breaking [Alves, J.H.G.M., Banner, M.L., 2003. Performance of a saturated-based dissipation-rate source term in modeling the fetch-limited evolution of wind waves. J. Phys. Oceanogr. 33, 1274–1298.] hasbeen implemented and tested in a third-generation wave model. Its effect is assessed against the standard WAM Cycle 4formulation and observations in the Irish Sea. The integrated spectral parameters computed by the new implementation of wavebreaking tend to be larger (between 10% and 15% for significant wave height and mean period) than those computed by thestandard formulation of WAM, especially on the eastern coast of the Irish Sea. It is found that, in the Liverpool Bay area, the onlypossibility for the waves to resuspend sediment is the occurrence of northwesterly wind conditions. In these situations fetch-limitedgrowth is observed and both standard and new implementations provide similar results. In the southern Irish Sea, stronger mixedsea-swell conditions are predicted by the new formulation, which may have an impact in the description of the areas susceptible tosediment resuspension.Crown Copyright © 2006 Published by Elsevier B.V. All rights reserved.

Keywords: Wind waves; Deep-water wave breaking; Model validation; Irish Sea

1. Introduction

Third-generation wave models are widely used forpredicting wave conditions in a number of complexsituations; from relatively low spatial resolution (on theorder of few tens of kilometers) to provide operationalforecasting, up to short-term, high spatial resolution

⁎ Corresponding author. Tel.: +44 151 7954849; fax: +44 1517954801.

E-mail address: [email protected] (J. Wolf).

0924-7963/$ - see front matter. Crown Copyright © 2006 Published by Elsdoi:10.1016/j.jmarsys.2006.09.003

hindcasting experiments designed to improve the physicsincluded in the models. The accuracy level of the latestgeneration of wave models provide a key role inatmospheric/oceanic forecast systems implemented in anumber of meteorological agencies (Bidlot et al., 2002;Tolman et al., 2002; Janssen, 2004).Although reliable, theoperational application of third-generation wave modelsstill depends on calibrations, approximations, and thequality of the measurements used for assimilation.Parameterizations of poorly understood physical process-es may lead to discrepancies between observations andmodel results, as concluded by Caires et al. (2004).

evier B.V. All rights reserved.

mailto:[email protected]

http://dx.doi.org/10.1016/j.jmarsys.2006.09.003

60 P. Osuna et al. / Journal of Marine Systems 67 (2007) 59–72

A number of studies (Banner and Young, 1994;Tolman and Chalikov, 1996; Alves and Banner, 2003)have shown that the main drawback of the third-gene-ration wave models is basically the inaccurate estimateof the energy source terms (e.g. wind input, non-linearinteraction, and whitecapping). Cumulative errors in theestimate of the energy balance in deep waters are usuallypropagated into coastal areas, which has an impact onthe evaluation of processes associated with the wavefield, like bed shear stresses and sediment resuspension.

The objective of the present study is to assess theeffect of a new formulation for the computation of thewhitecapping dissipation in the third-generation wavemodel WAM Cycle 4 (Komen et al., 1994) and its effecton the estimate of wave conditions on the continentalshelf. The assessment is based on the intercomparison ofmodel results and the comparative analysis of numericalresults and observations in the Irish Sea region. Thegeneral aim is to advance the development of the third-generation wave models as a tool for hindcasting andforecasting wave conditions in coastal waters.

The organization of the paper is as follows. A briefexplanation of the wave model and the terms included inthe different experiments is given in Section 2. Section 3provides a description of the model setups and themeasurements available for comparison with modelresults. Results of the numerical simulations and theircomparison with observations are described in Section4. Finally, the results are summarized and conclusionsare presented in Section 5.

2. Wave model description

The wave conditions were numerically simulatedusing the wave model WAM Cycle 4, modified in orderto allow its optimal implementation in coastal waters(Monbaliu et al., 2000, hereafter ProWAM). In WAM,the development of the wind-wave field is describedin terms of the evolution of the energy density wavespectrum, F (σ, θ), as a function of the relative angularfrequency σ (=2πf) and direction θ. The most generaldescription of the time-space evolution of the wavefield, in cartesian coordinates, reads

AFAt

þ A

AxðcxFÞ þ A

AyðcyFÞ þ A

AhðchFÞ

þrA

Arcr

Fr

� �¼ S;

ð1Þ

where cx,y,σ,θ are the components of the wave propaga-tion in (x, y, σ, θ) spaces. The function S includes theparameterizations of sources and sinks of energy in-

duced by wind, wave breaking, non-linear interactionbetween the different wave components in F (σ, θ), andbottom friction dissipation. A thorough description ofthe formulation on which each term is based is given inKomen et al. (1994).

2.1. Source terms

The formulation that describes the momentum transferfrom wind to waves, Sin, is based on the quasi-linearmodel for the sea surface boundary layer described byJanssen (1991). In this formulation, the input source termis given by

Sin ¼ gxF; ð2Þ

where ω is the absolute angular frequency and thefunction γ is a parameterization of the growth rate of thewaves that depends on the friction velocity and the waveage. In Janssen's formulation, it is assumed that the windprofile is logarithmic, with an effective roughness lengththat depends on the sea state. The effective roughnesslength is given as a Charnock-like expression, modified inorder to account for the development of the wave field. Adetailed account and discussion of this theory can befound in Janssen (2004).

During an early stage of development, the energytransferred from the atmosphere to the waves is quicklyredistributed to lower frequencies by means of non-linear interaction between wave components. This is animportant term in the evolution and stabilization of thespectral shape. The standard Cycle 4 of WAM includesan approximate solution of the Boltzman equation thatfulfills the requirement of energy, momentum and actionconservation; the Discrete Interaction Approximation,or DIA (Hasselmann and Hasselmann, 1985). The im-plementation of the DIA is extended to finite depthwaters using a scaling factor that depends on the dimen-sionless wave number bkN h, where bkN is the meanwavenumber and h is the water depth. Nowadays, it iswell known that the DIA approximation misrepresentssome of the main features of the exact non-linearinteraction solution. One of the main problems is itstendency to overestimate the interactions above thespectral peak, which results in higher energy levels (anddirectional broadening) in the equilibrium range (Tol-man and Chalikov, 1996). Although other strategies forimproving the accuracy of the non-linear interactionwithout compromising too much the computation timehave been developed (see Van Vledder, 2001), DIA isstill widely used in operational versions of third-gene-ration wave models.

61P. Osuna et al. / Journal of Marine Systems 67 (2007) 59–72

The description of deep water wave dissipation bybreaking is based on the quasi-linear model introduced byHasselmann (1974). The general expression for thisparameterization is described in Komen et al. (1994) as

Sds ¼ −CdsaaPM

� �m

ð1−1Þ kbkN

þ 1k

bkN

� �2" #n=2

bxNF;

ð3Þwhere k= |k| is the wavenumber, α=EtotbkN

2 is a meanwave steepness, Etot, is the total wave energy in thespectrum, and αPM=4.57×10−3 is the wave steepness ofthe Pierson-Moskowitz spectrum. In WAM Cycle 4,ffiffiffiffiffiffiffiffiffibkN

p ¼ RFðkÞdk= R FðkÞdk= ffiffiffi

kp

and bωN= ∫F(k)dk /∫F(k)dk /ω are used for the mean wavenumber and meanangular frequency, respectively. In Eq. (3), Cds, ς, m, andn are numerical coefficients that need to be determined.

In order to improve the solution of deep-water break-ing dissipation in the presence of combined sea and swellwave conditions, Bidlot et al. (2005) suggested a seriesof modifications to WAM Cycle 4. Those modificationshave to dowith new definitions of themean wavenumberð ffiffiffiffiffiffiffiffiffi

bkNp ¼ R ffiffiffi

kp

FðkÞdk=RFðkÞdkÞ and the mean fre-quency (bωN=

RωF(k)dk /

RF(k)dk), which give more

emphasis to the high-frequency part of the spectrum.There is also a new definition of the dynamic upper limitfor the prognostic frequency range that involves themean frequency of the wind sea only. A thoroughdescription and assessment of these modifications can befound in Bidlot et al. (2005).

Alves and Banner (2003) developed an alternativedescription of the whitecapping spectral dissipationbased on the assumption of a strong nonlinear depen-dency of the deep-water wave breaking on the wave-group dynamics. The breaking occurs when individualwaves reach a critical threshold amplitude. The ex-pression of Alves and Banner (2003) reads,

Sds ¼ −CdsðEtotk2pÞm

kbkN

� �n BðkÞBr

� �p=2bxNF; ð4Þ

where kp is the peak wavenumber, B(k)=k4F(k) is alocal saturation parameters, Br is a threshold saturationlevel, and Cds, m, n, and p are coefficients to bedetermined numerically. Note that Eq. (4), as opposed toEq. (3), shows a nonlinear dependency on the energyspectrum, which may have serious implications for thenumerical solution of the source terms, specificallyduring short-fetch conditions when high spatial resolu-tion (∼1.0 km) is used.

For the bottom friction dissipation, an expressionbased on the formulation of Madsen et al. (1988) is used.

Here, a spectral form of the dissipation is obtained aspart of the solution of the turbulent bottom boundarylayer flow induced for the waves. The model is based onthe linearized form of the boundary layer equation and asimple eddy viscosity formulation of shear stress. Thegeneral equation is given as

Sbf ¼ −Cbfk

sinh2khF ; Cbf ¼

ffiffiffi2

pfwhU2

b i1=2; ð5Þ

where ⟨Ub2⟩1/2 is the root-mean-square of the wave or-

bital velocity at the bottom, and fw is a non-dimensionalfriction factor computes as

fw ¼ 0:3 forAb

KNV1:57

1

4ffiffiffiffifw

p þ log101

4ffiffiffiffifw

p� �

¼ mf þ log10Ab

KN

� �for

Ab

KNN1:57;

ð6Þwhere mf is a constant (defined here as −0.08), Ab is thenear-bottom orbital excursion amplitude computed as afunction of the wave orbital velocity spectrum at thebottom, and KN is the equivalent Nikuradse roughnesslength (defined here as 0.02 m).

3. Model implementation

The ProWAM model was implemented for a domainthat comprises the whole North West European Conti-nental Shelf (CS3) from 48°7′N to 62°53′N and from11°50′W to 12°50′E, using a grid resolution of 1/9°latitude by 1/6° longitude (approximately 12 km). Openboundary conditions for the CS3 domain were obtainedfrom a coarser 1°×1° implementation of ProWAM for theNorth East Atlantic area, forced by six-hourly EuropeanCenter for Medium- Range Weather Forecast (ECMWF)ERA40 Re-analysis surface winds interpolated to a1.0°×1.0° regular latitude/longitude grid. For the CS3implementation, hourly resolution United KingdomMeteorological Office (UKMO) surface winds, with thesame spatial resolution as thewavemodel grid, were used.

Although the numerical simulation is carried out forthe whole North West European continental shelf, theanalysis in this study will be focused on the Irish Seaarea; from 51°N to 56°N and from 7°W to 3°W. Thesimulation was carried out for a two-month period,between January and February 2003.

3.1. Test cases

In this study, two different whitecapping formula-tions have been evaluated using three experiments: (a)

Fig. 1. Bathymetry in the Irish Sea domain. The position of measure-ments are indicated by the square (LivB) and the dot (AbpB). The blacktriangle indicates the position of on-land wind measurements. Depthcontours are drawn at 10, 20, 50, 100, and 150 m.


the standard solution implemented in the WAM Cycle 4model and described by Eq. (3) [hereafter referred asK94], (b) the standard solution implemented in WAMCycle 4 plus the modifications proposed by Bidlot et al.(2005) [hereafter referred as BJA05], and (c) theformulation proposed by Alves and Banner (2003)[hereafter referred as AB03]. The free parameters usedin each formulations are listed in Table 1.

It is worth noting that, for the implementation of theAB03 formulation, the definition of bωN, bkN, and theprognostic frequency range proposed in BJA05, are used.The coefficient values for K94 and BJA05 formulationsare those suggested in the original papers. The values usedfor AB03 formulation were obtained through calibrationof the wave model results against Kahma and Calkoen(1992) fetch-limited wave growth curves.

The spectral resolution used in all the cases was 25frequencies, with a logarithmical distribution between0.041772 Hz and 0.411447 Hz, and 24 directions.

3.2. Measurements

Directional waverider buoy information at LiverpoolBay (LivB station) for the analysis period were providedby the Centre for Environment Fisheries and AquacultureScience (CEFAS). These data, which include significantwave height (Hs), second moment (hereafter referred alsoas mean) and peak periods (Tz and Tp, respectively),mean direction of the peak (Wdp), mean wave spreading(Wsp), and sea surface temperature, are originally repor-ted every 30 min. Unfortunately, for the analysis periodthe quality of the data is not good and the time seriescontain many gaps. Hourly time series of Hs and Tz onlyfrom a moored buoy at Aberporth Bay (AbpB station)were also made available by the UKMO for the analysisperiod.

Table 1Free parameters for the different formulations of Swc

Formulation Parameters

K94 Cds=9.40×10−5

m=2n=2ς=0.5

BJA05 Cds=4.39×10−5

m=2n=2ς=0.6

AB03 Cds=5.75×10−3

m=1n=2p ¼ 2 1:0−tanh BðkÞ

Br

� �h i; BðkÞNBr

p ¼ 0 ; BðkÞVBrBr=2.5×10−3

The LivB data were complemented with ADCPobservations deployed near the buoy location within theframework of the Coastal Observatory program ofProudman Oceanographic Laboratory. The 600 kHzRDI ADCP, fitted with a pressure sensor, was mountedon a sea bed frame and setup to sample hourly bursts of17 min at 2 Hz. The wave parameters were computedfrom the directional wave spectra of a near-surfaceorbital velocity spatial array (Strong et al., 2000).

Between January and March 2003, a sea bed framefitted with Doppler instruments was also deployednearby the LivB station. The instruments, an ADCP andan ADV, were deployed to take measurements close tothe bottom in order to compute Reynolds stresses andsuspended particulate matter (Souza and Howarth,

Table 2Location and mean depth of the instruments where measurements weretaken

Latitude[North]

Longitude[West]

Depth Pressure[frombottom]

Currents[frombottom]

ADCP 53°31.991′ 3°21.352′ 28 m 0.65 m bins(1.0 m)

ADV 53°31.962′ 3°21.932′ 28 m 1.02 m 1.60 mBuoy

(LivB)53°39.150′ 3°21.036′ 22 m – –

Buoy(AbpB)

52°21.954′ 4°26.500′ 26 m – –


2005). The ADCP, a 1.2-MHz Workhorse RDI, wassetup to sample hourly bursts of 10 min at 1 Hz, with abin spacing of 0.5 m. The ADV, a 5-MHz SonTek, wasset up to sample hourly bursts of 10 min at 25 Hz. Bothinstruments collected data from January 23 2003 at10:00 GMT to March 06 2003 at 16:00 GMT. For thisstudy, observations from the ADV and ADCP will bepresented.

The positions of the stations are indicated in Fig. 1.The geographical positions and depths of the differentinstruments used in this study are described in Table 2.

Fig. 2. Wind data from ECMWF (dots) and UKMO (black line) interpolatedtaken at a land station, near LivB.

3.3. Additional remarks

It was observed that, in the Liverpool Bay area, thewave simulation using ECMWF ERA40 Reanalysiswinds (not shown here) underestimates wave parameters(Hs and Tp) in the order of 30–50% during the stormperiods. This problem is associated with the relativelylow spatial resolution of the ECMWF Reanalysis data-set. The UKMO and ECMWF wind magnitude anddirection (this last reported in meteorological conven-tion) interpolated to the position of the LivB station(black square in Fig. 1), as well as wind data measuredon land (black triangle in Fig. 1), near the buoy location,are shown in Fig. 2. A linear regression analysisbetween UKMO and ECMWF winds for the periodshown in Fig. 2 indicates a correlation coefficient of0.89 and a standard deviation of the data with respectto the regression line of 1.4 m/s. The only significantdifference in the comparison of these two wind data-bases is the underestimation of wind magnitude byabout 5 m/s during the strongest wind event, on lateJanuary and early February. The regression analysisbetween the two wind databases against on-land ob-servations (see Fig. 1) indicates correlation coefficients

to the LivB station. The gray line corresponds to wind measurements


of 0.84 and 0.76 for UKMO and ECMWF, respectively,and standard deviation of 2.16 m/s and 2.09 m/s forUKMO and ECMWF, respectively.

The problem of using interpolated winds from a lowresolution data set for the simulation of waves in coastalwaters, as well as other issues associated with orographyand characteristics of the storm, are addressed inCavaleri and Bertotti (2003, 2004). The problem ofland-sea interpolation of the winds is partially alleviatedby using a higher spatial resolution wind data set.

4. Results

4.1. Initial assessment using BJA05 and AB03

Bidlot et al. (2005) showed that their modifiedimplementation of Sds has an important effect on thegrowth and evolution of the wave field. During a wintermonth (December 2003), monthly mean differences ofHs and Tz on the western region of the North WestEuropean continental shelf were of the order of 4 cm and0.25 sec, respectively. They report positive differencesin Hs for this region, which indicates larger valuescomputed using the modified wave model. The oppositebehavior was found for the Tz differences.

Fig. 3. Maps of monthly mean differences (as a percentage of the referencepanels show differences of (a) Hs and (b) Tz computed using the BJA05 and KTz between AB03 and K94 implementations. Hs and Tz values are given in mto enhance differences and the areas where they occur.

According to our implementation, the normalizedmonthly mean differences between the BJA05 and K94implementations [(BJA05−K94) /K94] correspondingto the month of January 2003, were between 1% and 3%for Hs (Fig. 3a) and up to 2% for Tz (Fig. 3b). Strongerwind events during this month correspond to north-northwesterly wind conditions, although the mean waveconditions were predominantly southwesterly. Themonthly differences of Hs tend to become negative onthe western Irish Sea coast and in Liverpool Bay due tothe geometry of the basin and the wind direction. It isworth mentioning that BJA05 tends to correct thenormally observed overestimation of the wave energy inshort fetch conditions whenever a low spatial resolutionof the standard WAM Cycle 4 is used (Janssen, 2004).The monthly Hs differences on larger fetches are stillnegative but smaller (about 1%). Larger positive differ-ences of Tz on the eastern coast of the Irish Sea seems toindicate the presence of more energy in lower fre-quencies predicted by the BJA05 implementation.

The numerical results from the AB03 implementa-tion, which includes the modifications proposed byBidlot et al. (2005), suggest a larger sensitivity to theAlves and Banner (2003) expression for the wave energydissipation. The monthly differences for January 2003

K94 values) of wave parameters corresponding to January, 2003. Top94 implementations. Bottom panels show differences of (c) Hs and (d)eters and seconds, respectively. Different color scales are used in order


between AB03 and K94 implementations [(AB03−K94) /K94] are between 10% and 18% for Hs (Fig. 3c)and between 2% and 14% for Tz (Fig. 3d). In this case,the Hs differences in the Irish Sea are always positive,with smaller differences in places where short fetchconditions are observed. Larger Hs values computed bythe AB03 implementation are associated to the presenceof larger amounts of energy in the lower frequencies, asobserved in the Fig. 3d.

Given the relatively larger effect of the AB03 imple-mentation with respect to the BJA05 one, the analysis ofthe effect of wave energy dissipation in the Irish Sea willbe focused on theAB03 implementation andBJA05 is notconsidered further as an independent case for the rest ofthis study.

4.2. Time series of integrated parameters

From Fig. 4, it is possible to identify a number ofhigh wave events at station LivB: one of themregistered by the ADCP and the buoy where Hs reachesvalues larger than 2 m (January 14 to 16), another oneregistered by the ADCP, around January 23, with Hsbetween 2 m and 3 m, and one more measured by the

Fig. 4. Time series of significant wave height (top panel), and pe

buoy where Hs values reach up to 3 m height. The threeevents were generated by north-northwesterly windconditions and the observed Tp values, rangingbetween 5 s and 9 s, correspond to those expected forwaves under fetch limited conditions in the northernIrish Sea. It is worth noting the remarkable agreementbetween ADCP and buoy data, even during small waveconditions.

The Hs values computed using both the K94 andAB03 implementations (Fig. 4, top panel) agree verywell with the observations, except for the period be-tween January 13 and 18, where the Hs values computedby the two implementations overestimate the observedvalues by about 50 cm and up to 1m around January 17.The computed Tp values (Fig. 4, bottom panel) alsooverestimate the observations during most of this stormperiod (between 1.0 and 2.0 s).

The Hs values computed by the AB03 implementa-tion are systematically larger than the values computedby K94 during storm events by about 10% and up to20% during some events. In general, the results fromK94 show a better agreement with the observed valuesin the Liverpool Bay area. The second moment meanperiods (not shown here) computed by the AB03

ak period (bottom panel) computed by the models at LivB.

Table 3Bias and root-mean-square error (RMSe) computed for Hs and Tz atAbpB station

K94 AB03

Bias RMSe Bias RMSe

Hs −0.33 m 0.43 m −0.13 m 0.36 mTz −0.51 s 1.22s 0.02 s 1.16 s


implementation tend to be about 8% larger than thosecomputed by the K94 implementation.

The time series of Hs and Tz registered by the buoy atAbpB (Fig. 5) show the same pattern observed in LivB,with high waves generated by northerly winds producedby the passage of low pressure systems over the IrishSea. The qualitative comparison between the time seriesof Hs shown in Fig. 5 (top panel) indicate a betteragreement between measurements and the results ob-tained from the AB03 implementation. The quantitativecomparison of model results and observations ispresented in Table 3. The analysis is carried out forvalues larger than 0.5 m (minimum reported by thebuoy) resulted in bias and RMS error of −0.33 m and0.43 m, respectively, for the K94 implementation. Usingresults from the AB03 implementation, the computedbias and RMS error are −0.13 m and 0.36 m, respec-tively, i.e. the use of Alves and Banner (2003) formu-lation improves the bias by about 20 cm and reduces theRMS error by about 10 cm at AbpB.

The Tz values computed at this station by both modelimplementations are in good qualitative agreement withthe observations (Fig. 5, bottom panel). The bias andRMS error computed for the results of the K94 imple-

Fig. 5. Time series of significant wave height (top panel), and second mom

mentation were −0.51 s and 1.22 s, respectively, whilefor the AB03 implementation were 0.02 s and 1.16 s,respectively.

The Hs values computed by the AB03 implementa-tion are generally larger than those computed by the K94by about 10% during mild wind conditions and by about20% during some storm events. The Tz values com-puted by AB03 are larger by about 8% and up to 20%during some events.

An indication of the effect of using a differentformulation of Sds in the computation of the wave fieldcan be observed from the time series of Tz computed atAbpB. As for LivB station, the Tp values computed atAbpB location by both K94 and AB03 implementationare practically identical (not shown here), however the

ent wave period (bottom panel) computed by the models at AbpB.


Tz values computed by AB03 are significantly largerthat those computed by the K94 implementation. Thisseems to indicate the presence of more energy at swellfrequencies from the AB03 implementation.

In coastal areas, high energy levels at lower frequen-cies may have a direct impact on the computation of thewave bottom boundary layer parameters, and indirectlyon the estimate of sediment resuspension through thecomputation of the wave shear velocity, u⁎b. From thetime series of significant wave height and periodsobserved by the buoy and ADCP at LivB, and the buoyat AbpB, it is possible to compute time series of u⁎b usingthe formulation of Madsen et al. (1988). In order to makethe buoy and ADCP u⁎b values equivalent to thoseobtained from the wave model, the observed Hs and Tpvalues are used to construct a double peaked Torsethau-gen spectra (TheWAFO Group, 2002) and from there thecorresponding near-bottom orbital excursion amplitudevalues are computed. Maximumwave shear velocities arecomputed as u⁎b ¼

ffiffiffiffiffiffiffiffiffifw=2

pUb using the wave friction

factor and orbital velocity computed as in Eq. (6). In thecase of AbpB, where only Tz values are reported, the peakfrequency is estimated using the relationship Tz=0.781Tp (Soulsby, 1997). A critical shear velocity for sediment

Fig. 6. Time series of wave shear velocity computed at LivB (top panel), andvelocity corresponding to sand quartz of 0.2 mm diameter.

resuspension is also computed following Li and Amos(2001);

Ws ¼ ½−3mþ f9m2 þ gðD=2Þ2qwðqs−qwÞð0:00015476þ 0:099205DÞg1=2�=½qwð0:00011607þ 0:074405DÞ�;

ð7Þ

where Ws is the settling velocity of the particle, and thecritical shear velocity is approximated as,

u⁎cr ¼ 0:8Ws: ð8ÞFor the computation of u⁎cr in the Irish Sea, we

assumed that the sediment is quartz sand of diameterD=0.2 mm, a fluid density of ρw=1025 kg/m3, a sedi-ment density of ρs=2650 kg/m3, and dynamicviscosityof ν=1.3×10−3 kg/ms. In this case, the computed cri-tical shear velocity was u⁎cr=0.016 m/s.

The comparison between the u⁎b values computedfrom the buoy and ADCP data and those computed bythe wave model implementations is shown in Fig. 6.A time series of bottom shear velocity derived fromReynolds stresses measured by the ADV (see Section 3)are also included in Fig. 6. The corresponding critical

AbpB (bottom panel). The gray broken line represents the critical shear


shear velocity for sand quartz of 0.2 mm diameter isshown by a broken line.

The values of u⁎b computed by the ProWAM imple-mentations at LivB (Fig. 6, top panel) generallyoverestimate the values computed using observationsduring the period 12–22 January. This is consistent withthe overestimation of the Hs and Tp values predicted bythe model implementations during the same period. FromJanuary 24, u⁎b values computed from direct observationof Reynolds stresses by the ADV were used as a base tovalidate the model results and the values inferred frombuoy measurements. It is worth noting that the stressesmeasured by the ADV include the wave effect on the totalstress through the combined wave-current interactionprocess, so the semidiurnal signal observed in the timeseries of u⁎b is induced by tidal currents (Osuna andWolf,2005). A good agreement is observed between ADV dataand model results during the two large wave events of lateJanuary and early February, especially the maximumvalues which are better reproduced by the AB03 imple-mentation. It is worth noting that the Madsen et al. (1988)bottom boundary layer model allows us to estimate maxi-mum values of u⁎b, so it is more fair to evaluate theagreement betweenmodel results and observations duringthe occurrence of peak values. The u⁎b values computedfrom the buoy data, available again from February 2, are

Fig. 7. Maps of mean integrated wave parameters corresponding to the percomputed using the K94 implementation. Bottom panels show Hs and θd (c) avalues are given in meters and seconds, respectively.

in good agreement with the values computed by themodelimplementations during the whole range of waveconditions.

After the high-wave event of early February, thestresses become dominated by currents, with magni-tudes of u⁎b that exceed the critical shear velocity. Thetidal range after February 15 is larger than 6 m, and up to8 m on February 21. During this period of time, thewave conditions computed by the models are not highenough to resuspend fine-medium size sediments bythemselves, although in some cases the u⁎b computedfrom the buoy observations are larger than the criticalshear velocity. It is worth noting that the buoy u⁎b valuesare in good agreements with the ADVobservations alsoduring this low wave energy period, and even seem toreproduce the time variability associated with currenteffects. In general, the high concentration of suspendedsediments in Liverpool Bay observed from SeaWiFSimagery (not shown here) might be associated with ahigh, current-dominated, shear velocity period.

There is also good agreement between the u⁎b valuescomputed at AbpB by the two model implementationsand those computed using buoy data (Fig. 6, bottompanel). The comparison between model implementa-tions indicates that the mean of the differences betweenu⁎b computed by both model implementations at AbpB

iod 28–30 January, 2003. Top panels show Hs and θd (a) and Tp (b)nd Tp (d) values computed using the AB03 implementation. Hs and Tp


is about 25% larger than in LivB. As in the case for Hs,larger values are computed using the AB03 implemen-tation. The excess of energy computed by the AB03implementation, associated with the presence of a moreenergetic swell, has a potentially important impact onthe computation of boundary layer parameters, espe-cially in the southern Irish Sea.

4.3. Spatial distribution of integrated parameters andspectra

In Fig. 7, maps of mean wave parameters for a periodof strong north-northwesterly winds conditions (28–30January, 2003) computed by the two implementationsare presented. During this period, the mean wind patternand the computed mean wave direction (θd) indicate theoccurrence of a strong locally generated wave field. Thespatial distribution of Hs values computed by both im-plementations shows the same pattern, with larger valuescomputed by AB03 (Fig. 7c). The spatial distribution ofTp is also similar in both implementations, but with moreinfluence of swell from the Celtic Sea in the southernIrish Sea region predicted by AB03 (Fig. 7d).

Fig. 8. Wave spectra at stations LivB (top panels) and AbpB (bottom pimplementations for date 29th January 2003 at 00GMT. Energy contours arconnected to the circle indicates wind direction (going to).

The 2D energy spectra computed at LivB and AbpBby the two implementations for 29th January 2003 at00GMTare shown in Fig. 8. It is possible to observe thatthe shape and energy content of the spectra computed atLivB by AB03 (Fig. 8b) is very similar to the onecomputed by the standard K94 implementation (Fig. 8a).In AbpB, the spectra computed by both implementationsstill present the same structure, with almost the sameamount of energy in locally generated components, but astronger swell signal predicted by the AB03 implemen-tation (Fig. 8d). This produces larger values of Tp in thefrequency spectra computed by the AB03, as well aslarger values of Hs. The larger Hs and Tp valuescomputed by the AB03 implementations in the north-eastern Irish Sea, off Liverpool Bay (see Fig. 7), might bedue to the influence of the southern swell.

During a period of mild southerly wind conditions(18–20 February, 2003), the impact of the AB03implementation is very clear in the southern Irish Sea(see Fig. 9). Although the Hs values computed by the twoimplementations look very similar, it is possible toobserve differences in the computed mean wave direc-tions (θd). The θd computed by the K94 implementation

anels) computed by the K94 (left panels) and AB03 (right panels)e given for 0.1, 0.5, 1.0, and then every 1.0 m2/Hz/deg. The splinter

Fig. 9. Idem as in Fig. 7 but for the period 18–20 February, 2003.

Fig. 10. Idem as in Fig. 8 but for date 19th February 2003 at 00GMT.



(Fig. 9a) is more aligned to the wind direction, while thearrows corresponding to θd values computed in thesouthern Irish Sea by the AB03 implementation (Fig. 9c)are rotated north-northeast by swell effect. The Tp mapcomputed by the AB03 implementation (Fig. 9d)indicates a larger region of long waves off CardiganBay and around Anglesey.

In Fig. 10, the 2D energy spectra computed at LivBand AbpB for 19th February 2003 at 00GMTare shown.For that specific date, the wind blows from land with anintensity of 10.6 m/s at LivB and 8.4 m/s at AbpB. Therelatively short fetch condition in LivB produce an Hs ofabout 0.9 m although, according to AB03, the mostenergetic component corresponds to swell coming fromthe southwest (see Fig. 10, top panels). The locallygenerated wave components at AbpB are less energeticthan those generated at LivB (Fig. 10, bottom panels).Here, the swell signal predicted by the AB03 imple-mentation is much larger than that predicted by K94,which is reflected as an increment of the local waveheight by a factor of two.

5. Summary and conclusions

Two versions of the wave energy dissipation bydeep-water wave breaking (whitecapping) have beenimplemented in the ProWAM model (Monbaliu et al.,2000); the expression included in the standard Cycle 4,and one based on the new formulation proposed byAlves and Banner (2003). The latter implementationincludes the modifications suggested by Bidlot et al.(2005) to better deal with the growth and evolution ofthe wave field in a combined sea-swell situation. Theeffect of both whitecapping formulations on thesimulation of the wave field evolution in the Irish Searegion has been assessed in the Irish Sea region. Theimpact of the modifications was evaluated in terms oftheir differences in the computation of several integratedwave parameters (e.g. significant wave height, mean andpeak periods, wave direction, and wave induced shearvelocity), as well as in the frequency-direction spectraldomain, against a standard implementation of theProWAM model. In this study, a two-month periodthat includes fetch-limited wave growth and sea-swellconditions were analyzed. The performance of themodel implementations was also assessed using buoy,ADCP and ADV data at two locations of the Irish Sea.

In the Irish Sea, the numerical solution that includesonly the modifications suggested by Bidlot et al. (2005)has a smaller effect on the computation of mean para-meters than the formulation of Alves and Banner (2003).On average, during January 2003, the integrated spectral

parameters computed by the AB03 implementation tendto be larger (between 10% and 15%) than those computedby the standard K94 implementation, especially on thesoutheastern coast. The differences are mainly associatedwith the larger wave energy levels at lower frequencies(swell) predicted by the AB03 implementation.

The integrated wave parameters computed by bothmodels at some location on the eastern coast are in goodagreement with those observed by instruments at the seasurface and the bottom. Due to the sheltered position ofthe LivB station, the high wave events are associated tofetch-limited wave conditions, which the modelsmanage to reproduce quite well. AbpB station is locatedin a more open position, so the occurrence of morecomplex wave conditions (e.g. sea-swell interaction) isreflected as larger differences between the standard K94and the new AB03 implementation. Both models tend tooverestimate the overall spectral energy at LivB, butshow a better qualitative agreement at AbpB. In this laststation, the results obtained with the AB03 implemen-tation show a better quantitative agreement with theobservations than those results obtained from K94; Hsbias and RMS error are reduced by 20 cm and 10 cm,respectively, while Tz bias is reduced by about 0.5 s.

In the Irish Sea, the differences between K94 andAB03 implementations may have an impact on thedescription of potential sediment resuspension regionsand the computation of the total bottom shear stress duringcombined sea-swell conditions. In accordance to thedifferences between wave height and periods computedby both implementations, AB03 tend to predict largerwave shear velocities values than the standard K94 im-plementation. Both implementations provide wave shearvelocity values in good agreement with observations. It isfound that, in the Liverpool Bay area, the only possibilityfor the waves to resuspend sediment is the occurrence ofnorthwesterly wind conditions. In these kind of situationsa fetch-limited condition is observed and both K94 andAB03 implementations provide similar results. In Cardi-gan Bay, mixed sea-swell conditions are predicted. Thelarger swell computed by AB03 can be important in theamount and type of sediment resuspended by wave effect.

Acknowledgements

The authors would like to thank the CEFAS,ECMWF, UKMO and POL's Coastal Observatoryprogram for providing the wind and wave data used inthis study. The authors are grateful to John Howarth forproviding the ADCP wave data, postprocessing prog-rams and helpful information about the deployment ofinstruments in the Liverpool Bay. Two anonymous


reviewers provided useful remarks and helped toimprove the clarity of this paper.

References

Alves, J.H.G.M., Banner, M.L., 2003. Performance of a saturated-based dissipation-rate source term in modeling the fetch-limitedevolution of wind waves. J. Phys. Oceanogr. 33, 1274–1298.

Banner, M.L., Young, I.R., 1994. Modeling spectral dissipation in theevolution of wind waves. Part I: assessment of existing modelperformance. J. Phys. Oceanogr. 24, 1550–1570.

Bidlot, J.-R., Holmes, D.J.,Wittmann, P.A., Lalbeharry, R., Chen, H.S.,2002. Intercomparison of the performance of operational oceanwave forecasting systems with buoy data. Weather Forecast. 17,287–310.

Bidlot, J., Janssen, P., Abdala, S., 2005. A revised formulation forocean wave dissipation in CY29R1. Internal Memorandum.ECMWF, Reading, United Kingdom.

Caires, S., Sterl, A., Bidlot, J.-R., Graham, N., Swail, V., 2004.Intercomparison of different wind-wave reanalyses. J. Climate 17(10), 1893–1913.

Cavaleri, L., Bertotti, L., 2003. The characteristics of wind and wavefields modelled with different resolutions. Q. J. R. Meteorol. Soc.129, 1647–1662.

Cavaleri, L., Bertotti, L., 2004. Accuracy of the modelled wind andwave fields in enclosed seas. Tellus 56A, 167–175.

Hasselmann, K., 1974. On the spectral dissipation of ocean waves dueto white-capping. Boundary - Layer Meteorol. 6, 107–127.

Hasselmann, K., Hasselmann, S., 1985. Computations and parameter-izations of the nonlinear energy transfer in a gravity-wave spectrum.Part 1: a newmethod for efficient computations of the exact nonlineartransfer integral. J. Phys. Oceanogr. 15, 1378–1391.

Janssen, P.A.E.M., 1991. Quasi-linear theory of wind wave generationapplied towindwave forecasting. J. Phys. Oceanogr. 21, 1631–1642.

Janssen, P., 2004. The Interaction of Ocean Waves and Wind.Cambridge University Press, Cambridge. 300 pp.

Kahma, K., Calkoen, C.J., 1992. The dynamical coupling of a wavemodel and a storm surge model through the atmospheric boundarylayer. J. Phys. Oceanogr. 23, 1856–1866.

Komen, G.J., Cavaleri, L., Donelan, M., Hasselmann, S., Hasselman, K.,Janssen, P.A.E.M., 1994. Dynamics andModelling of OceanWaves.Cambridge University Press, Cambridge. 532 pp.

Li, M.Z., Amos, C.L., 2001. SEDTRANS96: the upgraded and bettercalibrated sediment-transportmodel for continental shelves. Comput.Geosci. 27, 619–645.

Madsen, O.S., Poon,Y.K., Graber, H.C., 1988. Spectral wave attenuationby bottom friction: theory. Proceedings of the 21st InternationalConference on Coastal Engineering, vol. 1. ASCEE, Malaga, Spain,pp. 492–504.

Monbaliu, J., Padilla-Hernández, R., Hargreaves, J.C., Carretero-Albiach, J.C., Luo, W., Sclavo, M., Gunther, H., 2000. The spectralwave model WAM adapted for applications with high spatialresolution. Coast. Eng. 41, 41–62.

Osuna, P., Wolf, J., 2005. A numerical study on the effect of wave-current interaction processes in the hydrodynamics of the Irish Sea.Procc. 5th Int. Conf. on Ocean Wave and Analysis, WAVES2005.Madrid, Spain.

Soulsby, R., 1997. Dynamics of Marine Sands: A Manual for PracticalApplications. Thomas Telford Publications. 249 pp.

Souza, A.J., Howarth, M.J., 2005. Estimates of Reynolds stresses in ahighly energetic shelf sea. Ocean Dyn. 55, 490–498.

Strong, B., Blumley, B., Terray, E.A., Stone, G., 2000. The performanceof ADCP-derived directional wave spectra and comparison withother independent measurements. Proc. 2000 MTS/IEEE OceansConf. Providence, RI, USA, pp. 1195–1203.

The WAFO GROUP, 2002. WAFO — A Matlab Toolbox for forAnalysis of RandomWaves and Loads— Tutorial Version 2.0.02.Lund Institute of Technology. 113 pp.

Tolman, H.L., Chalikov, D., 1996. Source terms in a third-generationwind wave model. J. Phys. Oceanogr. 26, 2497–2518.

Tolman, H.L., Balasubramanuyan, B., Burroughs, L.D., Chalikov, D.V.,Chao, Y.Y., Chen, H.S., Gerald, V.V., 2002. Development andimplementation of wind-generated ocean surface wave models.Weather Forecast. 17, 311–333.

Van Vledder, G.Ph., 2001. Improved algorithms for computing the non-linear quadruplet wave–wave interactions in deep and shallowwater.ECMWF Workshop on Ocean Wave Forecasting. European Centrefor Medium-Range Weather Forecast, Reading, United Kingdom.

Effects of the deep-water wave breaking dissipation on the wind-wave modelling in the Irish Sea

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