Effect of a seagrass (Posidonia oceanica) meadow on wave propagation

MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 456: 63–72, 2012doi: 10.3354/meps09754

Published June 7

INTRODUCTION

Sediment stabilization and coastal protection arekey ecosystem services provided by seagrasses,aquatic angiosperms that colonize shallow marinehabitats (Hemminga & Nieuwenhuize 1990, Fonseca1996, Koch et al. 2009). Submerged plants increasebottom roughness, thus reducing near-bed velocityand modifying the sediment transport (Koch et al.2006) and increasing wave attenuation (Kobayashi etal. 1993, Méndez & Losada 2004). In addition, sea-grass rhizomes and roots extend inside sediment andcontribute to its stabilization (Fonseca 1996).

Flume and in situ measurements have shown thatwater velocity is reduced inside meadows. In sparsecanopies, turbulent stress remains elevated withinthe canopy, while in dense canopies turbulent stressis reduced by canopy drag near the bed (Luhar et al.2008). The reduction in velocity due to seagrasscanopies is lower for wave-induced flows compared

to unidirectional flows, because the inertial term canbe larger or comparable to the drag term in oscilla-tory flow (Lowe et al. 2005, Luhar et al. 2010). Exceptfor intertidal systems, where currents are dominant,most seagrass meadows lie in wave-dominated habi-tats. Interaction between seagrass canopies andoscillatory flow has, however, been much less studiedthan the interaction with currents. Near-bed turbu-lence levels inside seagrass canopies are lower thanthose on sands under wave-generated oscillatoryflows (Granata et al. 2001). Wave energy and sedi-ment resuspension are also reduced by seagrasses(Terrados & Duarte 2000, Verduin & Backhaus 2000,Gacia & Duarte 2001).

Wave attenuation by seagrass canopies has beenmeasured only in shallow systems where canopiesoccupy a large fraction of the water column (Fonseca& Cahalan 1992, Koch & Beer 1996, Mork 1996, Chenet al. 2007, Bradley & Houser 2009). Posidonia ocean-ica, which is the dominant seagrass species in the

© Inter-Research 2012 · www.int-res.com*Email: [email protected]

Effect of a seagrass (Posidonia oceanica) meadowon wave propagation

E. Infantes1, A. Orfila1,*, G. Simarro2, J. Terrados1, M. Luhar3, H. Nepf3

1Instituto Mediterráneo de Estudios Avanzados (CSIC-UIB), 07190 Esporles, Spain2Institut de Ciències del Mar, ICM-CSIC, 08003 Barcelona, Spain

3Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA

ABSTRACT: We demonstrate the utility of using the equivalent bottom roughness for calculatingthe friction factor and the drag coefficient of a seagrass meadow for conditions in which themeadow height is small compared to the water depth. Wave attenuation induced by the seagrassPosidonia oceanica is evaluated using field data from bottom-mounted acoustic doppler veloci -meters (ADVs). Using the data from one storm event, the equivalent bottom roughness is calcu-lated for the meadow as ks ~ 0.40 m. This equivalent roughness is used to predict the wave frictionfactor ƒw, the drag coefficient on the plant, CD, and ultimately the wave attenuation for otherstorms. Root mean squared wave height (Hrms) is reduced by around 50% for incident waves of1.1 m propagating over ~ 1000 m of a meadow of P. oceanica with shoot density of ~600 shoots m−2.

KEY WORDS: Wave attenuation · Posidonia oceanica · Seagrass meadow · Bottom roughness · Friction coefficient · Drag coefficient · Wave damping

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Mar Ecol Prog Ser 456: 63–72, 2012

Mediterranean Sea, forms extensive meadows indepths up to 45 m (Procaccini et al. 2003) and thecanopy often occupies less than 20% of water columnheight. Al though commonly assumed to occur(Luque & Templado 2004, Boudouresque et al. 2006),wave attenuation by P. oceanica meadows, or by anymeadow occupying a small fraction of the water col-umn, has not been accurately assessed in the field. Inthis study we evaluate the effect of a P. oceanica sea-grass meadow on wave propagation under naturalconditions. To quantify wave attenuation due to P.oceanica meadow in the field, we measure waveheights and orbital velocities along a transect abovethe meadow for 3 storms.

Most coastal models introduce bottom effectsthrough the equivalent roughness, ks, and thereforeit is practical to consider if such a characterizationcan apply to seagrasses. The equivalent roughnesswill be used to account for the effects of both thesandy bed and the meadow. Moreover, Bradley &Houser (2009) already suggested the use of an equiv-alent roughness to describe wave attenuation due toa canopy, but to date, no attempt has been made torelate this quantity to the drag coefficient whichdescribes the drag associated with the individualblades. The underlying assumptions of our approachare, first, that the boundary layer is rough turbulentand, second, that water depth is much larger than theblade length.

MATERIALS AND METHODS

The bottom boundary layer is the region in whichthe velocity field drops from the value in the core ofthe fluid to zero at the bed. In a bottom covered byseagrass the boundary layer is modified by thecanopy, which influences the mean velocity, turbu-lence and mass transport (e.g. Nepf & Vivoni 2000,Ghisalberti & Nepf 2002, Luhar et al. 2010). In thisanalysis, we assume that the seagrass exists withinthe bottom boundary layer and thus can be repre-sented as a bottom roughness. A list of symbols usedin the analysis is given in Table 1.

The dimensionless parameter relating the velocityoutside the boundary layer, ub, and the bed shearstress transmitted to the combined seagrass and bot-tom, τb, is the wave friction factor defined as ƒw �2|τb|�ρub

2, where ρ is the fluid density. The frictionfactor ƒw depends on the Reynolds number, ub

2�νω,and on the relative roughness, ksω�ub. Here, ν is thekinematic viscosity of the water, ω the wave angularfrequency (ω = 2π�T, with T the wave period), and ks

a length characterizing the bottom equivalent rough-ness. For bare beds, the equivalent roughness, ks, isrelated to the sediment size and the bed form height.If the boundary layer is smooth (namely ks��τb��ρ�ν <~3.3), then ƒw depends mainly on the Reynolds num-ber. Otherwise, if the boundary layer is rough(ks��τb��ρ�ν >~ 3.3), the friction factor depends mainlyon the relative roughness. At this point, we assumethat the boundary with seagrass is rough, and we willlater check this assumption.

Accounting for signs, the definition of ƒw impliesτb = ρƒwub|ub|�2. Though this approach is valid as afirst order approximation, it is known to be an over-simplification of the problem. For instance, it is wellknown that the shear under monochromatic waves isnot in phase with velocity. This has led to modifica-tions of the friction factor to introduce the phase lag(Nielsen 1992), and to redefine the friction factor as(Jonsson 1967) ƒw � 2τb,max�ρub

2,max, where the sub-

script refers to the maximum value of the variablewithin a wave period. With this redefinition, for roughconditions, the friction factor proposed by Nielsen(1992) as a modification of the semi-empirical for-mula of Swart (1974) for sandy bottoms is:

64

a Wave amplitude (m)ab Orbital wave excursion (m s−1)av’ Plant surface area per unit height (m)b Characteristic length of the plant (m)cg Group velocity (m s−1)CD Drag coefficientCD, SG Drag coefficient as defined by Sánchez-

Gonzáles et al. (2011)E Wave energy (J m−2)ƒw Wave friction coefficientg Acceleration of gravity (m s−2)h Water depth (m)Hrms Root mean squared wave height (m)Hrms,0 Incident root mean squared wave height (m)H c

rms, i Computed wave heights (m)H m

rms, i Measured wave heights (m)kp Peak wave number (m−1)ks Bottom equivalent roughness (m)γ Wave attenuation coefficient (m−1)λp Peak wave length (m)lv Vegetation length (m)N Number of shoots per unit area (m−2)T, Tp Wave period and wave peak period (s)u Fluid velocity (m s−1)ub Near-bottom orbital velocity (m s−1)x Horizontal distance (m)εD Rate of energy dissipation (J m−2 s−1)ρ Seawater density (kg m−3)τb Bottom shear stress (N m−2)ν Kinematic viscosity of water (m2 s−1)ω Wave angular frequency (s−1)

Table 1. Symbols used in the paper

Infantes et al.: Wave attenuation by Posidonia oceanica seagrass meadow 65

(1)

Recent work (e.g. Méndez & Losada 2004, Sánchez-González et al. 2011) suggests that the friction dueto seagrasses can be determined in terms of the Keulegan-Carpenter number (i.e. KC � uT�b with ua characteristic velocity of the flow and b a character-istic length of the plant, usually the width). Assumingthat the boundary layer generated by the vegetationis rough, and noting that KC−1 has the same func t -ional structure as the relative roughness ksω�ub, wepropose the use of Eq. (1) for ƒw with ks being theequivalent roughness of the seagrass meadow.

Assuming that linear wave theory is valid andassuming straight and parallel bathymetric contours,the conservation of wave energy for random wavesmay be written as

(2)

with the energy E being E � ρgH 2rms�8, with g the

acceleration of gravity, Hrms the root mean squaredwave height, εD the energy dissipation, and cg thegroup velocity given by

(3)

with the peak wave number, kp = 2π�λp, where λp isthe wave length corresponding to the peak period(Tp), and h the local water depth.

Previous theoretical, numerical and observationalworks on wave propagation over vegetated fieldshave dealt with the question of obtaining the dissipa-tion term, εD, in order to integrate Eq. (2) (Kobayashiet al. 1993, Méndez & Losada 2004, Bradley & Houser2009). The dissipation term is

(4)

with the overbar standing for time average. We de finelv as the canopy height and use linear wave theory todescribe the time-varying wave-induced velocity atthe top of the canopy, z = −h + lv. Then, following theprocedure proposed by Méndez & Losada (2004) tohandle irregular waves, Eq. (4) becomes

(5)

Alternatively, following Dalrymple et al. (1984),Méndez & Losada (2004) obtained the dissipation interms of the blade drag coefficient, CD,

(6)

where N is the number of plants per unit of horizontalarea, and a’v is the plant area per unit height. A similarapproach is used by Plew et al. (2005) to de scribewave interaction with the suspended ropes of amussel farm. By comparing Eqs. (5) & (6), the relation-ship between the friction coefficient ƒw and the dragcoefficient CD follows, which for kplv << 1 reduces to

(7)

If the equivalent roughness ks of a Posidonia oce -anica meadow can be found, as we propose, the fric-tion coefficient ƒw (and, therefore, εD) can be computedthrough Eqs. (1) & (5). For irregular waves, we con-sider ub,rms as the corresponding velocity in Eq. (1).Once εD is estimated at each point, the wave heightHrms can be computed by integrating Eq. (2). We usea finite difference scheme for numerical integration.

The wave attenuation over a constant depth hasreceived special attention in the literature. AssumingCD constant in Eq. (6), Dalrymple et al. (1984) andMéndez & Losada (2004) analytically integratedEq. (2) to get

(8)

with Hrms,0 = Hrms (x=0) and where the attenuationcoefficient γ (m−1) is

(9a)

Similarly, for wave propagation over constantdepth, if we assume constant ƒw, the above solution(Eq. 8) would also hold for our approach, now being

(9b)

Using the solution in Eq. (8), the wave attenuationper wavelength, 1 − Hrms(x =λp)�Hrms,0, is 1 − (1 + γ λp)−1.

Departing from a different differential equation,Kobayashi et al. (1993) and Sánchez-González et al.(2011) obtain the following solution for the constantdepth case

Hrms = Hrms,0exp(−γx) (10)

with γ given in Eq. (9) for Kobayashi et al. (1993) anda slightly different expression for Sánchez-Gonzálezet al. (2011). Differences between Eqs. (8) & (10) are<10% up to γx <~ 0.5.

Field measurements

Field measurements were carried out in Cala Millor,on the northeast coast of the island of Mallorca,

12

ƒD b b w b b2u u uε = τ = ρ

ε ρπ ωDw p

p

p

p

= ⎛⎝⎜

⎞⎠⎟

ƒ cosh ( )

cosh ( )2 2

3 3

33

gk k l

k hHv

rms

ε ρπ ωD

D

p

p

p

p p= ⎛⎝⎜

⎞⎠⎟

+C a N

k

gk k l kv v’ sinh ( ) sinh(

6 2

33 3 ll

k hHv )

cosh ( )33

prms

ƒ ’w DC a l Nv v=

1rms

rms,0HH

x=

+ γ

’3

sinh ( ) 3sinh( )

(sinh2 2 ) sinh( )D

3p p

p p pp rms,0

C a N k l k l

k h k h k hk Hv v vγ =

π+

+

ƒ sinh ( )

(sinh2 2 ) sinh( )w p

3p

p p pp rms,0

k k l

k h k h k hk Hvγ =

π +

Ec

x

∂∂

= −ε( )g

D

21

2

sinh 2g

p

p

pc

k

k h

k h( )= ω +⎧

⎨⎩

⎫⎬⎭

ƒ exp . ..

ws

b

= ⎛⎝

⎞⎠ −

⎧⎨⎩

⎫⎬⎭

5 5 6 30 2k

uω

Mar Ecol Prog Ser 456: 63–72, 2012

Mediterranean Sea (Fig. 1a−c). Cala Millor is an inter-mediate barred sandy beach formed by biogenic sedi-ments with median grain values ranging be tween0.28 and 0.38 mm at the beach front (Gómez-Pujol etal. 2007). The beach is in an open bay with an area ofabout 14 km2. At depths from 6 to 35 m, the seabed iscovered with a meadow of Posidonia oceanica (In-fantes et al. 2009). The bay is microtidal, with a springrange of less than 0.25 m (Orfila et al. 2005), and thenear-bottom mean currents during the period of studywere small (<0.05 m s−1). The bay is located on theeast coast of the island, and is therefore exposed to in-coming wind and waves from NE to ESE directions.

From 7 to 23 July 2009, 4 self-contained AcousticDoppler Velocimeters ADVs (Nortek, Vector) withpressure sensors were deployed on a transect perpen-dicular to the coast at depths of 6.5, 10, 12.5 and 16.5 mand of total length 942 m (Fig. 1d). ADVs weremounted over galvanized iron structures, with thepressure sensors located at 80 to 100 cm above the bot-tom, i.e. just above the seagrass canopy (Fig. 2). Stabil-

ity of the equipment was verified with compass,tilt and roll sensors (Infantes et al. 2011). Veloc-ity data were collected at 80 to 100 cm abovethe bottom in bursts of 15 min every 2 h at asampling rate of 4 Hz, sampling volume givenas 14.9 mm and a nominal fluid velocity rangeof ±1 m s−1. With this sampling rate we wereable to capture waves with a period above 2 s.For waves with periods below 2 s, linear wavetheory indicates that the velocities transmittedto the bottom are negligible compared to thosecorresponding to the peak period.

Root mean squared wave height (Hrms), hor-izontal components of velocity (ub,rms andvb,rms), and peak period (Tp) were processedusing Nortek (QuickWave v.2.04) software(Nortek 2002). Wave data were filtered toremove waves not approaching perpendicularto the beach. To exclude wave energy lost bywhite capping, we excluded wave recordswhen mean wind velocities were higher than10 m s−1 (data from the Spanish HarborAuthority ‘Puertos del Estado’).

The area is subject to cyclogenetic activitythrough out the year (Cañellas et al. 2007). In-deed, during the instrument deployment,3 events with Hrms larger than 0.60 m at thedeepest location (significant wave height,Hs, > 0.85 m) affected the area (Fig. 3a). Here-after ‘storms’ refer to events where the signifi-

66

Fig. 1. Locations of (a) the island of Mallorca in the Mediterranean Sea,(b) the study area, (c) the transect and deployment sites in Cala Millor.(d) Bathymetric profile and distance between the deployment sites

Fig. 2. Acoustic doppler velocimeter (ADV) deployed in the Posidonia oceanica seagrass meadow

Infantes et al.: Wave attenuation by Posidonia oceanica seagrass meadow 67

cant wave height is large, regardless of local windconditions. The first storm began on 13 July andlasted 44 h with a maximum Hrms of 1.31 m. The sec-ond storm began on 18 July, lasted 16 h and reachedHrms = 1.19 m. The third storm began on 21 July,lasted 14 h and reached Hrms = 0.74 m. The equivalentroughness of the meadow, ks, which is assumed to re-main essentially constant for all storms, was calcu-lated from the third storm and then used to compute,integrating Eq. (2), the wave attenuation for the first 2storms. The computed wave attenuation was thencompared to the corresponding experimental data.

Determination of equivalent roughness

As stated, the equivalent roughness ks is a criticalparameter for the characterization of the friction fac-tor in rough turbulent flows. We expect it to be afunction of the meadow morphology (number ofshoots, shoot height and leaf width mainly), and itwill be assumed to be constant during the experi-mental duration. This is a fair assumption since allmeasurements were done in summer over a shortperiod of time (16 d). Posi donia oceanica leaf lengthsand leaf widths were measured for 10 vertical shoots

collected at locations 1 to 4 (Fig. 1, top). The meanshoot length, lv, was 0.8 ± 0.1 m (mean ± SE) and leafsurface area per plant 211 ± 23 cm2 (mean ± SE), sothat a’v ≈ 0.0264 m. Shoot density, N, was also mea-sured at the same 4 locations, and was 615 ± 34 m−2

(mean ± SE).Velocities and wave heights measured along the

transect during the third storm (21 July ) were used toobtain ks. Specifically, we found the value of ks thatminimizes the error

(11)

between the observed and computed wave heights,where i = 2,3,4 correspond to moorings 2 to 4 (at x =337, 664 and 942 m respectively). In Eq. (11), H m

rms,i

are the measured values and H crms,i are the values

computed by integrating Eq. (2) starting from thevalue measured at the first mooring, i.e.H m

rms,i. In thenumerical integration, the bathymetry was ad justedby fitting a third order polynomial to the depths at the4 moorings (Fig. 1d).

The value of ks minimizing the above error wascomputed for a total of 14 h corresponding to thethird storm, and the average for all records was cal-culated. Once ks was determined for the Posidonia

rms,c

rms,m 2

2

4

H Hi ii∑ −=

07

a

b

08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23

070

0

0.05

0.5

1.5

1

0.15

0.2

0.1

08 09 10 11 12 13 14 15July

u b,r

ms

(m s

–1)

Hrm

s (m

)

16 17 18 19 20 21 22 23

Mooring 1

Mooring 2

Mooring 3

Mooring 4

Fig. 3. (a) Root mean squared wave height, Hrms, at mooring 1 (16.5 m depth); mooring 2 (12.5 m); mooring 3 (10 m) and moor-ing 4 (6.5 m). Grey areas indicate the 3 storms. (b) Corresponding near-bottom orbital velocities at the same locations

Mar Ecol Prog Ser 456: 63–72, 2012

oceanica meadow, we computed ƒw and wave atten-uation for the other 2 storms, and compared the com-puted results with the field measurements to validatethe model approach. To obtain ƒw from Eq. (1) wealways assumed purely oscillatory motion; this is afair assumption for the experimental data since meanvelocities are one order of magnitude lower than theoscillatory component.

RESULTS

During the 3 storms the measured Hrms decreasedas the wave travelled onshore (Fig. 3a). The waveattenuation from mooring 1 to 4 was 30 to 60% in all3 storms. In contrast, but as expected by linear wavetheory, the corresponding near-bottom orbital veloci-ties (ub,rms) increased at shallower depths (Fig. 3b). InFig. 3, the lag between the peaks in Hrms and ub,rms isdue to the influence of the wave period, whichchanged within the storm.

Following the procedure described above, theequi valent roughness obtained during the third

storm, on 21 July 21, is ks (m) = 0.42 ± 0.12. Using ks =0.42 m and Eq. (1) for ƒw, the computed values of τb atall moorings ranged between 12.7 and 24.9 N m−2 forthis storm, so that ks��τb��ρ�ν > 5.2 × 104 >> 3.3, as pre-viously assumed (rough turbulent).

At midnight on 13 July, Hrms = 0.65 m was mea-sured at mooring 1 (16.5 m depth). For this first storm,wave heights Hrms above 0.65 m were recorded for44 h with maximum Hrms = 1.31 m. Measured Hrms

normalized by the incident root mean squared waveheight (Hrms,0) at the 4 moorings is displayed for themiddle 24 h of this storm in Fig. 4). The numericalintegration of Eq. (2) and the uncertainty in the pre-dictions, based on a 15% error in the measurement ofthe initial wave height and period, are also shown.Now the minimum computed ks��τb��ρ�ν is 4.7 × 104

(>>3.3). As shown in Fig. 4, fairly good agreement isobtained between the measured and predicted Hrms.Note that H m

rms,4 ≈ 0.5 H mrms,1.

The second storm lasted 16 h starting on midnightof 18 July. Similar to Fig. 4, Fig. 5 presents the resultsfor this event at 2 h intervals. The measured dataare well represented by the predictions although

68

0200

04:00 h 06:00 h 08:00 h

10:00 h 12:00 h 14:00 h

16:00 h 18:00 h 20:00 h

22:00 h 00:00 h 02:00 h

4006008000

0.5

1

0200400600800 0200400600800

0

0.5

1

0

0.5

1

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0.5

1

x (m)

0200400600800 0200400600800 0200400600800

0200400600800 0200400600800 0200400600800

0200400600800 0200400600800 0200400600800

Hrm

s�H

rms,

0

Fig. 4. Normalized root mean squared wave height, Hrms�Hrms,0, over horizontal distance for the first storm. The plots refer toconditions every 2 h, beginning at 04:00 h on 13 July. Solid black line: computed Hrms including the dissipation due to the Posi-donia oceanica meadow. Circles: measured Hrms. Grey line: Hrms assuming no dissipation by the seagrass, i.e. εD = 0 in Eq. (2).Dashed lines: predictions for wave attenuation for a 15% error in the measurement of initial wave height and wave period

Infantes et al.: Wave attenuation by Posidonia oceanica seagrass meadow

some discrepancies appear at the shallow moorings.In this case H m

rms,4 ~ 0.6 H mrms,1 and ks��τb��ρ�ν > 5.7 ×

104 (>>3.3).For constant depth, given ks and an incoming con-

dition characterized by Hrms,0 and Tp, the wave atten-uation can be computed integrating Eq. (2) and usingEqs. (6) & (1) to evaluate εD and ƒw, as mentioned. Fora wave of Hrms,0 = 1 m and Tp = 5.5 s propagating overa depth of h = 10 m, Fig. 6 displays the wave attenu-ation across a 1000 m meadow. For the computationof ƒw one can consider linear wave theory for the cal-culation of the near-bottom orbital velocity. Because

the near-bottom velocity decreases as the waveattenuates over the meadow, ƒw increases with dis-tance over the meadow, according to Eq. (1), asshown in Fig. 6, so that the solution Hrms = Hrms,0�1+ γx in Eq. (8) is not valid.

For comparison purposes we consider the attenua-tion per wavelength. The attenuation per wave-length for ks = 0.42 m is displayed in Fig. 7 for Hrms,0

between 0.5 and 1.5 m and Tp between 4 and 10s, for3 different depths. The values range from 0.2 to3.5%. As a general trend, the greater the waveheight and period, the greater is the attenuation perwavelength; also, the shallower the water depth, thegreater is the attenuation.

DISCUSSION

We obtained an equivalent roughness that re -mained essentially constant during the experiments.The values were ks = 0.35 ± 0.09 m, ks = 0.39 ± 0.09 mand ks = 0.42 ± 0.12 m for 3 independent storms.Note, however, that ks is likely to be a function ofmeadow geometry (blade length and shoot density),so these values cannot be confidently applied tomeadows of different geometry.

This study suggests that for incident waves with0.5 m ≤ Hrms,0 ≤ 1.5 m and 4 s ≤ Tp ≤ 10 s propagatingover a constant depth h = 8 m, the wave attenuationper wavelength for ks ≈ 0.42 m (corresponding to our

69

00:00 h 02:00 h 04:00 h

06:00 h 08:00 h 10:00 h

12:00 h 14:00 h 16:00 h

0

0.5

1

0

0.5

1

0.5

1

0

0.5

1

0

0.5

1

0.5

1

0

0.5

1

0

0.5

1

0.5

1

x (m)

0200400600800 0200400600800 0200400600800

0200400600800 0200400600800 0200400600800

0200400600800 0200400600800 0200400600800

Hrm

s�H

rms,

0

Fig. 5. Normalized root mean squared wave height, Hrms�Hrms,0, over horizontal distance for the second storm. The plots refer to conditions every 2 h, beginning at midnight on 18 July. Lines and symbols as in Fig. 4

02004006008001000

0.8

1

1.2

1.4

1.6

1.8

2

x (m)

Hrms�Hrms,0

ƒw�ƒw,0

Hrm

s�H

rms,

0 o

r ƒ w

�ƒw

,0

Fig. 6. Normalized root mean squared wave height, Hrms�Hrms,0 (solid line), and friction coefficient ƒw�ƒw,0 (dashedline) for an incoming wave of Hrms,0 = 1 m and Tp = 5.5 s

propagating over a constant depth h = 10 m

Mar Ecol Prog Ser 456: 63–72, 2012

meadow with N ≈ 600 shoots m−2 and lv ≈ 0.8 m)ranges between 1.5 and 3.5% Fig. 7c). Bradley &Houser (2009), using the exponential expressionEq. (10), measured an exponential attenuation coeffi-cient γ ranging from 0.004 to 0.02 m−1 for waves ofpeak period 1.5 in water depths h ≈ 1.0 m (λp ≈ 3.3 m),which is equivalent to an attenuation per wavelengthof 1.3 to 6.4%. These authors suggest a bottom equiv-alent roughness ks ≈ 0.16 m, which is consistent withthe value obtained in this study (ks ≈ 0.40 m). Thelower equivalent roughness obtained by Bradley &Houser (2009) may be explained by the fact that Thalassia testudinum, considered in their study (withlv ≈ 0.3 m), is shorter than Posidonia oceanica (lv ≈ 0.8 m). Fonseca & Cahalan (1992) observed muchhigher rates of attenuation, but they considered con-ditions with leaf length equal to the water depth,which is far from the conditions we assumed, lv << h.They evaluated wave attenuation for 4 seagrass species (Zostera marina, Halodule wrightii, Syringo -dium filiforme and T. testudinum) in a laboratorystudy. They found a ~15 to ~27% reduction in wave

energy per wavelength, i.e. wave attenuation perwavelength of 7 to 15%.

Sánchez-González et al. (2011) studied wave atten-uation due to seagrass meadows in a scaled flumeexperiment using artificial models of Posidonia oce a -ni ca and concluded that CD is better related with KCthan with Reynolds number. Specifically, theseauthors found that

(12)

for 15 ≤ KC ≤ 425. For comparison purposes, Fig. 8shows the drag coefficient (CD) derived in this studyversus the drag coefficient provided by Sánchez-González et al. (2011) (CD,SG). For the comparison weused the above reported meadow values av’ ≈0.0264 m, lv ≈ 0.8 m and N ≈ 615 m−2 and also ks =0.42 m. Recall that ksω�u, required to compute our ƒw,is related to KC as

(13)

Therefore, for a given KC, we compute CD,SG fromEq. (12) and CD from Eqs. (13), (1) & (7). For our fieldconditions, good agreement is obtained between the2 approaches, even though CD,SG was obtained fromphysical flume experiments (Fig. 8).

The approach followed in the present study as -sumes that the water motion is mainly induced bywaves. For our experiment, this is a reasonable as -sumption for the storms analysed since near- bottomorbital velocities measured by the ADVs are oneorder of magnitude larger than mean currents. Incoastal environments where waves become nonlin-ear or currents and waves might be of the same orderof magnitude, one has to explicitly solve the bound-

C = 22.9KC

D 1.09

2KC

s sku

kb

ω = π

70

0.00

2

0.00

4

0.00

6

0.00

8

0.01

0.01

2

0.014

0.016

h = 16 m

0.00

40.

006

0.00

80.

010.

012

0.01

4

0.01

6

0.01

8

0.02

0.02

2

h = 12 m

0.01

5 0.02

0.02

5

0.03 0.035

h = 8 m

0.5

1.5

1

0.5

1.5

1

0.5

1.5 a

b

c

1

54 76 98 10

54 76 98 10

54 76 98 10

Hrm

s,0

(m)

Tp (s)

Fig. 7. Wave attenuation per wavelength for constant depthsof (a) h = 16 m, (b) h = 12 m, and (c) h = 8 m, with ks = 0.42 m

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

CD,SG

CD

Fig. 8. Drag coefficient (CD) obtained from Eq. (13) versusthe experimental drag coefficient provided by Sánchez-González et al. (2011) (CD,SG). Gray dashed line: 1:1 ratio

Infantes et al.: Wave attenuation by Posidonia oceanica seagrass meadow

ary layer using a specific model (Grant & Madsen1979, Orfila et al. 2007, Simarro et al. 2008).

Two aspects should be considered in detail forfuture research. First, the link between the equiva-lent roughness and meadow properties has to be fur-ther explored. Second, the limitation of this approachfor increasing non-dimensional blade length (lv�h)has to be assessed. Understanding the interaction be -tween waves and bottom canopies such as Posidoniaoceanica seagrass meadows is crucial for assessingthe importance of these communities in coastal pro-tection as well as to determine the final wave para-meters which will drive sediment motion. This workshows that a P. oceanica meadow reduces the waveheight reaching the beach. Parameters such as ks andCD are necessary in order to run more precise wavepropagation models over seagrass meadows. More-over, for meadows that occupy a small fraction of thewater depth, it may be appropriate to use relationsfor bare beds, specifically Eq. (1), to characterize thedrag imparted by the canopy.

Acknowledgments. E. Infantes acknowledges the financialsupport received from the Spanish Ministerio de Educaciony Ciencia, FPI scholarship program (BES-2006-12850). G.Simarro is supported by the Spanish government throughthe Ramón y Cajal program. A. Orfila and G. Simarro aregrateful for financial support from Spanish MICINN throughproject CTM2010-12072. M. Luhar was supported on grantnumber 0751358 from the U.S. National Science FoundationOcean Sciences Division. Thanks to the Club Náutico deCala Bona which kindly made available its harbour facilitiesfor executing the field work. Comments from 3 anonymousreferees who helped to improve the work are gratefullyacknowledged.

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Editorial responsibility: Catriona Hurd, Dunedin, New Zealand

Submitted: July 18, 2011; Accepted: April 7, 2012Proofs received from author(s): May 8, 2012