ARTICLE IN PRESS

0278-4343/$ - se

doi:10.1016/j.cs

�Correspondi

E-mail addre

Continental Shelf Research 25 (2005) 185–196

www.elsevier.com/locate/csr

Coastal trapped waves in the northwestern Mediterranean

A. Jordi�, A. Orfila, G. Basterretxea, J. Tintore

IMEDEA (CSIC-UIB), Instituto Mediterraneo de Estudios Avanzados, Miquel Marques, 21, 07190 Esporles, Spain

Received 14 January 2004; received in revised form 25 August 2004; accepted 23 September 2004

Available online 30 November 2004

Abstract

This paper presents a study of coastal trapped waves on the continental margin of the northwestern Mediterranean.

Cyclonically propagating waves along the coast were determined by cross-correlating alongshore current and sea level

time series measured at different locations. Significant correlations between alongshore current time series were

obtained at different time lags corresponding to the first three coastal trapped waves (CTW) modes. However,

correlations between sea level time series were just found for the first CTW mode. The wind-forced coastal trapped

theory (with bottom friction and scattering) was applied to the region and model output was compared with data. This

application used five coastal sections, a summer or winter stratification, and winds from five coastal sites. The model

was able to successfully reproduce observed alongshore current fluctuations in the Catalan Sea. The impact of

stratification on CTW was proposed as the mechanism which reduces the effect of the complex topography on low-

frequency alongshore flow.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Coastal trapped waves; Alongshore current; Northwestern Mediterranean; Catalan Sea; Gulf of Lions

1. Introduction

Coastal trapped waves (CTW) propagate alongthe continental margins of many of the world’socean with the coast on the right (left) in theNorthern (Southern) Hemisphere with periodsranging from a few days to weeks. These wavesaccount for a major part of the large scale, low-frequency sea level and current variability alongthe shelf. They are generated by a full variety of

e front matter r 2004 Elsevier Ltd. All rights reserve

r.2004.09.012

ng author. Fax: +34 971611 761.

ss: vieaajb@uib.es (A. Jordi).

mechanisms including winds at remote locations,the scattering of waves produced by the irregula-rities in the shelf topography and also by oceaniceddies offshore (Huthnance et al., 1986). Coastaltrapped waves can exert an important influence onocean-margin circulation, exchange and mixing(Huthnance, 1995).

Analytical theory explaining wave behavior isquite well established for freely and/or wind drivenpropagating CTW in idealized contexts (assuminguniform along-shelf bathymetry) and where thelong wave approximation can be made (waveperiods of a few days to weeks and alongshore

d.

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196186

scales of motion much greater than the shelfwidth). These coastal trapped waves can berepresented by a sum of modes whose structuresand phase velocities depend on cross-shore topo-graphy and stratification. The amplitude of suchmodes depends on the wind forcing, the dissipa-tion by friction and the scattering of energy toother modes or other kinds of motion. The coastaltrapped wave formalism can predict alongshorecurrent and pressure time series which have beensuccessfully compared with observed time series(Brink, 1991, gives a review).

There are situations however where the CTWformalism should not be expected to yield goodpredictions, i.e., if frictional damping is too strongor if a strong mean flow is present (Brink, 1991).On the other hand, CTW calculations are onlyexpected to resolve shelf processes having largealongshore scales (i.e., pressure and alongshorecurrent). Cross-shelf currents tend to have shortspatial scales (Brink et al., 1994) and are con-sequently poorly hindcast, both in terms ofamplitude and correlation (Chapman, 1987).Furthermore, significant changes in shelf topogra-phy over scales much shorter than length scalesintroduce the possibility of significant scattering ofCTW energy between modes (Wilkin and Chap-man, 1990). Johnson (1991) showed that stratifica-tion plays an important role in the scatteringof CTWs, which is suppressed by a strongstratification.

Identification of CTWs has involved extensivefield studies along many shelves around the worldto confirm that the waves observed have across-shelf modal structures and propagation character-istics consistent with those expected from thetheoretical background (Battisti and Hickey,1984; Freeland et al., 1986; Schumann and Brink,1990). However, to our knowledge there are noprevious studies of coastal trapped waves in thecontinental margin of the northwestern Mediter-ranean. Several studies related to the flow varia-bility seem to indicate the presence of wavespropagating along that shelf. In the Catalan Sea,a mesoscale activity with periodicities around 3and 7.7 days (not correlated with the local wind)has been observed by Font et al. (1995). In theGulf of Lions, Flexas et al. (2002) also observed a

similar type of synoptic variability with a periodi-city around 3.5 and 7 days. Furthermore, Millot(1985) associated an 8 day oscillation on the slopeoff the Gulf of Lions with a propagating wavetrapped by the bottom slope.

The objective of this study is to identify thepresence of coastal trapped waves on the con-tinental margin of the northwestern Mediterra-nean and to determine quantitatively to whatextent the alongshore velocity field can beaccounted for by a wind-forced coastal trappedwave response. The understanding of phenomenaimportant to ocean-margin circulation is requiredfor the coastal/shelf environmental prediction(Pinardi et al., 2003). First, we determine correla-tions at different time lags between records ofalongshore currents and sea level measured atdistant locations. Such correlations are associatedwith southward propagating waves along theCatalan Sea. Next, we apply the theory of wind-forced, frictional, long, coastal trapped wavesalong the coast and compare model predictionswith observations.

2. Material and methods

2.1. Study area

We center the study in the northwesternMediterranean, more specifically in the continentalmargin of the Gulf of Lions and Catalan Sea (Fig.1). Bottom topography is characterized by a broadshelf in the Gulf of Lions and a rather narrow shelfin the Catalan Sea. The regional oceanography isdominated by a cyclonic along-slope density frontwhich forms the northern branch of circulation inthe northwestern Mediterranean, called NorthernCurrent (Millot, 1999). The current separates low-salinity shelf waters with continental influencefrom denser open-sea waters (Font et al., 1988;Alvarez et al., 1996). Its core is typically confinedto the upper 300 m of the water column, has awidth of 30 km and a mean surface velocity ofapproximately 30 cm/s (Garcıa-Ladona et al.,1996). Outside the core the background flow is afew centimeters per second. Stratification largely

ARTICLE IN PRESS

SeteMarseille

Roses

L'Estartit

Vilassar de Mar

BegurPalamós

Mediterranean

A

B

Section 1

Section 2

Section 3

Section 4

Section 5

Gulf ofLions

Catalan Sea

2500

2000

1500

1000

500

200

Fig. 1. Bathymetry in the continental margin of the Catalan

Sea and Gulf of Lions. The triangles represents metrological

observations, squares sea level observations and closed circles

current meter observations. The five topographic sections used

in the forced coastal trapped wave calculations are shown.

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196 187

depends on the season, reaching its highest valuein summer.

2.2. Data and methodology

Time series of currents were collected from fourrecording current meters deployed at moorings Aand B (Fig. 1) at depths of around 1200 m fromJuly13th to November 27th, 2001. Each mooringline was equipped with two current meters atestimated depths of 250 and 500 m, recordingcurrent speed and direction with a 30-min sam-pling period, although current data were hourlyvector-averaged and rotated into the local isobathframe of reference. The current time series will benoted hereafter with their respective mooring letterplus a number indicating their depth (1 for thecurrent meter deployed at 250 m depth and 2 forthe current meter deployed at 500 m).

Sea level data were obtained from an analogicalsea level recorder at L’Estartit and digitized every2 h from March 16th to May 31st 2001. Further,pressure data was obtained from a tide gauge atPalamos during the same period. The original 1-minute pressure time series was adjusted to sealevel with atmospheric pressure obtained at Begur(scale factor 1 cm/mb) and resampled every 2 h forcomparison with sea level at L’Estartit.

To determine possible relationships betweentime series of alongshore currents at 250 m (A1and B1), alongshore current at 500 m (A2 and B2)and sea level, cross-correlation functions were

computed. However the cross-correlation functionstrongly depends on the structure of the originaltime series through the auto-correlation, implyingfictitious cross-correlations between time series ifthey are auto-correlated and computations aredirectly carried out with the original records (Katz,1988). Since oceanic time series are commonlyhighly auto-correlated (Orfila et al., in press) it isnecessary to reduce original time series to residualseries which are not auto-correlated. We accom-plished this reduction using a pre-whitening methodin order to avoid artificial cross-correlations.

Briefly, pre-whitening method consists in fittinga p-order autoregressive model -AR(p)- of the form

xðtÞ ¼ a1xðt � 1Þ þ � � � þ apxðt � pÞ þ fðtÞ (1)

to the original time series x, sufficient to reduce theresiduals f to white noise. The time series x is thenfiltered with the model (1) to obtain the white noiseresidual series f (Katz, 1988). The filter order p ofthe autoregressive process was selected prior to theanalysis following the Akaike Information Criter-ion (AIC) which determines the model order p by ageneralization of the maximum likelihood criter-ion (Akaike, 1974; Konyaev, 1990). The residualsof the time series f obtained after fitting the AR(p)process are not auto-correlated and were used tocompute the cross-correlation functions.

2.3. Coastal trapped waves theory

In this section we summarize the CTW theoryfor completeness. Details of the model formulationare not reproduced here, but they are given by theworks cited below. Considering a linear Boussi-nesq, hydrostatic and free-surface ocean withfrequencies smaller than the inertial frequency f

and with alongshore scales larger than the cross-shelf scales, the equations of motion can be solvedby expanding the perturbation pressure p as freeCTW modal structures Fn and their associatedamplitudes fn (Chapman, 1987)

pðx; y; z; tÞ ¼X1n¼1

Fnðx; zÞfnðy; tÞ; (2)

where x, y and z are cross-shelf, alongshore andvertical coordinates, t is time and n represents the

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196188

CTW mode. The free CTW modal structures aresolutions to the following eigenvalue problem

Fnð Þxx þ f 2 ðFnÞz

N2

� �z

¼ 0; (3a)

subject to the boundary conditions

ðFnÞz þ N2hxf �2½ðFnÞx þ fc�1

n F n ¼ 0

at z ¼ �hðxÞ; ð3bÞ

gðFnÞz � N2F n ¼ 0 at z ¼ 0; (3c)

ðFnÞx þ fc�1n F n ¼ 0 at x ¼ 0; (3d)

Fn ! 0 at x ! 1; (3e)

where N2ðzÞ is the buoyancy frequency, h(x) is thewater depth which increases monotonically offshoreuntil reaching a constant depth, subscripts x and z

represent partial differentiation, f is the Coriolisparameter, and the free-wave phase velocity (cn) isthe eigenvalue of this problem. The boundaryconditions represent no flow through the bottom(3b), a free surface (3c), no flow through the coast(3d), and coastal trapping (3e). The modal structuresFn are orthonormalized in a way that satisfies energyconservation (Brink, 1989).

Following Clarke and Van Gorder (1986), theamplitudes fn in (2) which vary along the coastand in time satisfy a set of coupled first-order waveequations subject to forcing by the alongshorewind stress tyðy; tÞ

ðfnÞy � c�1n ðfnÞt þ

X1m¼1

anmfm ¼ bntyðy; tÞ; (4a)

where

anm ¼1

f

Z 1

0

Fnðx;�hÞfrðxÞ � ½Fmðx;�hÞxgxdx

þ1

f

Z 0

�h

F nðx; zÞ½Fmðx; zÞxrðxÞ

h xð Þ

����x¼0

dz; ð4bÞ

bn ¼1

hð0Þ

Z 0

�h

Fnð0; zÞdz (4c)

and ann is the frictional decay, anm is the frictionalcoupling to mode m, bn is the wind couplingcoefficient and r(x) is the linear bottom frictioncoefficient.

To compute the wave response along the coast,the coastal zone is divided into sections whereFnðx; zÞ and cn are computed from (3) and anm andbn from (4b) and (4c). Then (4a) is integrated alongthe coast to find fnðy; tÞ: The resulting fnðy; tÞ arecombined with F nðx; zÞ to predict p from (2).Similary, alongshore current can be estimated from

vðx; y; z; tÞ ¼�1

r0f½pðpðx; y; z; tÞx

¼�1

r0f

X1n¼1

½Fnðx; zÞxfnðy; tÞ; ð5Þ

where r0 is the mean density and g is gravity.The stratification parameter S measures the

relative importance of stratification and bottomtopography in coastal trapped waves and isdefined as NH/fL, where N, H and L are typicalvalues of buoyancy frequency, depth and cross-shelf horizontal scale, respectively. For Sb1 thewaves are affected mainly by stratification andrespond baroclinically. Conversely, for S51 thewaves are affected mainly by bottom topographyand approach to (barotropic) continental shelfwaves. When coastal trapped waves pass throughan irregularity on the bottom shelf topography,energy can be transfered between modes (scatter-ing). Johnson (1991) gave a simple formula fordetermining the amplitude of transmitted modes ifthe flow is confined to frequencies low comparedto the product of the stratification parameter andthe Coriolis parameter (o5S � f )

qnm ¼

Z 0

�hð1Þ

Fþn ðdþðzÞ; zÞF

�mðd�ðzÞ; zÞdz; (6)

where qnm is the scattering ratio of the amplitudeof scattered mode n to that of incident mode m,F is evaluated before (+) and after (�) theirregularity in shelf topography, and d(z) is thedistance of isobath z from the coast.

2.4. Application of CTW theory to the

northwestern Mediterranean

To compute the free CTW modal structuresalong the northwestern Mediterranean coast, weapplied a modified version of the Brink andChapman (1985) model. The coastal zone was

ARTICLE IN PRESS

Cross-correlation

Cross-correlation

-correlation

(a)

(b)

(c)

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196 189

divided into 5 sections (Fig. 1). A single cross-shelftransect was defined for each coastal section usinga depth profile averaged along-shore in therespective section and a vertical coastal wall of15 m. A stratification profile N2ðzÞ along eachtransect was horizontally averaged from Medar/

medatlas II database (http://modb.oce.ulg.ac.be/Medar) for winter and summer periods. Thebottom friction coefficient r was taken to beconstant for simplicity. For each coastal section,a regular grid in the cross-shelf direction andstretched in the vertical direction to enhanceresolution in shallow areas was implemented. Weused 60 points in the horizontal and 100 levels inthe vertical. This rather fine resolution wasnecessary to determine correctly modal structuresin Section 1 (see below).

To calculate the amplitude of free CTW modeswe followed the algorithm of Clarke and VanGorder (1986) with a time step (Dt) of 6 h and analong-shore distance (Dy) of 10 km. The along-shelf topography and stratification are uniform foreach coastal section and correspond to profilesused for the computation of free CTW modalstructures. The boundaries between sections aretopographic discontinuities where scattering be-tween CTW modes is computed using (6). Theeastern edge of the Gulf of Lions was chosen as theorigin of integration of the wave equations (4) andthe amplitude here was taken to be zero. Thisassumes that free CTW activity entering the modeldomain at the origin does not reach the regionwhere current time series were collected. The windstress field tyðy; tÞ was approximated from avail-able stations (Fig. 1) along the coast using linearinterpolation. However, Section 1 was forced bythe wind stress from Marseille since no wind dataeast of Marseille was available.

Cross

Fig. 2. Cross-correlation between (a) alongshore current time

series at 250 m depth at mooring A and at mooring B, (b)

alongshore current time series at 500 at mooring A and at

mooring B, and (c) sea level time series at L’Estartit and at

Palamos. Grey lines indicate the 95% confidence levels

generated by Monte-Carlo simulations.

3. Results

3.1. Time series results

Cross-correlation functions were calculatedfrom the residuals of alongshore current and sealevel time series obtained after the prewhiteningmethod. The order of the prewhitening filter

selected with the AIC was p ¼ 38 for A1 andp ¼ 65 for B1; p ¼ 41 for A2 and p ¼ 48 for B2;and p ¼ 21 and p ¼ 31 for sea level at Palamosand L’Estartit. Auto-correlation functions werecomputed to check that resulting filtered timeseries were not significantly auto-correlated.

Relevant cross-correlation between alongshorecurrent time series at 250 m depth (A1 and B1) andat 500 m (A2 and B2) was found at time lags of 1and 4 h, as shown in Fig. 2a and b. Even thoughcorrelations are significant at time lags of 10 and22 h for A1 and B1 and at 9 and 23 h for A2 andB2, evidence is not too strong. No relevant cross-correlations were found at higher time lags.Taking into account that points A and B wereseparated by 33 km, these time lags would beassociated with southward propagating waves withphase speeds of 920, 230, 90 and 40 cm/s.

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196190

Conversely, correlation between sea level timeseries occurred at the first four hours of time lag(Fig. 2c). Comparing with the correlations foralongshore currents, we found the same cross-correlation at 4 h since the distance between sealevel stations was similar to the distance betweencurrent meters. The correlation at 1 h could bemasked by sea level correlations between 0 and 4 hsince the time resolution for sea level time serieswas 2 h (notice that correlation at 2 h was obtainedfor sea level). But alongshore current correlationsat 9–10 and 22–23 h were not found for sea leveltime series. Furthermore, as expected by thegeographical proximity of the locations wherethe time series were measured, tides yield aninstantaneous correlation (not found for along-shore currents) between sea level time series.

3.2. Free CTW modes

Free CTW parameters calculated for summerstratification are shown in Table 1. Only the firstthree modes were computed because of theincreased sensitivity of the higher modes to the

Table 1

Values of stratification parameter (S), phase speed (cn), wind

forcing coefficients (bn) and frictional decay coefficients (ann) for

the first three CTW modes off the coast of the northwestern

Mediterranean

Section S Mode cn

(cm/s)

bn

(s1/2 cm�1/2)

ann

(10�8 cm�1)

1 16.48 1 108 0.98 4.73

2 58 0.81 8.20

3 37 0.54 9.80

2 0.61 1 226 1.10 2.11

2 110 0.79 3.40

3 49 0.81 8.71

3 0.15 1 244 0.75 1.15

2 119 0.61 2.33

3 59 1.15 14.5

4 1.94 1 243 0.82 0.95

2 85 0.85 5.32

3 50 0.92 16.61

5 1.41 1 243 0.76 0.93

2 85 0.70 6.27

3 46 0.71 11.23

The values were calculated for a mean topography of each

coastal section and for summer stratification. The ann were

calculated for a bottom friction coefficient of 0.005 cm s�1.

input parameters (Chapman, 1987). Phase speedsin Sections 2–5 were rather similar and higher thanthose calculated in Section 1 where the stratifica-tion parameter was larger. Notice that phasespeeds in Sections 4 and 5 were very similar.Frictional decay affects higher modes much morethan lower modes and this decay tends to be slowfor modes 1 and 2 in the higher-numberedsections. The alongshore decay scale in the firstsection ða�1

nm ¼ 211 kmÞ; which was shorter than thedistance from the origin to the region wherecurrent time series were collected, justified thatno free CTW activity entering the model domainat the origin reached this region of interest.

The first three free CTW modal structures forthe alongshore current are shown in Fig. 3.According to the stratification parameter, CTWmodes approached barotropic waves in Section 3and modes in other sections were less affected byvariable bottom topography. In general, CTWmode 1 had a simple structure in comparison withother modes as expected. Mode 2 was moreinfluenced by the stratification and had a bot-tom-trapped minimum. Mode 3 had a two layerKelvin-wave-like structure with the maximumvalues at coast. Only the CTW modes for summerstratification have been described here, but calcu-lation for winter stratification gave similar resultsalthough structures were more barotropic.

To check if CTW modes were well determinedwe calculated the orthonormality of modes. As aresult of this orthonormality, the product dmn ofthe CTW modes should ideally be zero for man

(one for m ¼ n). Maximum values of 0.15 for dmn

(man) were obtained in Section 1. The ratherextreme topography/stratification combination ofSection 1 apparently stretched to the limit thisnumerical method for mode determination (Brinkand Chapman, 1985). Poor orthonormality in dmn

were obtained when coarsening the spatial resolu-tion in the numerical model. To determine thesensitivity of the model to context, we completedseveral tests for variations in the vertical coastalwall, depth profiles, stratification profiles andbottom friction coefficient. The phase speed forthe first three CTW modes was relatively un-affected (less than 10%) by moderate changes inthe context parameters.

ARTICLE IN PRESS

00

0

0

0

0

0

0

0

0

0

00

00

0

0

-2

1

1

1

1

1

1

1

1

-1

-1

-1

-1

-1 -1 -1

-1

-1-1

-1

-1

-1

-1-2

2

-2

-2

-2

-2

-3-3

-3

2

2

3

B1 B1 B1

B2 B2 B2

A2 A2 A2

A1 A1 A1

Fig. 3. The first three theoretical CTW modal structures for the calculated alongshore velocity using summer stratification for each

coastal section. Shading represents sign and the scaling is arbitrary. Closed circles represent the position of current meters on Sections 4

and 5.

Table 2

Energy (in %) entering the section boundary scattered among

other modes ð1 � q2nnÞ calculated for summer stratification

Mode Section boundaries

1–2 2–3 3–4 4–5

1 0.0 8.5 13.3 1.1

2 1.7 9.3 15.3 2.7

3 4.5 13.3 19.8 4.9

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196 191

The energy entering the section boundariesscattered among other CTW modes is shown inTable 2. We found more scattering of CTW energywhere stratification was weaker since strongstratification suppresses scattering, in agreementwith previous works (Wilkin and Chapman, 1990;Johnson, 1991). In Sections 4 and 5 boundary,although stratification was moderate, the energyscattered was low because depth profiles before

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196192

and after the boundary were quite similar. Theabove scattering formulation satisfies energy con-servation for an infinite number of modes. Sincewe used only the first three modes, the total energycrossing a section could be less than that crossingto the next section. In practice such truncationerror may not be important since most CTWenergy is usually concentrated in the lowest modes(Pizarro and Shaffer, 1998). The results belowshow that, in our case.

3.3. Comparison between CTW theory and

observations

To compare simulation outputs (from theapplication of wind-forced CTW theory to thenorthwestern Mediterranean) with alongshorecurrent observations, a number of simulationswere performed using different inputs. Table 3presents a selection of these comparisons quanti-

Table 3

Results of the comparison between CTW model simulations at the pos

observed currents

Number of modes r Scatt A1

Corr Reg

Summer stratification

1 0 0.70 0.74

2 0 0.70 1.30

3 0 0.71 0.88

1 0.005 No 0.70 0.84

2 0.005 No 0.67 1.36

3 0.005 No 0.63 0.73

1 0.005 Yes 0.69 0.83

2 0.005 Yes 068 1.05

3 0.005 Yes 067 0.70

1 0.02 No 0.63 1.34

1 0.02 Yes 0.63 1.30

Winter stratification

1 0 0.70 0.84

2 0 0.70 1.20

1 0.005 No 0.70 1.01

2 0.005 No 0.69 1.36

1 0.005 Yes 0.70 1.02

2 0.005 Yes 0.69 1.28

1 0.02 Yes 0.67 0.86

Simulations use different numbers of modes, different bottom friction

topography or no scattering.

fied by a linear regression fit using correlation andregression coefficients (Mitchum and Clarke, 1986;Chapman, 1987; Pizarro and Shaffer, 1998). Someof the changes in the correlation and regressioncoefficients in Table 3 were statistically significantonly at a rather low confidence level. In general,de-meaned observed and predicted current timeseries were correlated more than 50% and smallvariations in the input parameters reflected smallchanges in the fit.

The best fit to data was achieved with the modelof the first three CTW modes and no bottomfriction (Table 3). Fig. 4 shows a comparisonbetween low-passed alongshore flow observed andsimulated. In this case, the correlation was quitegood, but fluctuation amplitudes were under-estimated at all current meters. Table 3 showsthat the model predictions were relatively insensi-tive to the number of modes used in the calcula-tions and to the inclusion of scattering.

itions of current meters and de-meaned, low-passed, alongshore

A2 B1 B2

Corr Reg Corr Reg Corr Reg

0.65 1.40 0.66 0.65 0.60 0.85

0.63 0.66 0.66 1.34 0.59 0.74

0.68 0.67 0.68 0.67 0.66 0.84

0.62 1.22 0.65 0.71 0.58 0.94

0.69 0.74 0.57 1.25 0.59 1.31

0.57 1.32 0.58 1.44 0.54 0.83

0.62 0.62 0.65 0.71 0.58 0.93

0.69 1.28 0.67 1.24 0.61 1.31

0.54 1.33 0.59 1.26 0.51 1.32

0.48 1.24 0.53 1.04 0.47 1.33

0.47 1.23 0.53 1.01 0.47 1.30

0.66 0.68 0.67 0.74 0.62 0.98

0.68 0.80 0.68 1.34 0.63 0.58

0.64 0.96 0.67 0.88 0.61 1.17

0.69 0.70 0.68 1.46 0.63 0.61

0.65 0.97 0.67 0.89 0.61 1.17

0.69 0.76 0.68 1.45 0.64 0.60

0.56 1.34 0.59 0.61 0.52 1.21

coefficients (r, in cm/s), and scattering due to changes in bottom

ARTICLE IN PRESS

Fig. 4. Comparison between the de-meaned, low-passed, observed alongshore currents (black line) and the simulated alongshore

currents (grey line) at A1, A2, B1 and B2 (top to bottom). Simulations are for the first three CTW modes and no bottom friction.

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196 193

Simulations including bottom friction degradedthe model fitting to the data. For winter stratifica-tion, the energy scattered was more importantsince stratification is weaker. However for thiscase, simulations including scattering did not leadto significant improvement in fit to data comparedto simulations without scattering.

In general, the correlation between observedand simulated alongshore currents was better at250 m (A1 and B1) than at 500 m (A2 and B2) inagreement with the fact that the CTW modes havetheir largest signal on the continental shelf.Furthermore, the agreement was better for current

meters located at the north (A1 and A2) than forthose located at the south (B1 and B2). This couldbe due to the submarine canyon located betweenboth current meter moorings. It is a well knownfact that submarine canyons affect the spatialpattern of regional circulation; however, meanflow at some distance above the canyon( 50–100 m) is generally little affected due tostratification (Hickey, 1997). Thus, the modifica-tions produced by the interaction of the currentwith the canyon would have their largest signals atthe deeper parts where stratification is less intense.In light of these and other possible complications,

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196194

it is notable that the simple model used here is ableto hindcast the observed alongshore currents asshown here.

4. Discussion

In the present paper, the analysis of currentmeter and sea level time series collected in thecontinental margin of the northwestern Mediter-ranean evidenced common features. Significantcorrelations between alongshore current timeseries were obtained at time lags of 1, 4, 10 and22 h, which were associated with southwardpropagating waves at phase speeds of 920, 230,90 and 40 cm/s, respectively. Concerning sea leveltime series, correlations occurred at the first 4 h oftime lag but no significant correlations were foundfor other time lags. Furthermore, as expected bytidal effects, sea level time series were alsocorrelated instantaneously.

In order to explain the correlation between timeseries, we worked out the phase speeds that mightbe related to free CTW modes using the modeldeveloped by Brink and Chapman (1985), asstated. The model yield values of 243, 85 and46 cm/s for the first three CTW modes, which werequite close to the last three phase speeds obtainedfrom alongshore current time series correlations.Therefore, these results provided evidence thatcorrelations described above may be related toCTW. Further, it was not surprising that sea leveltime series were just related by the phase speed of230 cm/s (with the exceptions of the instantaneouscorrelation caused by tides and correlation at a timelag of 1 h explained bellow) since the dynamics forthe coastal pressure field can essentially be describedby the first mode (Brink, 1982).

Although there are to our knowledge noprevious studies of CTW in the northwesternMediterranean, Echevin et al. (2003) studied theinteraction of a baroclinic costal current associatedwith a Kelvin wave with idealized shelf topogra-phy of the Gulf of Lions using an analytical model.In fact, for large S the behavior of CTW modes islike that of internal Kelvin waves (Brink, 1991).Echevin et al. (2003) found that the interactiongenerated a system of a baroclinic wave and a

barotropic/baroclinic double Kelvin wave thatpropagated along the shelf break of the gulf atspeeds of around 180 and 90 cm/s respectively,which are close to the speed of the two first CTWmodes. Thus, perturbations of the NorthernCurrent in the form of Kelvin waves, generatedeast of the gulf, can trigger CTW when they reachthe eastern edge of the Gulf of Lions shelf.

The analysis of our results with regard to datadeserves attention too. As mentioned in theintroduction, the presence of waves propagatingalong the shelf has been dated with periodicitiesaround 3–3.5 days and 7–8 days. Millot (1985)associated the 7–8 days oscillation with a wavetrapped by the bottom slope and did notinvestigated CTW because records did not revealfeatures similar to those observed in the lower partof the slope. On the other hand, the most energeticsignal for the 3–3.5 days variability over thecontinental slope of the Gulf of Lions has beendetected near the shelf and at surface (Flexas et al.,2002). This fact supports that the 3–3.5 daysperiodicity could be due to CTW.

These results suggested that wind-forced coastaltrapped wave theory may predict time seriesobserved in the continental margin of the north-western Mediterranean successfully. Here we appliedthis theory using five coastal sections with a depth-averaged cross-shelf transect defined for each sectionand a mean buoyancy profile from climatologicalvalues. We also assumed zero CTW amplitude at theeastern edge of the Gulf of Lions, the starting pointfor our forced wave integration. We forced themodel with wind records from five weather stationsalong the coast of the northwestern Mediterranean.Simulation outputs were compared with observedlow-frequency alongshore currents.

Our results indicated that the correlationbetween the model outputs and the observedalongshore currents was highly significant. How-ever, other applications of CTW models to shelfand slope circulation have had greater correlationsbetween predicted and observed data (e.g., Chap-man, 1987). The rather complex bathymetry in thecontinental margin of the northwestern Mediter-ranean could be an obstacle for the classic CTWformalism. However, Codiga et al. (1999) foundthat coastal trapped wave propagation in a

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196 195

continuously stratified ocean remains largely un-modified by submarine canyons and the loss ofenergy by scattering is weak. In fact, the effect ofstratification is to limit the vertical extent of theinfluence of the canyon topography on the flowpattern (Ardhuin et al., 1999; Jordi et al., in press).This argument is also supported by the lack offrictional and scattering effects found in compar-ing simulation and predictions.

Another obstacle for the CTW theory could bethe Northern Current. As mentioned, Kelvinwaves associated with the Northern Current andgenerated east of Gulf of Lions can generate CTWwhen they interact with the gulf shelf. Further-more, the presence of a mean alongshore flow overthe shelf can alter the free wave properties throughDoppler shifting and/or modification of the back-ground vorticity field by allowing the growth ofinstabilities (Brink, 1991). The agreement betweenthe phase speed observed and predicted by theCTW theory discards a modification of the freewave properties. However, the presence of mean-ders in the Northern Current generated bybaroclinic instability has been reported (Flexas atal., 2002) and could explain the discrepanciesbetween the wind-forced CTW model outputs andthe observed alongshore currents. Nevertheless,the data used in this study were taken in summerand earlier autumn when the intensity of theNorthern Current and its mesoscale activity isrelatively low (Font et al., 1995).

The CTW model predictions were relativelyinsensitive to the number of modes used incalculations. The second and third CTW modesdo not seem to help much the fit of the simulationto observation. This weakens the evidence for thepresence of second and third CTW modes.However, the best fit between simulated andobserved alongshore currents was achieved withthe first three modes. Previous simulations havebeen applied using different numbers of modes,ranging from one (Battisti and Hickey, 1984) toseven (Mitchum and Clarke, 1986). The number ofmodes necessary to predict a particular quantity isnot clear and depends on the quantity (i.e.,pressure, alongshore currenty) and the locationwhere the CTW model has been applied (Clarkeand Van Gorde, 1986).

5. Conclusion

We have identified the presence of coastaltrapped waves in the northwestern Mediterranean.Our results indicate alongshore propagation ofcoastal trapped waves along the continentalmargins of the Gulf of Lions and Catalan Sea.The analysis of current meter and sea level timeseries collected in the continental margin evi-denced common features which were explainedby a coastal trapped wave response. Phase speedsof the waves were determined by cross-correlatingthe time series and successfully compared with thetheoretical values.

The wind-forced coastal trapped wave theoryappears to be able to successfully describe low-frequency alongshore current fluctuations on thecontinental margin of the northwestern Mediter-ranean. Our results also demonstrated that coastaltrapped waves account for a significant percentageof the low-frequency alongshore currents over theCatalan shelf. Because of its success, this theoryrepresents an important tool for both under-standing the wind forced response of shelf watersat low frequencies and inferring the relativeimportance of other forcing mechanisms.

Acknowledgements

This work has been partially supported by theCANYONES (MAR1999-1060) CICYT projectand by the European Comission (D. G. Research)funded projects SOFT (EVK3-CT-2000-00028)and MFSTEP (EVK3-CT-2002-00175). Theauthors would like to thank Dr. K. Brink andDr. D.C. Chapman for supplying the numericalCTW model. Anonymous reviewers made relevantcomments which were very useful in improving themanuscript.

References

Akaike, H., 1974. A new look at the statistical model

identification. IEEE Transactions Automatic Controrl 19,

716–723.

Alvarez, A., Tintore, J., Sabates, A., 1996. Flow modification of

shelf-slope exchange induced by a submarine canyon off the

ARTICLE IN PRESS

A. Jordi et al. / Continental Shelf Research 25 (2005) 185–196196

northeast Spanish coast. Journal of Geophysical Research

101, 12043–12055.

Ardhuin, F., Pinot, J.M., Tintore, J., 1999. Numerical study of

the circulation in a steep canyon off the Catalan coast.

Journal of Geophysical Research 104, 11115–11135.

Battisti, D.S., Hickey, B.M., 1984. Application of remote wind-

forced coastal trapped wave theory to the Oregon and

Washington coasts. Journal of Physical Oceanography 14,

887–902.

Brink, K.H., 1982. A comparison of long coastal trapped wave

theory with observations off Peru. Journal of Physical

Oceanography 12, 897–913.

Brink, K.H., Chapman, D.C., 1985. Programs for computing

properties of coastal-trapped waves and wind-driven mo-

tions over the continental shelf and slope. Technical report,

Woods Hole Oceanogr. Inst., Woods Hole.

Brink, K.H., 1989. The effect of stratification on seamount-

trapped waves. Deep-Sea Research 36, 825–844.

Brink, K.H., 1991. Coastal-trapped waves and wind-driven

currents over the continental shelf. Annual Review of Fluid

Mechanics 23, 389–412.

Brink, K.H., LaCasce, J.H., Irish, J.D., 1994. The effect of

short-scale wind variations on shelf currents. Journal of

Geophysical Research 99, 3305–3315.

Chapman, D.C., 1987. Application of wind-forced, long,

coastal-trapped wave theory along the California coast.

Journal of Geophysical Research 92, 1789–1816.

Clarke, A.J., Van Gorder, S., 1986. A method for estimating

wind-driven frictional, time-dependent, stratified shelf and

slope water flow. Journal Physical Oceanography 16,

1013–1028.

Codiga, D.L., Renouard, D.P., Fincham, A.M., 1999. Experi-

ments on waves trapped over the continental slope and shelf

in a continuously stratified rotating ocean, and their

incidence on a canyon. Journal of Marine Research 57,

585–612.

Echevin, V., Mortier, L., Crepon, M., 2003. Interaction of a

coastal current with a gulf: application to the shelf

circulation of the Gulf of Lions in the Mediterranean Sea.

Journal of Physical Oceanography 33, 188–206.

Flexas, M.M., Durrieu de Madron, X., Garcia, M.A., Canals,

M., Arnau, P., 2002. Flow variability in the Gulf of Lions

during the MATER HFF experiment (March–May 1997).

Journal of Marine Systems 33–34, 197–214.

Font, J., Salat, J., Tintore, J., 1988. Permanent features of the

circulation in the Catalan Sea. Oceanologica Acta 9, 51–57.

Font, J., Garcia-Ladona, E., Gorriz, E.G., 1995. The season-

ality of mesoscale motion in the Northern Current of the

western Mediterranean: several years of evidence. Oceano-

logica Acta 18, 207–219.

Freeland, H.J., Boland, F.M., Church, J.A., Clarke, A.J.,

Forbes, A.M.G., Huter, A., Smith, R.L., Thompson,

R.O.R.Y., White, N.J., 1986. The Australian Coastal

Experiment: a search for coastal-trapped waves. Journal

of Physical Oceanography 16, 1230–1249.

Garcıa-Ladona, E., Castellon, A., Font, J., Tintore, J., 1996.

The Balearic current and volume transports in the Balearic

basin. Oceanologica Acta 19, 489–497.

Hickey, B.M., 1997. The Response of a steep-sided, narrow

canyon to a time-variable wind forcing. Journal of Physical

Oceanography 27, 697–729.

Huthnance, J.M., Mysak, L.A., Wang, D.P., 1986. Coastal

trapped waves. In: Mooers, C.N.K. (Ed.), Baroclinic

processes on the continental shelves. American Geophysical

Union, Washington, pp. 1–18.

Huthnance, J.M., 1995. Circulation, exchange and water

masses at the ocean margin: the role of physical processes

at the shelf edge. Progress Oceanography 35, 353–431.

Johnson, E.R., 1991. The scattering at low frequencies of

coastally trapped waves. Journal of Physical Oceanography

21, 913–932.

Jordi, A., Orfila, A., Basterretxea, G., Tintore, J., Shelf-slope

exchanges by frontal variability in a steep submarine

canyon. Progress in Oceanography, in press.

Katz, R.W., 1988. Use of cross correlations in the search for

teleconnections. Journal of Climate 8, 241–253.

Konyaev, K.V., 1990. Spectral Analysis of Physical Oceano-

graphic Data. Rus. Trans. Ser., vol. 81, 217 pp., A.A.

Balkema, Rotterdam.

Millot, C., 1985. Evidence of a several-day propagating wave.

Journal of Physical Oceanography 15, 258–272.

Millot, C., 1999. Circulation in the Western Mediterranean Sea.

Journal of Marine Systems 20, 423–442.

Mitchum, G.T., Clarke, A.J., 1986. Evaluation of frictional,

wind-forced long-wave theory on the West Florida shelf.

Journal of Physical Oceanography 16, 1029–1037.

Orfila, A., Alvarez, A., Tintore, J., Jordi, A., Basterretxea, G.,

Climate teleconections in the Ligurian Sea inferred from

satellite data. Progress in Oceanography, in press.

Pinardi, N., Allen, I., Demirov, E., De Mey, P., Korres, G.,

Lascaratos, A., Le Traen, P.-Y., Maillard, C., Manzella, G.,

Tziavos, C., 2003. The Mediterranean ocean forecasting

system: first phase of implementation (1998–2001). Anales.

De Geophysique 21, 3–20.

Pizarro, O., Shaffer, G., 1998. Wind-driven coastal-trapped

waves off the island of Gotland, Baltic Sea. Journal of

Physical Oceanography 28, 2117–2129.

Schumann, E.H., Brink, K.H., 1990. Coastal-trapped waves off

the coast of South Africa: Generation, propagation and

current structures. Journal of Physical Oceanography 20,

1206–1218.

Wilkin, J.L., Chapman, D.C., 1990. Scattering of coastal

trapped waves by irregularities in coastline and topography.

Journal of Physical Oceanography 20, 396–421.