statistical analysis of the surface circulation in the algerian current using lagrangian buoys

Ž .Journal of Marine Systems 29 2001 69–85www.elsevier.nlrlocaterjmarsys

Statistical analysis of the surface circulation in the AlgerianCurrent using Lagrangian buoys

Jose Salasa,b, Emilio Garcıa-Ladonaa,), Jordi Fonta´ ´a Institut de Ciencies del Mar, CSIC, Passeig Joan de Borbo, srn. 08039 Barcelona, Spain`

b CICESE en BCS Miraflores 334, ErMulege y La Paz, 23050, Baja California Sur, Mexico

Received 15 October 1999; accepted 29 August 2000

Abstract

Ž .The Algerian Current AC is one of the most energetic flows in the Mediterranean basin. A characteristic picture of thiscurrent is formed by a series of mesoscale eddies at different scales. Here, statistical analysis of 15 surface Argos buoytracks in 1996–1997 provides a complete Lagrangian view of the AC. The buoys, released upstream and across a coastalmeander between 08E and 18E longitude, were followed for 3 months. They travelled eastward at an average speed of 14cmrs and showed high energetic fluctuations related to several mesoscale eddies. The characteristic integral time and spacescales are highly anisotropic. For the zonal component, these are about 4 days and 66 km, and for the meridional component,about 2 days and 26 km. Representative values of effective diffusivities from single dispersion statistics are within0.7–1.3=108 and 1.5–6.0=107 cm2rs for the zonal and meridional directions, respectively. A local analysis shows thatmesoscale motions are particularly relevant in the region 1–38E and 7–88E, provided the considerably high values of eddykinetic energy in comparison with the mean kinetic energy. Eddy–mean current interactions are evidenced by the significantchanges of sign of horizontal covariance from west to east. Finally, an Eulerian picture of the AC is built, exhibiting similartrends than previous and recent field observations.q2001 Elsevier Science B.V. All rights reserved.

Keywords: Surface circulation; Algerian Current; Lagrangian buoys

1. Introduction

Surface Atlantic waters enter the Mediterraneanbasin through the Strait of Gibraltar and circulatewithin the Alboran Sea. By mixing with residentwaters, they give rise to modified Atlantic waters,

Ž .hereafter called MAW Gascard and Richez, 1985 .At the eastern border of this region, MAW encoun-ter surface Mediterranean waters, forming theAlmerıa–Oran front oriented in a NW–SE direction´

) Corresponding author. Fax:q34-93-221-7340.

Ž .Tintore et al., 1988 . The MAW jet reaches the´North African coast near 18W and then flows alongthe Algerian and Tunisian coasts towards the Sar-dinia Channel and the Strait of Sicily. This flow ofMAW is currently known as the Algerian CurrentŽ .AC , and is the most energetic current in theMediterranean Sea. From 18E to 28E, the AC isaffected by mesoscale processes, which begin as ameandering of the stream and then producing eddiesthat may grow until they reach a characteristic diam-eter of about 50–100 km and propagate downstream.Some of them may detach from the current and

0924-7963r01r$ - see front matterq2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0924-7963 01 00010-0

( )J. Salas et al.rJournal of Marine Systems 29 2001 69–8570

persist up to several months offshore in the AlgerianŽbasin with a deep vertical signature Millot, 1985;

.Taupier-Letage and Millot, 1988 .These mesoscale eddies are very energetic, in the

sense that they have high eddy kinetic energy valuescompared with the mean flow, and strongly modifythe circulation in the Algerian basin. Their role in thedistribution of heat, salt and momentum through thewhole Algerian basin is a question that has not yetbeen sufficiently addressed, but which certainly hasa large impact on the dynamics of the WesternMediterranean. For several reasons, few field studieshave been undertaken in this region, remote sensingbeing the most important source of data to dateŽ .Taupier-Letage and Millot, 1988 . Thus, within the

Žframework of the MATER project second phase,1996–1999, of the Mediterranean Targeted Project

.of the EU MAST program , great effort was put intostudying the Algerian basin to understand the dy-namics of the mesoscale eddies and their effects onthe marine ecosystem.

As part of the MATER project, a field experimentŽ .ALGERS’96 was carried out to study the dynamicsof the mesoscale eddies in the AC, and a set ofLagrangian buoys was released to track the path of

Ž .the MAW Font et al., 1998 . The use of Lagrangianbuoys is a low-cost alternative for surveying large,poorly known areas of the ocean; this being wellexemplified by the Algerian basin. Furthermore, La-grangian buoys have widely proved to be an appro-priate instrument in describing the evolution of largeand mesoscale motions of ocean currents, and inunderstanding the dynamic properties of the oceanŽi.e. Davis, 1985a,b; Poulain and Niiler, 1989; Bower,

.1989; Brink et al., 1991; Richez, 1998 .With the statistical properties inferred from the

trajectories, followed by Lagrangian buoys, it ispossible to characterize the diffusion properties in

Žseveral oceanic regions Colin de Verdiere, 1983;`.Haynes and Barton, 1991; Davis, 1994 . This can be

used to know how mesoscale activity acts as aneffective mechanism for distributing energy, momen-tum and heat in such regions, and also to validate therepresentation of oceanic mixing in numerical mod-els. For example, large mesoscale eddies generallyobserved in the open ocean have Lagrangian spaceand time scales ofL;50–100 km andT;10 days,respectively, with horizontal Lagrangian diffusivities

K;107 cm2rs. In coastal areas where eddies mayhave smaller Lagrangian characteristic scales,L;30km, andT;1–2 days, typical diffusivities areK;

4 6 2 Ž .10 –10 cmrs Davis, 1985b . The analysis ofbuoys released during the ALGERS’96 experimentprovided us with new, different and complementaryapproach to the AC, and allowed us to quantify thevariability of the mesoscale activity present in suchcurrent.

ŽDuring MEDIPROD-5 experiment June 1986–.March 1987 , combined Lagrangian and Eulerian

measurements were undertaken to study the dynam-Ž .ics of the AC Millot, 1991 . Five buoys were re-

leased close to 28E and started to progress toward theeast within the AC. Between 48E and 68E, the buoyswere drastically affected by the mesoscale variabil-ity, deflected to the north, and did not follow theusual MAW flow, which goes from the Alboran Seato the Strait of Sicily. From the analysis of severalmooring arrays deployed along the Algerian shoreŽ .between 18E and 58E , it was possible to infer somestatistical properties of the variability of the ACŽ .Millot et al., 1997 . A mean eastward transportparallel to the isobaths was observed in almost alllocations and at several depths. In the uppermost

Ž .records 100-m depth , the mean values in coastalareas decrease toward the east. Variances did notvary significantly, but were larger than the meanvalues in the easternmost part. Time correlation scales

Žalong the coast were larger than across it 6–16 and.4–10 days, respectively , with a progressively east-

ward increase of such values for the cross-shorecomponent. The representativity of the statistical re-sults was, in part, affected by the number and loca-tion of the mooring arrays. In addition, data recordedby currentmeters at 100 m could not quantify ade-quately the surface variability of the AC. In fact,more recent observations and laboratory experimentshave shown that rapidly evolving surface mesoscalestructures may develop in the AC, and that onlysome of them have a deep signature, the so-called

Ž .events Obaton et al., 2000 . During the ALGERS’96experiment, a relatively high number of buoys wasdeployed, and the trajectories covered a domainranging from 08E to 98E. The spatial extent and thegreat variability exhibited by the buoy tracks consti-tute a good opportunity to make a more completestatistical description of the AC from a Lagrangian

( )J. Salas et al.rJournal of Marine Systems 29 2001 69–85 71

point of view, in order to characterize the propertiesof the mesoscale variability present in the AC.

The paper is organized as follows. In the follow-ing section, the buoy data are briefly described.Section 3 is devoted for the main results and discus-sion separated in three parts. In the first part, theprimary statistics and the integral scales from thetotal ensemble of data are computed. In the second,an analysis of single particle dispersion is applied toboth the total ensemble of data and, locally, to28=28 boxed regions, where diffusivities, mean andeddy kinetic energy and horizontal covariances arecomputed. In the third part, an Eulerian view of theAC is obtained. Finally, we summarize the mainresults in the last section.

2. Buoy data

In mid-October 1996, it was observed from in-frared satellite images that the AC started to develop

Ž .a paired eddy structure near 1–28E Fig. 1 . An in

situ experiment, the ALGERS’96 cruise, was orga-nized to carry out a multidisciplinary survey of themesoscale structure, which consisted of a small cy-clonic eddy upstream of a meander with a deep

Ž .anticyclonic eddy below it Moran et al., 2001 .´Eighteen near-surface buoys were launched in theAC on October 17–18, 1996 from the Spanish R.V.Hesperides. Two sets of 3 and 15 buoys separated by´5–10 km were released along two cross-sections:one upstream of the meander, and the other acrossthe main flow and the cyclonic part of the perturba-

Ž .tion Fig. 1 . The buoys were models A104 andA111 from Brightwaters Instruments, equipped withan Argos transmitter and, only for model A104, a

Ž .GPS receiver data from GPS were not used . Thewind drag on the transmitters was reduced by mini-mizing their area of exposure over the sea surface.From the buoys, a 5-m line was attached with asubsurface TOGA-WOCE standard holey sockdrogue to allow a maximum drag 10 m below the sea

Žsurface more details can be found in Font et al.,.1998 . The Argos satellite tracking system at this

Fig. 1. The meander event in the AC seen in the SST image of mid-October during the ALGERS’96 experiment. Marks correspond tolocations where drifters were released. Ec and E1 indicate the cyclonic and anti-cyclonic structures respectively.


Fig. 2. ASpaghettiB diagram of all 18 buoys tracked during the ALGERS’96 experiment, overplotted to isobaths of 1000 and 2000-m depth.Markers indicate the release positions of buoys.

latitude gives fixes six to eight times per day with anaccuracy of around 500 m.

To estimate velocities from the fixes, daily posi-tions were computed from the six to eight satellitefixes. The time series were averaged at daily posi-tions, and then re-sampled every 6 h with a cubicspline to obtain a suitable temporal resolution. Then,the velocity was computed using centered finite dif-ferences of positions, with a time interval of 6 h.Although tidal, and mainly, inertial frequencies arepresent in segments of some trajectories, with theabove procedure, the tidal and inertial motions wereremoved from the original data.

The full buoy tracks of the whole data set duringthe sampling period are plotted in Fig. 2. We canappreciate the clear trend of the MAW flow towardsthe east, from the boundary of the Alboran basin tothe Strait of Sicily, despite the rather complexmesoscale motions. The trajectories reveal several

Ž .eddies closed loops with different scales, particu-larly evident around 28E and from 68E to 88E. Dur-ing the first few days, the buoys moved according totheir position with regard to the mesoscale eddies.Some of them were trapped in the cyclonic eddy anddrifted to the west before being re-introduced in theAC. Further to the east, other buoys displayed some

loops related to the presence of coastal anticycloniceddy. Then, they were expelled by the interactionbetween the mean and mesoscale flow from the eddyand drifted downstream following the AC. At theeastern end of the Algerian basin, the trajectories areagain complicated: some buoys travelled along thecoastline while others moved offshore, delineating alarge anticyclone. Buoys trapped in this structure

Žremained recirculating for more than 7 days Salas et.al., 2001 .

The analysis presented here is based on the datafrom 15 buoys that were tracked between 25 daysŽ . Žthe shortest trajectory and 3 months the longest

.trajectory . The total data ensemble constitutes 843buoy days through the autumn–winter period. Buoysdeployed in the main flow of the AC remained in theAlgerian basin for 50–60 days, while buoys thatwere released in the cyclonic part of the meanderlasted for 70 days or longer before quitting the basin.

3. Results and discussion

3.1. Primary statistics and integral scales

The global properties of the ensemble of driftermotions are summarized in Table 1. Average veloci-


Table 1ŽGlobal properties of the ensemble of drifter motions 843 buoy

.days

² :Õ Õ T L Krms i i i i2Ž . Ž . Ž . Ž . Ž .cmrs cmrs days km cmrs

8Ž .Zonal u 13.9 21.1 3.8 66.3 0.7–1.3=107Meridional 1.3 17.2 1.6 26.1 1.5–6.0=10

Ž .Õ

See in text the details of how the values are computed.

Ž² : ² :. Ž .ties for the global data set areu , Õ s 14.0,1.3Ž ." 1.4,1.2 cmrs, where, as usual,u and Õ are the

eastward and northward components of the flow.X2Given the varianceu , the 95% confidence intervali

for mean values given by thet-test is computed asX2("2 u rN , where N is the number of degrees ofi

freedom estimated as the total number of buoy daysdivided by the Lagrangian time scaleT. From theindividual drifters trajectories, the maximum instan-taneous velocity found is of the order 70 cmrs. Theycorrespond to those buoys that, after contouring thebig eddy located between 78E and 88E, accelerated

Ž .toward the south Fig. 2 . As expected, the meanzonal velocity component is larger than the meanmeridional component, given the predominantly east-ward flow of the MAW depicted by all trajectories.This is also seen in the mean zonal values, computedover the individual drifters, that range from 7 to 25cmrs, while the mean meridional velocities arewithin the 0–3.5-cmrs interval, except for one buoy,which has a net westward component and ceased totransmit few days later after release. This buoybelongs to a group of buoys that was launched at theoffshore edge of the meander, travelled towards theSpanish coast between 08W and 28W, remained inthe area for a long time and finally re-entered theAlgerian Current.

The different behaviour of the mean zonal andmeridional components is not totally reflected in theroot mean square velocities, which are roughly simi-lar. This also occurs in the values for individualvelocity trajectories, which, in some cases, zonal rmscomponents are clearly similar to meridional rms, oreven smaller. Despite the strength of the mean zonalcurrent, the high values of both the zonal and merid-ional fluctuating components are indications of theturbulent regime of the Algerian Current. The mean

kinetic energy is lower than the eddy kinetic energyfor the total ensemble of drifters, and also for mostof them, with the exception of one buoy that fol-lowed a very smooth trajectory. The path was almostuniformly eastward until it contoured the big anticy-

Ž .clone structure near Sardinia Salas et al., 2001 .Characteristic integral space and time scales can

be defined from the autocorrelation of Lagrangianvelocity components given by

1 Ta X XR t s u t u tqt dt 1Ž . Ž . Ž . Ž .HX Xi j i ju u T 0i j a

X Ž .whereu t su yu is the residual velocity compo-i i i

nent of the drifter at timet and at a fixed location,tis the time lag,T is the length of time series, anda

the overbar means an ensemble average. IntegralLagrangian time and space scales,T and L, are thencomputed as

`

T s R t dt ,Ž .Hi i i i0

`X2 X2( (L s u R t dts u T 2Ž . Ž .Hi i i i i i i i

0

which are measures of the time and space scales, inXŽ .which the drifter velocity u t is correlated with

itself. Generally, natural processes have a character-Ž .istic behaviour, in whichR t is high for shorti i

times and decays for very long times. Two questionsarise in computing such scales from real data: first,the time series has a finite length, and second, theautocorrelation functions are usually close to zero forlong lags but often exhibit a systematic trend of

Ž .oscillations that mask the evaluations of Eq. 2 . ByŽ .definition, R t is time-dependent and does noti i

approach a constant limit ast increases. We thenŽ .apply the usual approximation of integratingR ti i

from the origin up to the time of the first zeroŽcrossing Poulain and Niiler, 1989; Haynes and Bar-.ton, 1991 , which leads to values that must be re-

garded as upper bounds rather than true characteris-Žtic scales Krauss and Boning, 1987; Poulain and¨.Niiler, 1989 .

The resulting average time scales are about 3.8and 1.6 days for the zonal and meridional compo-nents, respectively, and the corresponding spacescales are about 66 and 26 km. However, computedfor individual drifters, the time scale fluctuates within


the range of 1–7 days and the spatial scale within therange of 7–140 km. Larger values are found in thebuoy trajectories, in which eddy motions predomi-nate along their mean drift and, in some cases, thetime scale is close to the revolution time in loopingtrajectories. For individual drifters, both the time andthe spatial scales for the zonal component are greaterthan those for the longitudinal component, an indica-tion of the anisotropic regime of the flow.

3.2. Single particle dispersion and local analysis

An initial approach to describe the dispersioncharacteristics of the flow may be to compute diffu-sivities from the statistics of the ensemble of trajec-tories. This is interesting to compare with Taylor’s

Ž .theory of single particle dispersion Taylor, 1921 , asa simplified model to understand the dispersion ofthe mesoscale eddies present in the AC. This theoryhas been widely and successfully used to analyzeLagrangian data measurements in the oceans world-wide as a framework to interpret dispersion resultsŽColin de Verdiere, 1983; Krauss and Boning, 1987;` ¨

.Brink et al., 1991; Haynes and Barton, 1991 . Ac-cording to Taylor’s theory, for a statistically station-ary and homogeneous regime, the Lagrangian dif-fusivity and particle dispersion are related to theLagrangian correlation function as

1 d tX X X2K ' x x su R t dt 3Ž . Ž .Hi i i i i i i2 dt 0

tX2 X2x t s2u tyt R t dt 4Ž . Ž . Ž . Ž .Hi i i i0

where xX is the random particle displacement due toiX Ž .u . Expression 3 allows two ways of computingi

diffusivities, one by directly evaluating the derivativeof the left-hand side, and the other by the numericalintegration of the right-hand side. In this case, thecontribution from the mean trajectory must be re-moved. Under such conditions, two limiting casescan be found that are independent of the detailed

Ž .behaviour ofR t

X2 2 Ž . Ž .u t , t- T and R t ™ 1,iX2Ž .x t si X2½ Ž .2u tT whent™` or approximatelyt4 T and R t ™ 0i i

5Ž .

The first case is the behaviour for short times andthe second asymptotic limit corresponds to the ran-dom walk regime. In order to test Taylor’s theory,we must consider whether the assumptions of no

Ž .mean flow consequence of homogeneity and sta-tionarity can be applied to analyze our Lagrangiandata set, and whether the measurement strategy iscoherent with such assumptions. The former is aquestion related only to the AC dynamics, but thelatter is clearly a problem related to the experimentaldesign. The ensemble average is approached by seg-menting the trajectories into intervals and consider-ing each as an independent sample of the sameprocess after the mean drift has been removed. It is areasonable procedure if the segmenting interval islonger than, or at least equal to, the decorrelationscales both in time and space. This method has beenwidely used for open ocean environments, in which

Žthe assumptions are reasonably satisfied i.e. Colin.de Verdiere, 1983; Krauss and Boning, 1987 . Also,` ¨

it has been applied as a first order approximation innear coastal regions, where the flow is anisotropicŽ .Davis, 1985b; Haynes and Barton, 1991 .

In our case, in order to generate enough samplesfor a reliable statistics, and simultaneously to guaran-tee the statistical independence, trajectories are seg-mented and restarted in intervals of 7 days, which isslightly longer than the largest decorrelation timeŽ .6.8 days . Taking into account the redundancy dueto the close similarity of some buoy tracks, this

Ž .interval produces a total of 112 segments Fig. 3 .Ž .For longer periods)50 , the number of artificial

generated observations is less than 30, which isinsufficient to obtain statistically reliable results.Thus, the statistical analysis was always done withsample sizes larger than 30. The figure obtained byplotting all tracks, as if they were initially located atthe same origin, resembles a point source of parti-cles, such as chimney-emitted smoke dispersing in a

Ž .homogeneous turbulent field Fig. 4 . The evolutionof the center of gravity of the ensemble of trajecto-ries is represented in Fig. 5. As can be seen, the

Ževolution of the center of gravity estimated from.112 artificial tracks is almost linear in time, espe-

cially for the zonal component. For small timesŽ .t-20 days , it is in agreement with the mean drift

Žof the flow computed from the entire data set 14.cmrs . The behaviour of the meridional displace-


Fig. 3. Number of releases as a function of the time interval used to generate artificial trajectories.

ment of the center of gravity is, for small timesŽ .t-25 days , almost linear and very close to theglobal mean flow value. For larger times, deviationsfrom this linear regime appear, exhibiting strongvariations, which reflect the underlying spatial vari-ability of the mean velocity. The displacement in-creasingly underestimates the mean flow with longertimes.

Dispersion and diffusivities are then computedonce the mean drift is suppressed. Here, the meanflow has been removed by subtracting the time evo-

Ž .lution of the center of gravity Fig. 5 . In Fig. 6, wehave represented the time evolution of dispersion forboth the zonal and meridional directions. Although,the dispersion in the two directions is qualitativelysimilar, the detailed behaviour is different whencomparing with the asymptotic limits given by Eq.Ž .5 . The characteristics of the long time limit aredifferent for the two components. Zonal dispersion isconsistent with the long time limit in the 20–30-dayinterval, while the meridional dispersion clearly sep-arates and ceases. The presence of the coast, togetherwith the meridional gradients, prevents water parcelsto disperse in the south–north direction. Also, we

have estimated diffusivities directly from the left-Ž .hand side of Eq. 4 , and indirectly through the

Ž .integration of the autocorrelation function Fig. 7 .Ž .After an initial period -5 days of rapid growth,

where both methods provide similar results, zonaland meridional diffusivities behave differently andthe results strongly depend on both methods. For thezonal direction, the direct estimates are growingcontinuously up to 10 days and then slowly decreasein average during the 10–30-day period. With theindirect method, diffusivity remains constant be-tween 7 and 40 days, taking an average value of7.5=107 cm2rs. For the meridional component,after a shorter initial regime of 4–5 days, diffusivitydecreases rapidly when computed directly, whereasthe indirect method remains constant at around 6.0=

107 cm2rs. Results suggest that Taylor’s theory isroughly adequate for the zonal direction, where ho-mogeneity is at least better satisfied, than for themeridional, where this simple model does not work.

To explore the assumptions of uniformity andstationarity of the flow reflected in part by the greatvariability of the Lagrangian time and space scales,we have applied the same previous analysis to local


Fig. 4. Dispersive dye plume from the artificially generated trajectories resampling every 7 days. Upper portion: zonal direction. Lowerportion: meridional direction.

regions, where, in better approximation, the flowstatistics can be considered more uniform and sta-tionary. The domain is subdivided into six boxes ofsize 28=28, according to the characteristic flowpatterns observed in Fig. 2. The geographical loca-tions can be appreciated in Fig. 9a, and the statisticalproperties are listed in Table 2. The number of buoydays in boxes ranges between 70 and 250 days,which results in a great reduction in the number ofdegrees of freedom mostly greater than 60 and, in

the worse case, being 22 in boxa4. The first box inthe western part includes the place where the mean-

Ž .der of the AC was observed see Fig. 1 . The secondbox delimits a region in which the AC flows to theeast. The third box includes track segments, wherelooping trajectories reveal the presence of an anticy-clonic eddy. Boxa4 characterizes a region in whichthe traces of the AC eastern flow are clearly seen.The last two boxes are regions in which the buoysdispersed again. In boxa5, the flow is affected and


ŽFig. 5. Time evolution of the zonal and meridional displacements of the center of gravity for the ensemble of segmented tracks plus. Ž .symbol and the average linear drift continuous line .

partially deflected by the presence of a big eddy, andbox a6 corresponds to the last part of the buoytrajectories, in which the buoys returned toward thecoast at the end of the AC, south of Sardinia island.

By comparing with the mean global statisticalproperties, we observe that integral time scales varysignificantly, with respect to the global value for the

zonal component. For the meridional component, theintegral time scales are within the range of variation.The decorrelation time is particularly high in boxa4, where the flow is very homogeneous in the eastdirection and corresponds to a great reduction in thedegrees of freedom because trajectories are well-cor-related. In Fig. 8, we have represented diffusivities


Fig. 6. Logarithmic plot of the dispersion as a function of time. Continuous quoted lines indicate the two regimes of Taylor’s theory.

associated to each box, computed in the same way asthose represented in Fig. 7. Zonal and meridionalvalues look generally smaller than those estimatedglobally. The discrepancy between direct and indi-rect estimates is less accused, at least in the first fiveboxes and for the zonal dispersion. The major differ-ences appear in boxa6, and, for the zonal compo-nent, perhaps related to the nonstationarity of themean flow due to strong accelerations of the buoysas they progress toward the Strait of Sicily. Buoys

that have contoured the large anticyclonic eddy areŽstrongly constrained to flow near the coast see Fig.

.2 . The zonal diffusion is always greater than themeridional diffusion, which in general fluctuates nearthe origin and, in some cases, takes negative valuesevidencing that particles are generally being trappedin the meridional direction.

This local analysis can be compared with theEulerian statistics computed during the MEDIPROD

Ž .experiment Millot et al., 1997 . The locations of the


Ž . Ž .Fig. 7. Smoothed zonal and meridional diffusivities as functions of time. Direct estimation solid line and via autocorrelation broken line .

mooring arrays should compare with the resultswithin boxesa2–4, being the effective number ofdegrees of freedom of the same order, and onlyslightly greater in our local analysis. The values forthe mean velocities, variances and integral scalesdiffer with respect to those found here, but they alsoexhibit some similar trends. In general, the meanvalues and variances were lower during theMEDIPROD-5 experiment than in the ALGERS’96,while the autocorrelation time scales were signifi-

cantly greater during the MEDIPROD-5 measure-ments. We think that the statistical results duringMEDIPROD-5 were too much dependent on theplace and depth where moorings were deployed rela-tive to the AC. In our case, the paths of buoysclearly mapped a wider region, including the spatialoffshore extent of several mesoscale structures de-veloped by the AC. The buoys clearly captured thesurface variability better than the measurements at100-m depth during the MEDIPROD-5 experiment,

Table 2Statistics of the local analysis in six boxes

X2 X2 X X 7 7Box Buoy days u Õ u Õ EKE u Õ MKE T days T days K =10 K =10u Õ u Õ

1 122 213.0 115.0 33.8 164.0 0.4 y2.7 3.6 1.6 2.2 6.1 y1.12 246 323.3 107.8 88.7 215.5 9.7 3.6 53.3 2.4 2.8 4.6 0.33 153 491.2 261.9 y5.2 376.6 19.0 y0.3 180.7 2.0 1.5 2.4 y1.44 104 343.0 235.8 y42.3 289.4 31.5 3.1 500.4 4.6 1.0 9.2 0.85 133 68.2 62.8 y83.3 65.5 18.4 1.0 170.4 1.8 1.6 5.0 0.066 71 462.5 540.0 61.1 501.3 18.0 y4.3 171.6 1.2 1.7 1.6 6.5

Values are rounded and all units are in the CGS system.


Fig. 8. Local analysis of dispersion computed for the six boxes considered in Fig. 9a. Continuous and broken lines correspond to directestimations for the zonal and meridional components, respectively, and symbols are estimations via the autocorrelation function.

and this explains the disagreement of the time corre-lation scales that we expect to be much more uncor-

related in the case of buoy observations. It has beenobserved that the AC develops, not only events with


a deep coherent structure but also, smaller surfacestructures rapidly evolving in time that may be betterreflected by shorter autocorrelation time scales.

3.3. Eulerian flow

The local analysis made for the six boxes showsthat the mean flow characteristics are definitely not

Ž .zonally uniform see Table 2 . The mean kineticŽ .energy MKE gradually increases from west to east

until it reaches a maximum in boxa4. Then, itdecreases and remains constant froma5 to a6. On

Ž .the other hand, eddy kinetic energy EKE alsoincreases from boxesa1 to a3, decreases throughboxes a4 and a5, and finally grows quickly inbox a6. The exchanges between MKE and EKE aredone through the shear production term given² X X : ² :u u EUrEx , where P means ensemble aver-i j i j

Ž .ages i.e. see Kundu, 1990 . When this term ispositive, transfer of kinetic energy is done from EKEto MKE and vice versa; if it is negative, the energygoes from the mean flow to the eddy field. The signof the shear production terms mainly depends on the

Ž .sign of the mean flow gradientsEUrEx and on thei jŽ² X X:.sign of the covariance u Õ . The AC is mainly

zonal but the mean flow is not zonally uniform as itcan be appreciated by the spatial distribution ofmean flow values from box to box. Given the valuesin Table 2, it is expected that the major contribution

² X2: ² X X:comes from u EUrEx and u Õ EUrE y. Themeridional gradients are much higher than zonal

² X X:gradients, compensating the lower valuesu Õ

² X2:with respect to u . For example, during the AL-GERS’96 cruise, from several hydrographic cross-sections to the Algerian Current, dUrd yf10y5rsin contrast to 10y6–10y7rs that can be roughlyestimated between boxes. The sign of covariancevalues is consistent with the local tendency of the

² X X:EKE to grow. When u Õ is maintained positive,from boxesa1 to a2 and from boxesa5 to a6,

² X X:EKE tends to grow, while froma3 to a5, u Õ

changes its sign and becomes negative as EKE de-creases. Remark that, within such area, the field

Ž .becomes more uniform see Figs. 2 and 9b and theMKE reaches its maximum value, suggesting thattransfers from eddy field to mean current through theshear production term could be important. Iudicone

Ž .et al. 1998 have found similar indications from a

statistical analysis of 2 years of altimetric data. Theycomputed the EKE and horizontal covariances in theMediterranean Sea for TOPEXrPOSEIDON alongtracks. The levels of EKE for the area of the AC arequantitatively lower than those found here, but thespatial distribution is qualitatively similar. The com-

² X X:puted values of u Õ for the region correspondingto boxa6 are of the same sign and order of magni-

Ž .tude see their Fig. 5 .The advantage of disposing of data covering the

zonal extent of the AC provides us with the possibil-ity of obtaining a mean Eulerian field associated tothis current. This should be considered with caution,because a representative scheme of the mean orseasonal circulation cannot be given for the obviousreason that the measurements are limited in timeŽ .autumn–winter period . Although to build Eulerianmaps from Lagrangian information is not a trivialtask, and there are several techniques for doing soŽe.g. Davis, 1985b; Davis et al., 1996; Poulain and

.Niiler, 1989; Owens, 1991; Eremev et al., 1992 , theamount of available data is crucial to have reliable

Žresults necessary for a good representativity Poulain,.2001 . In the case of 28=28 boxes considered above,

the degrees of freedom are still sufficient to maintainsuch conditions, but the spatial resolution is notenough to better appreciate the main effect of themesoscale eddies in the mean circulation. Thus, wehave considered subdividing the domain in squaredboxes of 0.58=0.58 and to average the velocitieswithin each box. The size is larger than the meansize of the loops described by several buoys, butsmall enough to resolve significant large-scale vari-ability and, according to previous results, of thesame order as the decorrelation length-scale. A draw-back is the great reduction of the equivalent numberof degrees of freedom that results in a statistics,

Ž .which, in most cases, is not confident less than 30 .Nevertheless, it is still useful to obtain the Eulerianpicture from our data set for qualitative comparisonwith the other measurements made in the zone, aswell as to help in the validation and understanding ofthe common output of actual numerical models. Weconsider it relevant for this region because system-atic field experiments are often difficult to undertake.

In Fig. 9b, we show the Eulerian picture foundfrom the Lagrangian data, in which the meanderingshape of the AC from west to east is observed. The


Ž . Ž .Fig. 9. a Boxes of the local analysis. Centered numerical labels indicate the buoy days for each box. b–c Mean Eulerian flow andvariance ellipses averaging Lagrangian data in boxes of 0.58=0.58.


variability, quantified as the root mean square withineach box, is maximum around 2.58E and 78E. Theflow appears to be significantly intensified at 3–68E,and circulates close to the coast. This agrees with theresults of the previous section, where a significantincrease in the MKE is produced simultaneously

Žwith a reduction in the level of EKE see values for.box a4 . Also near the Sardinia Channel, where

maximum Eulerian velocities are about 50 cmrs,there appears a significant intensification of the cur-rent. In Fig. 9c, the ellipses corresponding to the

Žprincipal axes of variance are represented Emery.and Thompson, 1997 . Near the coast, ellipses are

strongly oriented along the direction parallel to thecoast, where the variance ellipses increase by two orthree times their values offshore. Near the SardiniaChannel, which is an area characterized by the strongeddy activity seen in the Lagrangian paths, the axesare enlarged and slightly oriented along the N–Sdirection. The zone between 18E and 38E corre-sponds to the place where, usually, meanders andeddies in the AC are often seen from remote sensingŽ .Millot, 1985 . The mechanisms that generate suchstructures and their evolution are not completelyunderstood. Both laboratory experiments and in situdata sets agree with respect to the size and shape ofeddies, and the phase speed and growth of the AC

Ž .meanders Obaton et al., 2000 . The energy balancesin such experiments and the results of recent numeri-

Ž .cal simulations Gervasio et al., 2001 have shownthat the Algerian Current is intrinsically unstable ofmixed baroclinic–barotropic type, and that other ele-ments, such as atmospheric forcing or coastline andbathymetry irregularities, are not of major impor-tance as destabilizing mechanisms. Discrepancies be-tween laboratory results, numerical simulations andfield observations, mostly with regard to the verticalstructure of the developed eddies and their timeevolution once they are created, depend on eddy–mean current interactions. Some of them, usuallycalled events, are characterized by a deep signature.When these events reach a characteristic size, theystop growing and may detach as they are advected

Ž .by the AC Millot et al., 1997; Salas et al., 2001 .Very often, they reach the region around 6–88E,where they are blocked by the enlargement of the

ŽAlgerian continental shelf south of Sardinia see also.the buoys paths in Fig. 1 .

The representativity of our results can also bechecked by comparing with other kinds of measure-ments made in the region. A coarse sampling of thefull AC was carried out during the Western Mediter-

Žranean Circulation Experiment Perkins and Pistek,.1990; Arnone et al., 1990 . An Eulerian field of

velocity was obtained from hydrographic measure-ments and an ADCP sampling from a ship cruisecarried out along the African coast. The surface field

Žof dynamic height and ADCP velocities see Figs..3–4 in Arnone et al., 1990 have better resemblance

with the Eulerian field given in Fig. 9 than theturbulent aspect of the AC provided by the La-grangian picture of Fig. 2. The resolution and thelack of synopticity during the ship cruise were notenough to resolve the characteristic mesoscale fieldof the AC. Similarly, numerical results are alsoroughly in agreement with our picture in terms of the

Žmean seasonal circulation EUROMODEL, 1995;.Heburn, 1994; Beckers et al., 1994 . However, the

circulation patterns given by these models are verysensitive to the boundary conditions and the initialfields considered, even in simulations with realistic

Žforcing Pinardi and Navarra, 1993; Herbaut et al.,.1997 .

4. Summary

The autumn–winter Lagrangian observations ob-tained during the ALGERS’96 experiment allowedus to get a detailed picture of the spatial extent of theAC, and to estimate the statistical properties of theAlgerian Current. Buoys released near 18E within theAC drifted to the east up to the Sardinia Channel,allowing the capture of part of the mesoscale vari-ability in this region and the obtainment of the firstdirect quantitative measures of dispersion by eddiesin the Algerian Current. The current exhibits a strongturbulent regime revealed by the high intensity of thefluctuations measured from the buoy trajectories.From the Lagrangian autocorrelation function, weestimated the characteristic time and spatial scales ofthese fluctuations. Integral time scales are, on aver-age, about 3.8 and 1.6 days, and spatial scales areabout 66 and 26 km for the zonal and meridionalcomponents, respectively.


The dispersion and related diffusivities were di-rectly calculated and the results were compared withthose obtained using Taylor’s theory. The computedvalues are consistent with the applicability of Taylor’stheory in the short time behaviour. Differences ap-pear for both components when we look at the longtime limit. For the zonal component, the randomwalk regime is consistent with direct computationswithin the range of 20–50 days, but falls off at verylong times. The meridional component does not agreewith the random walk regime, probably due to theassumptions of stationarity and homogeneity of themean flow. There are considerable differences invariances and time scales for the two componentsthat result in different eddy diffusivities, the merid-ional component being smaller than the zonal one.The presence of the coast and the strong anisotropyof the flow inhibit the meridional dispersion of parti-cles. Nevertheless, the estimates of diffusivities canbe characterized as ranging between 0.7–1.3=108

7 2 Žand 1.5–6.0=10 cmrs zonal and meridional.components , which are of the same order as those

estimated in other areas with different oceanicŽ .regimes see Table 2 in Haynes and Barton, 1991 .

Ž .In the Adriatic sea Western Mediterranean , valuesalong basin direction, which are somehow equivalentto our zonal direction, are lower, while across thebasin direction, diffusivities are similar to those found

Ž .here in the meridional direction Poulain, 2001 .Besides the reported statistics in the Adriatic seabeing more robust for the ensemble of data, differ-ences in the zonal values could be explained by thefact that mesoscale is particularly strong in the AC.For the same period of the year, autumn to winter,the values for the EKE in the Adriatic Sea are half ofthose found in the Algerian basin.

Because the flow statistics are non-uniform, wealso carried out a local analysis by considering sixboxes covering the area of the AC from east to westmore appropriate and consistent with the hypothesisof stationarity and homogeneity. A closer agreementwith Taylor’s theory was found for the zonal direc-tion. Meridional diffusivities are very low in compar-ison with zonal diffusivities, with a strong evidencethat dispersion due to fluctuations within the ACcurrent tends to be more effective in the west–eastdirection. The meridional mean shear of the ACalong the coast limits the north–south dispersion of

the particles that tend to be trapped for long times.The local analysis of mean and eddy kinetic energiesalso indicates strong eddy–mean current interactionsexpected with the significant change of sign of thehorizontal covariances with high values of EKE foundin the areas close to 2–38E and around 7–88E.Covariance values in 7–88E are quantitatively inagreement with values computed from altimetric data.

Finally, an Eulerian view of the velocity field isgiven by spatially averaging. It reflects the incidenceof mesoscale features in the mean field, especially inthe area around 1–38E and near the Sardinia Chan-nel. These areas correspond to places where severalbuoys were trapped in looping trajectories, producingan offshore enlargement of the mean current. Al-though this view is the result of only one realizationof the current, it is based on sparse data and thestatistics is not very confident; the pattern obtainedretains some similarities with the other kind of ob-servations and results provided by numerical models.It would be interesting in the future to perform directLagrangian simulations of the AC that could becompared far more suitably with our results.

Acknowledgements

ŽThis is a contribution to MATER MTPII-. ŽMATERr031 and VARIABILIDAD MAR98-

.0840 projects. The data used in this study camefrom the ALGERS’96 experiment funded by theEuropean Union MAST program MATER Mediter-

Žranean Targeted Project phase II contract MAS-.CT96-0051 and Spanish National RqD Plan

Ž .AMB95-0901-C02 . We acknowledge the coopera-tion of the crew and colleagues onboard the R.V.Hesperides during ALGERS’96. We also thank the´reviewers for their constructive remarks and com-ments that helped improve the manuscript. J. Salaswas under Grant number 94789 from the Consejo

ŽNacional de Ciencia y Tecnologıa de Mexico CON-´ ´.ACYT .

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statistical analysis of the surface circulation in the algerian current using lagrangian buoys

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