A three-dimensional model study of the Mediterranean outflow

Ž .Journal of Marine Systems 24 2000 41–66www.elsevier.nlrlocaterjmarsys

A three-dimensional model study of the Mediterranean outflow

Johann H. Jungclaus ), George L. MellorProgram in Atmospheric and Oceanic Sciences, Princeton UniÕersity, Princeton, NJ 08544, USA

Received 1 January 1996; accepted 31 July 1998

Abstract

Evaporation over the Mediterranean basin produces a salty water mass that overflows the relatively narrow and shallowStrait of Gibraltar. The outflow is investigated with the three-dimensional Princeton Ocean Model. The model makes use ofa bottom-following, sigma-coordinate system and an imbedded turbulence closure scheme to simulate the bottom boundarylayer. Starting as a channel flow confined by the sidewalls of the trench of the westernmost part of the Strait, the bottomboundary current descends the steep continental slope of the eastern Gulf of Cadiz. The flow is controlled by a balance ofthe pressure gradient and the Coriolis acceleration, entrainment and bottom friction. Downslope Ekman fluxes are largest atthe shelf break near the entrance of the Strait where we observe the most pronounced entrainment of North Atlantic CentralWater. Profiles of modeled horizontal velocity, as well as scalar and turbulent quantities, show a remarkable resemblance toobserved features. The model reproduces the ‘‘nose’’ shape of the velocity profile that is typical for a density current; belowthe velocity maximum, there is a well-mixed layer and a stratified shear layer exists above the nose. The evolution of watermass properties along the path of the outflow agrees favorably with observations and the sensitivity of the Mediterranean

Ž .outflow MO to varying source water properties is investigated. The combined effect of initial stratification, differentialentrainment, and routing by the topography leads to the evolution of the well-known two-core structure of the bottom layer.Whereas the upper part of the outflow continues to follow the continental slope northward in the form of a bottom boundarycurrent after it passes Cape St. Vincent, the lower core separates from the slope and there is a lateral spreading of the saline

Ž .and warm outflow water in the depth range of the lower salinity maximum centered at about 1200 m . The outflow becomeshydrodynamically unstable and lenses of saline water shed from the core, carrying their water mass characteristic into theAtlantic. The model results confirm that the area of Cape St. Vincent is a prominent formation area for Mediterranean waterŽ . Ž .MW eddies Meddies . q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Mediterranean; plume; instability; modelling

1. Introduction

The deep and intermediate water masses of theNorth Atlantic are ventilated mainly by dense bottom

) Corresponding author. Max-Planck Institut fur Meteorologie,¨Bundesstrasse 55, Hamburg 20146, Germany. Fax: q49-40-41173-298.

Ž .E-mail address: [email protected] J.H. Jungclaus .

currents that have received their density contrast inadjacent marginal shelf seas where deep and bottomwaters are formed by intense air–sea interaction andsubsequent thermal and haline convection. Deter-mined by the initial water mass characteristics andthe local geometry of the topography, the initiallyrelatively dense water will find its equilibrium depthat different layers of the ocean. The gravity currentsnot only transport temperature and salinity into the

0924-7963r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0924-7963 99 00078-0

( )J.H. Jungclaus, G.L. MellorrJournal of Marine Systems 24 2000 41–6642

deep ocean, thus influencing the climate of the deepŽ .sea Price et al., 1993 , but they also carry passive

substances such as CO and anthropogenic tracers2

into the deep and intermediate ocean.In the Mediterranean Sea, the dry continental

climate, with evaporation exceeding precipitation,leads to the formation of saline water masses. The

Ž .outflowing Mediterranean water MW consistsmainly of two types: Levantine Intermediate WaterŽ .LIW , formed near Rhodes and characterizedthroughout the Mediterranean by a mid-depth maxi-mum of temperature and salinity, and Western

Ž .Mediterranean Deep Water WMDW which is lessŽ . Ž .saline S-38.435 psu and colder T-12.98 thanŽ .LIW Bryden and Stommel, 1982 . Directly at the

Ž .sill, Bryden and Stommel 1982 found a LIW watermass with Ts13.088 and Ss38.466 psu and the

Ž .densest WMDW- rich waters had a characteristicof Ts12.958C and Ss38.457 psu.

During the last few decades, the outflow of MWhas been investigated during a number of hydro-graphic campaigns. The surveys on sections across

Žthe continental slope in the Gulf of Cadiz e.g.,Ambar and Howe, 1979a,b; Ochoa and Bray, 1991;

. ŽPrice et al., 1993 and to the east of Portugal Zenk.and Armi, 1990; Daniault et al., 1994 have charac-

Ž .terized the Mediterranean outflow MO circulationas follows. The density contrast between the MW

Ž .and the less saline Atlantic water AW drives aninverse estuarine circulation in the Strait of Gibraltar.

ŽThe hydraulic flow through this shallow about 300. Žm at the Camarinal sill , and narrow about 15 km

.near Pt. Cires strait is controlled by the local geome-Ž .try Lacombe and Richez, 1983 . The deep flow is

funneled through the strait and remains constrainedto the deep outflow channel until it encounters theshelf break. Entrainment of North Atlantic Central

Ž .Water NACW is most pronounced at the shelfŽ . Žbreak Price et al., 1993 . In the Gulf of Cadiz Fig.

. Ž .1 , the MO also called Mediterranean undercurrentcan be described as a damped, nearly geostrophicgravity current flowing along the Iberian continentalslope. A common feature is the double core structure

Ž .where the upper generally warmer maximum ofMW content proceeds westwards separated from itslower, more saline counterpart by a horizontal dis-tance of a few tens of kilometers. The separation into

Ž .‘veins’, as Madelain 1970 calls them, is attributed

to the topographic steering by the various canyonsŽ .Madelain, 1970 and to differential entrainmentŽ .Baringer, 1993 , where the lower core mixes withdistinctively different versions of the NACW.

Proceeding westward, the upper part of the out-flow stays confined to the continental slope in adepth range of 600–1000 m, the saline core settles atabout 1200 m and the loss of excess density byentrainment inhibits a further descent down the slope.Through entrainment, the deep westward transportincreases approximately threefold between the

Ž 6 3Gibraltar Strait, where less than 1 Sv 1 Svs10 my1 .s overflows to the sill, and the Cape St. VincentŽ .Ochoa and Bray, 1991 .

Whereas the upper part continues to flow alongthe Portuguese continental slope in northward direc-tion, the lower core separates from the bottom and

Ž .partly spreads into the interior Atlantic Arhan, 1987 .Ž .Submesoscale eddies Meddies that separate from

Žthe outflow near Cape St. Vincent Bower et al.,. Ž .1995 and to the west of Portugal Kase et al., 1989¨

contribute significantly to the lateral transport ofwarm and saline anomalies originating in theMediterranean Sea leading to the intermediate salin-ity maximum in the entire subtropical AtlanticŽ .Arhan, 1987 . Although there is no bottom water

Ž .formed by the MO, Reid 1979 points to the impor-tant contribution of the MW to the preconditioningof the saline inflow of AW into those areas of theGreenland Sea and the Arctic Ocean where deepwater formation does occur.

1.1. Modeling the MO

The numerical modeling of gravity currents wasŽ .initiated by the stream-tube model of Smith 1975 .

ŽThis model, as well as refined versions e.g., Kill-.worth, 1977; Price and Baringer, 1994 , considers a

stationary, laterally integrated stream-tube with vari-Ž . Žable cross-sectional area. Baringer 1993 see also

.Baringer and Price, 1997a,b successfully applied theŽmodel to the MO and other deep overflows Price

.and Baringer, 1994 . She reproduces the cross-stream-integrated evolution of transports, salinity,and temperature in agreement with observation fromthe 1988 Gulf of Cadiz experiment. However, thestream-tube model does not resolve the horizontal

Žand vertical structures of the plume i.e., the separa-

( )J.H. Jungclaus, G.L. MellorrJournal of Marine Systems 24 2000 41–66 43

Ž . Ž .Fig. 1. Bottom topography of a the eastern Mediterranean Alboran Sea, the Strait of Gibraltar, the Gulf of Cadiz and adjacent areas of the´Ž . Ž Ž ..eastern North Atlantic Gulf of Cadiz, and b of the model domain indicated by a rectangle in a . The locations of vertical sections are

indicated by numbers 1–4.

tion into two cores and the routing of the flow by the.underlying topography . Jungclaus and Backhaus

Ž .1994 developed a two-dimensional transient re-duced-gravity plume model that resolves the horizon-tal structure of the plume and is able to simulate thesplitting and merging of dense plumes. The modelwas applied to the Denmark Strait overflowŽ .Jungclaus and Backhaus, 1994 . In the present case,however, we wish to include the processes connectedwith the separation of the MO in the vicinity of CapeSt. Vincent for which a 1.5 layer reduced-gravity

model is inadequate. Furthermore, the observationsfrom the Gulf of Cadiz show that the upper ocean isfar from stationary, contrary to the assumption of apassive upper layer in both the stream-tube and thetransient reduced-gravity model. Nevertheless, theknowledge obtained from the observational cam-paigns, together with the results of the model studiesmentioned above, anticipates requirements for athree-dimensional modeling approach. The major partof the mixing between the outflow and the ambientocean takes place over a rather small horizontal


Ž .distance some tens of kilometers and dependsŽstrongly on the local bottom topography Price and

.Baringer, 1994 so that a horizontal resolution of aŽfew kilometers is required Jungclaus and Backhaus,

.1994 . The turbulent energy required for the intensemixing is produced mainly by the shear between thefast outflow layer and the overlaying ambient watersŽ .Johnson et al., 1994a,b . Therefore, the model shouldalso resolve the vertical structure well enough. Thisis difficult for a z-coordinate model, especially whena depth range from a shallow shelf to a few-thou-sand-meters-deep ocean has to be accommodated;furthermore, the step-like representation of a slopingbottom does not favor the emulation of a bottom

Ž .boundary layer Gerdes, 1993 .Three-dimensional model studies, including the

simulation of dense water plumes, have been pub-lished only recently. Gawarkiewicz and ChapmanŽ .1995 consider dense water formation and off-shelftransport generated by an idealized coastal polynya.

Ž .Jiang and Garwood 1995 simulated the adjustmentprocess of a shelf front that is accompanied by theformation of small plumes by baroclinic instability.Both studies used numerical schemes with abottom-following vertical coordinate representation.

The model study presented here is carried outusing the three-dimensional sigma-coordinate Prince-

Ž .ton Ocean Model POM of Blumberg and MellorŽ .1987 . A terrain-following sigma-coordinate repre-sentation is especially useful for the simulation of adense outflow. Although the vertical resolution getscoarser with increasing water depth, relatively highresolution can be retained by applying a logarithmicsigma-level distribution within the bottom-boundary

Ž .layer Blumberg and Mellor, 1987 . The model usesthe hydrostatic and Boussinesq approximations andhas a free surface. The numerical scheme makes useof the split time-step technique where the externalmode calculates the vertically integrated transportsand the sea-surface elevations, and the internal modesolves the three-dimensional momentum, heat, andsalt equations. As has been shown by Jungclaus and

Ž .Backhaus 1994 , the bottom friction coefficient isan important parameter for the simulation of a bot-tom-trapped density current because it strongly influ-ences the magnitude of the ageostrophic downslopecomponent of the flow. In the POM model, the dragcoefficient is determined by matching the near-bot-

tom velocities with the logarithmic law of the wallwith a roughness length of 1cm. In those cases wherethe bottom boundary layer is not well-resolved, thecoefficient defaults to a drag coefficient, c s0.0025dŽ .Blumberg and Mellor, 1987 . Laplacian friction isimplemented along sigma-surfaces using the formu-

Ž . Ž .lation of Smagorinsky 1963 see also Mellor, 1992in which the coefficients of horizontal viscosity anddiffusion depend on the grid size and horizontalvelocity gradients:

1r22 2A sA sCD xD y u qÕ q u qÕ r2 ,Ž .M H x y y x

where a value, C, of 0.2 is applied. The mean( ) ( )temperature and salinity fields, T z , S z , are sub-

tracted before the horizontal diffusion is calculatedŽto minimize artificial diapycnal diffusion Mellor

.and Blumberg, 1985 . Vertical turbulent mixing pro-cesses are parameterized with the second-order tur-bulence closure scheme of Mellor and YamadaŽ .1982 . For further details of the model, see Blum-

Ž . Ž .berg and Mellor 1987 and Mellor 1992 . Recently,the POM model was applied to the general circula-

Žtion of the Mediterranean Sea Zavatarelli and Mel-.lor, 1995 . Their study includes the Strait of Gibral-

tar, but the outflow of MW into the Gulf of Cadizwas not discussed.

The first goal of this study is to test the sigma-co-ordinate model, previously used mainly for coastaland basin-scale problems, for the simulation of adense gravity current under realistic conditions. Cana three-dimensional model resolve the relevant pro-cesses? We wish to compare the model calculationswith observation and explore questions that are ac-cessible by means of a numerical model: What arethe mechanisms that lead to the double core structureof the MO and which role does the canyon-richtopography of the Gulf of Cadiz play? Is there anotable downslope transport by baroclinic eddies in a

Ž .way discussed by Gawarkiewicz and Chapman 1995or is the cross-isobath transport mainly achieved byEkman transport? How sensitive is the outflow tochanges in water mass characteristics of the sourcewaters and how do the results of the one-point

Ž .entrainment model of Baringer and Price 1994compare with the three-dimensional simulations? Theother goal of the paper is to demonstrate that theinstability of the Mediterranean undercurrent leads to


Ž .the formation of lenses of saline water Meddies offCape St. Vincent.

In Section 2, we describe the setup of the model.In Section 3, we begin the discussion of the numeri-cal experiment with a description of the evolution ofthe MW plume during the startup phase. Then resultsare presented after the model has reached a quasi-steady state. The baroclinic instability of theMediterranean undercurrent is discussed in Section3.5 while Section 3.6 presents a study on the sensi-tivity of the outflow to climatic changes of the

source water masses. We summarize the results inSection 4.

2. The model set-up

Since this is a process study focusing on theintrusion of the MW into the Gulf of Cadiz, the flowsystem of the Gibraltar Strait, and any external forc-ing like tides and wind, is excluded. Subsequentstudies will take these effects into account and will

Ž . Ž y3 . Ž .Fig. 2. Temperature 8C, dash-dotted line , density kg m , dashed line , and salinity solid line profiles used as initial conditions for theentire model domain.


include a discussion of the exchange flow in theStraits and its eastern and western approaches. Thetopographic data were interpolated from the 2.5X

Ždigital dataset DTM25 Geophysical Exploration.Technology, University of Leads, Great Britain to a

Cartesian grid that has a resolution of 5 km. Addi-tional smoothing was applied to reduce the ‘sigma-coordinate pressure gradient error’ discussed in Mel-

Ž .lor et al. 1994 . This procedure affected mainly thevery shallow areas near the land boundaries. Toperform a test, the model was run without any inflowforcing and a horizontal uniform density field which

should not produce any velocities. Erroneous speedswere generally less than 0.01 m sy1. Since baroclinicvelocities of 0.2–1.5 m sy1 are to be expected, theseerrors seem to be tolerable.

The model domain extends from 10830X W toX X Ž .5850 W and from 35815 N to 388N Fig. 1 . It

includes the Gulf of Cadiz and the Portuguese conti-nental slope up to a latitude just south of the Tejoplateau. To the east, we place the boundary next tothe Strait of Gibraltar, slightly to the west of the sillŽ .Fig. 1a . To the west of the domain, a dominanttopographic feature is the eastern flank of the Gettys-

Ž . Ž . Ž y1 . Ž .Fig. 3. Temperature 8C, dash-dotted line , salinity solid line , and normal velocity profiles cm s , dashed line at the inflow easternboundary.


burg Bank. Other important details are variouscanyons cutting into the continental slope and the

Ž .convergence of isobaths south of Portugal Fig. 1b .To the west, north and south, the model grid wasextended by 10 grid points with increasing grid sizeto remove disturbances created at the open bound-aries from the domain of interest. At the open bound-aries, radiation conditions were applied for externaland internal velocities normal to the boundaries, thecondition of no normal gradient was used for eleva-tion and a local upwind scheme was applied totemperature, salinity, and tangential velocities. Thevertical sigma-coordinate is represented by a total of40 levels, nine of them within a logarithmic bound-ary layer near the bottom.

The initial stratification for our model area isassumed to be horizontally uniform throughout the

Ž .model domain Fig. 2 . Typical profiles from theŽ .Gulf of Cadiz experiment Baringer, 1993 and from

Ž .Rhein and Hinrichsen 1993 , not directly affectedby the outflow, were taken into account. The salinityprofile shows a surface maximum that results fromthe strong evaporation over the entire subtropicalAtlantic. Waters at intermediate depth are character-ized by a decrease in both temperature and salinity.Here, we find the NACW. The water masses at about1200 m depth are permanently influenced by theoutflow from the Mediterranean Sea. They, there-

Ž .fore, show a salinity maximum that in realitydecays with distance from the EuropeanrAfricancontinent and that is visible throughout the entire

Ž .subtropical Atlantic Richardson and Mooney, 1975 .In the deeper waters, salinities and temperaturesdecrease toward the characteristics of the North At-

Ž .lantic Deep Water NADW .At the inflowroutflow channel on the eastern

boundary of the model, we prescribe temperature,Ž .salinity, and normal velocity profiles Fig. 3 derived

from observations from the western approaches ofŽthe Strait of Gibraltar Lacombe and Richez, 1983;

.Kinder and Bryden, 1990 . The velocity profile isadjusted so that an equal amount of water leaves themodel domain in the upper layer as enters into the

Žlower layer. In reality, some 10% more water Bryden.et al., 1994 flows into the Mediterranean to com-

pensate for the loss caused by evaporation. Theinflow and outflow transports are set to 0.78 Sv close

Ž .to the findings of Bryden et al. 1994 .

In the strait, there exists considerable time depen-dency that can be classified as tidal, sub-inertial andlong-term variability. Tides are large enough to re-verse the exchange flow near the Camarinal sill andthus contribute significantly to the mean transportsŽ .Bryden et al., 1994 . However, the influence ofthese variations decays with distance from the sillŽ .MacDonald et al., 1994 ; in fact, Johnson et al.Ž .1994a found only little tidal variations in theirrepeated XCP measurements. Atmospheric pressure

Žfluctuations caused by moving weather patterns e.g.,.Candela et al., 1989 contribute to ‘events’ of block-

ing or releasing of MW at the sill on sub-inertialŽ .time scales Grundlingh, 1981 . In this study, how-¨

ever, we stipulate a steady inflow.

3. Description of model results

3.1. The initial inflow phase

The model is started from rest and the normalvelocities at the eastern boundary are increased totheir prescribed values within one inertial period andare kept constant for the entire simulation whichcovered 2 years. The western approaches of theStrait of Gibraltar form a shallow and narrow chan-nel. The inflowroutflow conditions impose a two-layer flow where the saline and dense MW flowswestward, occupying the deeper parts of the channel,and the AW is driven out of the model domain in theupper layer. In the following, we concentrate on thesaline MW layer. Although the startup procedurewith no outflow plume present in the beginning may

Žnot be realistic there is no evidence for a total.absence of the outflow for a long period of time , it

is instructive to follow the evolution of the MWspreading onto the rather complicated bottom topog-raphy of the Gulf of Cadiz. Especially the inspectionof the early stage of development highlights theimportant role of the underlying topography. Here,the dense layer behaves rather similar to thereduced-gravity plumes presented by Jungclaus and

Ž .Backhaus 1994 . We do not see a break-up of thedownslope edge into small scale eddies as reported

Ž .by Gawarkiewicz and Chapman 1995 and JiangŽ .and Garwood 1995 for a shelf front. However, as


we will discuss later, the bottom plume does interactsignificantly with the overlaying water, contrary tothe assumption of a stagnant upper layer in thereduced gravity and stream-tube models.

Fig. 4a and b show contours of plume thicknessafter 2 and 8 days, respectively. The thickness isdefined to be the depth interval between the bottomand the point where the vertical salinity gradient is

Ž .maximum Smith, 1975 . In Fig. 4a, we have alsoindicated every other near-bottom velocity vectorŽhere as in the following, we use the sigma level 38

.to represent near-bottom quantities . At the easternedge of the model domain, the deep flow is con-strained to the narrow channel and the velocities aredirected along-channel. As the channel widens andthe plume encounters the steep topographic slope atthe shelf break near 6.208W, we observe the transi-

Ž .tion into another regime that Price et al. 1993called ‘‘the initial descent on the continental slope’’.Here the flow is no longer confined by sidewalls butforms a stream-tube with density fronts bounding thesaline bottom layer. The bottom slope imposes adownward-directed pressure force. The Coriolis ac-celeration tends to deflect the flow in a directionparallel to the isobaths, but Ekman transports due tobottom friction are large and add a strong downslopecomponent. In fact, the velocity vectors cross the

Ž .500 m depth contour almost at right angles Fig. 4a .Further downstream, however, there is a tendency ofthe vectors to follow bottom contours. Thus, weobserve a kind of ‘‘adjustment’’ from a stronglyageostrophic motion to a predominantly geostrophicbehavior that is characterized by flow along contoursof constant depth with a small downslope componentowing to Ekman veering. The model studies of Price

Ž .and Baringer 1994 and Jungclaus and BackhausŽ .1994 have shown that this ‘‘adjustment’’ dependscrucially on the entrainment. Entrainment not onlydiminishes the density contrast between the plumeand the ambient, leading to a decreased value of the‘‘reduced gravity’’ and therefore the pressure force,it also establishes cross-slope density gradients.These, via the thermal wind relation, counteract thegeostrophic along-slope flow in the upper part and

Žincrease it on the downslope side of the plume Ezer. Ž .and Weatherly, 1990 . Jungclaus 1994 showed that

neglecting the vertically integrated pressure gradientsresulting from horizontal density differences leads to

an overestimation of the downslope movement of adense bottom plume. It is important to note that thistransition is quite different from the frictionlessgeostrophic adjustment of a gravity current that was

Ž . Ž .described by Griffiths 1986 cf. his Eq. 3 . Theinertial overshoot in the frictionless case would onlyresult in a downslope movement of a few tens ofmeters. In our case, the dense flow on the continentalslope is controlled by a balance between the pressuregradient and Coriolis acceleration, bottom frictionand entrainment. It is the frictional component that

Ž .drives the flow downslope Smith, 1975 . Thus, inthe case of the MO, downslope movement of densewater through finger-like subplumes and barocliniceddies as discussed by Gawarkiewicz and ChapmanŽ .1995 plays a minor role in cross-isobath transports.

In Fig. 4a, a maximum of the plume thickness justbehind the front on the upslope side of the intrusion

Ždenotes the typical ‘‘head’’ structure Britter and. ŽLinden, 1980 of a gravity current. After 8 days Fig.

.4b , the maximum thickness is located near theleading edge at about 7.58W. There is another, muchsmaller maximum of plume height at 6.48W near the500-m depth contour. An inspection of a sequence of

Ž .plume height figures not shown here reveals thatthe plume head separates into two parts as thedownslope edge of it encounters a canyon. We indi-cate the pathways of the respective heads in Fig. 4b.

Ž .Whereas the upper head A continues to proceed ata water depth of about 600 m, the faster-moving

Ž .denser water is routed down the canyon B . In thetrench, the deep part of the flow is routed downslopeand it is constrained by sidewalls again. Hence, theinfluence of the Coriolis force is reduced and thebalance of the flow is dominated by the downslopepressure gradient, bottom friction and, to a lesser

Ž .part, entrainment Killworth, 1977 . The most salineŽ .water clearly follows this flow branch Fig. 4c .

Although, as we shall discuss later, the topographicsteering is not the only ingredient in establishing theobserved double-core structure of the MO, the actualseparation into two branches occurs here. It is inter-esting to note that no such downslope drainage hap-pens along the steeper canyon just west of the inflow

Žchannel denoted by a strong westward excursion of.the 1250 m depth contour in Fig. 1b . Although the

salinity contours show a slight excursion to thesouth, the transport down this channel is relatively


Fig. 4. The evolution of the dense-bottom plume during the initial phase in a limited domain near the Strait of Gibraltar. Plume thicknessŽ . Ž . Ž . Ž . Ž . Žcontour intervals20 m at a 2 days, and b at 8 days; c near-bottom sigma level 38 salinity at 8 days S)36.0 psu, contour

. Ž . Ž . Ž .intervals0.2 psu . Also shown in a are near-bottom velocity vectors every other grid point . In b , the dashed line depicts the pathwayof the upper ‘‘head’’ and the heavy line indicates the pathway of the lower ‘‘head’’ of the gravity current.


small. This agrees with the observations of MadelainŽ . Ž . Ž .1970 , Grundlingh 1981 , and Baringer 1993 who¨found that this pathway contributes little to the totaltransport. The canyon does not reach far enoughupslope to tap into the saline and dense core regionof the plume and the water that actually is trappedhere has already undergone considerable mixing andtherefore possesses only small density contrasts. Thebottom topography data are, however, not detailed

Ženough to resolve some smaller canyons down-. Ž . Ž .stream where Madelain 1970 and Zenk 1975

describe considerable routing.The saline plume continues to move westward

and spreads laterally on the continental slope southof Spain. Fig. 5a–d show the near-bottom salinityfields after 20, 80, 240, and 640 days of integration.In the three-dimensional simulation, the discrimina-tion between plume and the ambiance is less obviousthan in a layer model. We therefore follow BaringerŽ .1993 and define the 36.3 isohaline as the boundaryof the MW plume. The outflow roughly follows thebottom contours and its width increases up to about100 km in the central Gulf of Cadiz. Whereas theupper edge of the plume sinks from 450 m in thecentral Gulf to about 750 m south of Portugal, thelower edge remains confined to a depth of about1500 m. As the isobaths converge to the south ofPortugal and the flow is accelerated by the increaseddownslope pressure gradient, we observe a consider-able narrowing of the stream-tube west of Cape St.Maria. The leading edge of the plume follows theisobaths northward along the Portuguese continentalslope but the density contrast between the plume andthe ambient water has diminished significantly andthe 36.3 salinity contour does not proceed furtherthan Cape St. Vincent. There is some diffusivespreading at the upslope part of the MW layer, anddiffusion causes also the intermediate depths of the

Žambient water to become more saline cf. the south-ward extension of the 36.2 isohaline in the eastern

.Gulf of Cadiz in Fig. 5d because we have notincluded any restoring to the profile of Fig. 2. How-ever, the overall distribution of near-bottom salinityand temperature remains rather stable after, say, 150days of simulation and subsequent salt and heat fluxinto the model domain is laterally injected into inter-mediate depth layers. This will be discussed in Sec-tions 3.4 and 3.5.

The evolution of water mass properties in theGulf of Cadiz reflects the mixing between the MW

Žand the overlaying NACW. The salinity field Fig..5c,d shows a rapid decrease of 1 psu from the core

value at the eastern boundary of 38.3 within a hori-zontal distance of 50 km.

3.2. Comparison with obserÕations

Fig. 6 shows the downstream evolution of themaximum salinity on meridional transects comparedwith those found in the literature, and Fig. 7 depictsthe potential temperature at the position of the maxi-

Žmum salinity here, as in Sections 3.3 and 3.4, data.were analyzed after 640 days of simulation . The

observations from different years are obviously in-fluenced by seasonal and interannual variations. Themodel reproduces the decrease of the core salinityfrom more than 38 to about 36.5, and the cooling ofthe outflow from about 13.58 to less than 128 on theway from the Strait to the south of Portugal. Obser-vations from the west of Portugal, however, mostlyshow that the 36.3 isohaline extends further to the

Žnorth than the model predicts Zenk and Armi, 1990;.Daniault et al., 1994 . In Fig. 8, the cross-sectional

averages of density differences between the outflowŽ .layer and the ambient waters found in Smith 1975Žare compared with model-calculated averages where

.a similar averaging and weighting method was used .Save for an offset near the Strait, where the modelseems to predict an overly rapid decrease of thedensity contrast, the model predicts the downstreamslope of the evolution reasonably well. The loss ofdensity contrast is a measure of the subsequent mix-ing that occurs on the way through the Gulf ofCadiz. The most pronounced entrainment of fresherwater occurs directly to the west of the strait where

y3 Žwe observe a drop of 1.0 kg m more than two.thirds of the original value within a horizontal dis-

tance of less than 100 km. The mixing process mayfurther be elucidated by an inspection of a potentialtemperature–salinity diagram for the entire plumeŽ .Fig. 9 . The T–S curve is bounded on the low-salin-ity side by the prescribed ambient profile. Deviationsfrom this curve are products of mixing with theinflowing MW. We notice the broad temperature and


Ž . Ž .Fig. 5. The near-bottom sigma level 38 salinity field S)36.0 psu, contour intervals0.2 psu after 20, 80, 240, and 640 days ofsimulation.

Ž .therefore depth range cf. Fig. 2 of the mixing.However, the main mixing agent is the less salineNACW found between 200 and 800 m. There is a

particularly high density of T–S pairs at ss27.5 kgmy3 and ss27.8 kg my3 that indicate the twocores of the MW undercurrent and is a common


Fig. 6. Downstream evolution of maximum salinity. Model resultsŽ .at 640 days solid line compared with observations. Dots: Rhein

Ž . Ž .and Hinrichsen 1993 ; crosses: Ambar and Howe 1979a ; squaresŽ . Ž .open: spring; solid: fall : Ochoa and Bray 1991 ; triangles:

Ž .Baringer 1993 .

Žfeature of observed data e.g., Zenk, 1975; Hinrich-.sen et al., 1993 .

Fig. 7. Potential temperature at the location of the salinity maxi-Ž . Ž .mum cf. Fig. 6 Model results at 640 days solid line compared

Ž .with observations. Dots: Rhein and Hinrichsen 1993 ; crosses:Ž . Ž .Ambar and Howe 1979a ; triangles: Baringer 1993 .

Fig. 8. Meridionally averaged density difference between the MWbottom layer and the ambient water. Model results at 640 daysŽ . Ž .line compared with the cross-stream averages and error bars of

Ž .Smith 1975 .

3.3. The Õertical structure of the graÕity current

The simulation of the entrainment and the watermass transformation within the MO depends on theability of the model to calculate the vertical mixingcoefficients accurately. These are functions of thevertical distribution of speed and density. In Fig. 10,we show vertical profiles of vector and scalar quanti-ties from the region of most intensive mixing. Thevelocity profiles are presented in a similar way as in

Ž .Johnson et al. 1994a . The velocity is rotated intoplume coordinates and the cross-stream axis is 908 tothe right of the along stream axis. Since the MWoutflow is mainly salinity-stratified, we only showsalinity profiles to indicate the water mass properties.Fig. 10 reveals that the plume consists of a well-mixed, but strongly sheared bottom layer that ex-tends up to the velocity maximum some tens ofmeters above the bottom and an interfacial layer thatis characterized by strong shears in both salinity andspeed. As in the measurement of Johnson et al.Ž . Ž .1994a cf. their Fig. 4 , the plume nose is a mini-mum of velocity shear and also a minimum ofvertical mixing. Also the cross-stream profile resem-


ŽFig. 9. Potential temperature–salinity diagram for the entire model domain at 640 days every eighth horizontal and every second vertical. ŽU.grid point is depicted . The core salinity of the Mediterranean Water is indicated by an asterisk .

bles Johnson’s figure. The cross-stream velocity ismaximum in the interfacial layer. This indicates thatthere is strong Ekman veering within the interfaciallayer but relatively little in the bottom boundary

Ž .layer. As explained by Johnson et al. 1994a , thevertical extent of the Ekman layer is of the sameorder or larger than the bottom layer and the downs-lope deflection therefore affects the entire densebottom layer, leading to considerable downslopetransport.

3.4. Cross-sections

The different stages of the outflow can be visual-ized in more detail by the inspection of cross-sec-tions across the continental slope that are indicated

Ž .in Fig. 1b. Cross-section 1 Fig. 11 is located near

the eastern inflow boundary where the situation canbe characterized as a two-layer exchange flow. Theoutflow forms a bottom layer of about 70–100 mheight. The internal Rossby radius is of the samemagnitude as the channel width and rotation tilts theinterface down southward. However, it is interestingto note that there are distinct layers of very densewater in the deep trench that fill the lower, say 70 m.The lower part within the trench is more isolatedfrom the ambient waters than the flow along thenorthern wall which, in addition, mixes with thewarmer near surface water. Approximately, the ss27.5 kg my3 isopycnal separates here already thetwo distinct water masses that continue to mix withdifferent water types and take different routes on thecontinental shelf owing to the different density con-trasts compared to their surroundings. In our model,this is a result of the stratified inflow we impose onthe eastern boundary. Similar structures were found


Ž . Ž . ŽFig. 10. Vertical profile at 6.258W, 36.18N of along-stream velocity heavy line , cross-stream velocity thin line , and salinity dash-dotted.line .

Ž . Ž .by Zenk 1975 and Ochoa and Bray 1991 . Zenk,Ž .referring to earlier results of Siedler 1968 , pro-

posed that tidal mixing produces two distinct peaksin temperature and salinity properties that will thenspread differently according to their density levels.

ŽIn the central Gulf of Cadiz cross-section 2, Fig..12 , the deep flow is aligned to the Spanish continen-

tal slope. The salinity maximum has sunk to morethan 800 m. The westward velocities show twonear-bottom maxima at 450 m and between 600 and850 m and the maximum velocities have decreasedto about 0.2 m sy1. These are the two cores of the

Ž .outflow. The observations of Baringer 1993 fromthis region show similar velocity structures as well

Ž .as magnitudes cf. her Fig. 2.9e . The upslope salin-ity front seems to be more distinct in the observa-tional data. The strong temperature and salinityanomalies of the plume probably lead to unrealisticdiffusion along the sigma surfaces. Test runs with

greatly reduced diffusivity resulted in much steeperupslope fronts but were accompanied by overshoot-ing of salinity values, owing to the characteristicbehavior of the central difference scheme used forhorizontal advection. To overcome this problem, amore advanced advection scheme that requires lessdiffusivity might be used in subsequent studies.

Further to the west, as the outflow approachesŽ .Cape St. Vincent cross-section 3, Fig. 13 , the

Žtopographic slope becomes extremely steep about.1.58 . The lower core with S)36.5 lies at about

1200 m on the continental slope. Density contrastsare relatively small, as indicated in Fig. 13D by therelatively week excursion of the isopycnals near theslope. Maximum velocities have increased again as aresult of the much stronger downslope pressure gra-dient that is now balanced nearly geostrophically.Speeds of more than 0.4 m sy1 are found at about700 m, above the salinity maximum at 1200 m. The


Ž . Ž . Ž . Ž . Ž .Fig. 11. Cross-section 1 cf. Fig. 1b at 640 days of simulation. A Potential temperature 8C , B eastward solid contour lines , andŽ . Ž y1 . Ž . Ž . Ž . Ž y3 .westward dashed contour lines velocities cm s , C salinity S)36.2 psu shaded , and D potential density kg m .

lower core begins to separate from the bottom andforms an intrusion into the intermediate ambientsalinity maximum. In the MW layer, temperatures

Ž .are highest )128C on the upslope part, in agree-ment with the observations of Ambar and HoweŽ .1979a .



In Fig. 14, we present an east–west sectionŽ .cross-section 4 that runs from the eastern flank of

the Gettysburg Bank to Cape St. Vincent. Along-slope northward velocities are found here above 600



m, indicating the upper core characterized by its hightemperature and salinities above 36.10. The lowercore is separated from the seafloor and forms de-

tached salinity anomalies with a diameter of about40 km. These blob-like features appear as salinitymaxima between 900 and 1300 m and are associated


Ž . Ž . Ž . Ž . Ž .Fig. 14. Cross-section 4 cf. Fig. 1b at 640 days of simulation. A Potential temperature 8C , B northward solid contour lines , andŽ . Ž y1 . Ž . Ž . Ž . Ž y3 .southward dashed contour lines velocities cm s , C salinity S)36.2 psu shaded , and D potential density kg m .

with positive temperature anomalies above 800 m.Structures with similar water mass properties were

Ž .also described by Kase et al. 1989 and Daniault et¨

Ž . Žal. 1994 . Although they are somewhat weaker aswell in the magnitude of the T and S anomalies as in

.the azimuthal velocities compared with the classical


Ž .definition of Armi and Zenk 1984 , they are referredto as meddies.

3.5. The intrusion of MW into intermediate depth

The model produces isolated ‘‘blobs’’ of highMW content resembling meddies. To see this, it isnecessary to inspect the three-dimensional flow fieldin more detail. The instability of the MO is a resultof the dynamic interaction between the dense gravitycurrent and the overlaying water layer. As has been

Ž .shown by Schacht 1994 in a two-layer study, the‘‘head’’ of a gravity current is accompanied by avortex pair in the upper layer. As the plume initiallypenetrates the ambient water body, a water columnlying originally before the plume moves on top ofthe ‘‘head’’ and the compression leads to the forma-tion of anticyclonic vorticity. As the plume movesforward, the water column, which was previouslylocated over the ‘‘head’’, is stretched and the conser-vation of potential vorticity requires that cyclonicvorticity is produced. This interaction has much incommon with the respective one of an isolated blobof dense water that was investigated by Whitehead et

Ž .al. 1990 . The initial disturbance triggers an instabil-Ž .ity of the form described by Swaters 1991 ,

Ž .Gawarkiewicz and Chapman 1995 , and Jiang andŽ . Ž .Garwood 1996 . Swaters 1991 showed for a dense

filament on a sloping bottom that instability occursupon the release of mean potential energy whensome of the dense water is slumping down theinclined bottom. The nature of the instability istherefore baroclinic even though it does not necessar-ily depend on the vertical velocity shear. The denseanomalies at the downslope front form finger-likesubplumes, which may separate from the main fila-ment and form anticyclonic blobs of relatively densewater. In the upper layer, the anomalies take theform of coastally trapped topographic Rossby waves.

ŽLaboratory studies Smith, 1977; D. Ettling, 1995,.personal communication show that the downslope

movement of a dense gravity current is accompaniedby the formation of eddies in the upper layer. Thesurface signature of such eddies was detected by

Ž .Bruce 1995 using satellite imagery near the EastGreenland coast where the deep Denmark Straitoverflow carries cold water southward.

In our case, the eddies are formed in the Gulf ofCadiz. They move westward and the upper layercyclones are often trapped within the coastal bound-ary current that flows along the Iberian peninsula

Ž .toward the Strait of Gibraltar Fig. 15a,c . The ma-ture eddies have a diameter of about 100 km andazimuthal velocities of 0.1–0.3 m sy1. The velocity

Ž .signal reaches deep into the interior cf. Fig. 14Band is able to advect the saline MW layer off thecontinental slope. We demonstrate this by showingsurface elevations together with the salinity field onthe 1200-m depth level for 20, 80, 240, and 640 daysin Fig. 15. After 20 days, negative values of sea-surface elevation near the Spanish and Portuguesecoast denote the boundary current that supplies thesurface flow into the Mediterranean. The relativelyweak cyclone south of Cape St. Vincent is the

Ž .surface signature of the bottom plume cf. Fig. 5a .Southward velocities in the interior drive part of the

Ž .saline MW into the interior. At day 80 Fig. 15c,d ,there is a strong cyclone southwest of Cape St.Vincent and the mid-depth salinity fields show amushroom-shaped anomaly approximately of thesame size as the upper layer eddy. The saline waterleaves the slope to the south-west of Cape St. Vin-cent where velocities are directed north-westward.

Ž .Five months later day 240, Fig. 15e,f ,anothercyclone is just leaving the model domain and we

Ž .observe a patch of relatively saline water S)36.3near the Gettysburg Bank. After 640 days of integra-

Ž .tion Fig. 15g,h , the situation resembles that of dayŽ .80 Fig. 15c,d and another mushroom-shaped

anomaly is formed. The period of these formations isabout 80 days. Here, the anomaly is rather strongwith salinities exceeding 36.4. Once an intrusion isformed it becomes, itself, subject to instability andorganizes itself into smaller patches of high salinity

Ž .with a diameter of 30–50 km McWilliams, 1985 .The baroclinic velocities at the same depth levelŽ .Fig. 16 show an anticyclone west and a cycloniceddy southwest of Cape St. Vincent. The maximumrelative vorticity of the anticyclonic vortex readsy0.15 f. Although we are able to simulate the subse-quent separation of blobs of saline water, we havenot observed the formation of submesoscale anticy-clones with the strong negative relative vorticityŽ .minimum values approaching yf that is typical for

Ž .Meddies Prater and Sanford, 1994 . Probably the


eddy will gain momentum when it — retaining itshigh salinity and temperature signal — moves intoless saline and colder water further to the west, thus

Ž .forming a stronger anomaly. Armi and Zenk 1984found a Meddy of similar water mass characteristicwithin a layer of 35.8 salinity water in the Canary

.basin . However, it is likely that even the relatively

high horizontal resolution that we presently can af-Žford to apply about equal in size to the first internal

.radius of deformation of our model grid is insuffi-cient to simulate these small-scale vortices ade-quately. Furthermore, the numerical diffusion of thelevel model makes it difficult to maintain isolatedfeatures.

Ž . Ž . Ž . Ž . Ž . Ž .Fig. 15. Sea-surface elevation mm after a 20, c 80, e 240, and g 640 days of simulation. Salinity at the 1200 m depth level after bŽ . Ž . Ž . Ž .20, d 80, f 240, and h 640 days of simulation. Contour intervals are 10mm for elevation and 0.1 psu for salinity S)36.2 .


Ž .Fig. 15 continued .

Additional model studies using homogeneous am-bient water confirmed that the mechanism for theinstability is essentially the one described by SwatersŽ . Ž .1991 and Jiang and Garwood 1996 . However, inthe case of a realistically stratified ambient waterbody, the anomalies at the downslope edge cannottravel downslope, unrestrictively owing to the lack ofexcess buoyancy. Rather, there is a lateral injection

of saline and warm water that is slightly denser thanits surrounding. Therefore, there is a transfer ofenergy from the mean potential into eddy potentialenergy that is subsequently transferred into eddykinetic energy by the adjustment process.

The abrupt change in bottom topography obvi-ously supports the separation of the saline water.Several Meddies found in the literature were ob-


Fig. 16. Velocity vectors at the 1200 m depth level at 640 days.

served at locations that indicate the continental slopeŽto the west of Portugal as a formation area Kase et¨

.al., 1989 but others must have originated in the GulfŽof Cadiz and near Cape St. Vincent Rhein and

.Hinrichsen, 1993; Prater and Sanford, 1994 . Re-cently, Lagrangian data from floats that were de-

Žployed in the MO south of Portugal Bower et al.,.1995, 1997 have confirmed the speculation that the

region off Cape St. Vincent is one prominent forma-tion area for Meddies. However, there are severalquestions that are difficult to address with the pre-sent model setting. Especially, what is the role of the

Ž .bottom topography cross-slope canyons and ridgesand the form of the coastline in the Meddy formation

Ž .process? In a recent paper Jungclaus, 1999 , westudy the baroclinic instability of an intermediatedepth boundary current using idealized bottom to-pographies and explore the sensitivity of the instabil-ity to various parameters like the bottom slope.

3.6. The sensitiÕity of the MO to changes in sourcewater properties

In the previous sections, we have shown that themodel realistically simulates the water mass transfor-mation of the MW on its way into the Atlantic. Wenow use the model for a sensitivity study concerningthe response of the MO to changes in source water

Ž .properties. Bryden and Kinder 1991 found thatvariations in the cross-sectional area caused, e.g., bysea level changes, could significantly alter the salin-ity difference between the inflowing AW and theoutflowing MW. They raised the question if a moresaline outflow would descend deeper and possiblyform a new bottom water mass. This problem was

Ž .also addressed by Price and Baringer 1994 andthey arrived at a simplified input–output model. Theassumption, that most of the entrainments occurstrongly localized at the shelf break, leads to thedevelopment of a one-point entrainment model.Given the initial transport and density difference, andthe bottom slope at the shelf break, the model calcu-lates the output density difference and transport.

Ž .Price and Baringer 1994 pointed to a negativefeedback mechanism, which makes the output watermass properties relatively insensitive to changes inthe initial density contrast. An initially denserŽ . Ž .lighter plume flows faster slower , produces moreŽ .less vertical shear at the interface, and subsequently

Ž .entrains more less ambient water. Different entrain-ment rates, however, strongly affect the output trans-port rates. The simplicity of the one-point model isattractive and it is therefore useful to examine itsassumptions by comparing it with the more sophisti-

Žcated three-dimensional POM model J. Price, 1996,.personal communication .

In Experiments 2 and 3, the source water salini-Ž .ties are increased decreased by 0.8 psu compared to

Ž .the ‘standard’ experiment Experiment 1 . The initialŽ .density contrast therefore increases decreases by

y3 Ž0.62 kg m about 40% of the value used in.Experiment 1 . In Fig. 17, we present the results of

this sensitivity study as a diagram of deep westwardŽ . Ž y3transports in Sv in density classes 0.05 kg m

. Xbins from a section at about 7820 W. The standardŽ .experiment Fig. 17a gives a total transport of

roughly 2.5 Sv and we see two peaks at the densitylevels of the two cores of the flow where the lowercore is more pronounced. A transport-weighted aver-age gives a mean density of 27.72 kg my3. In the

Žcase of a denser source water Experiment 2, Fig..17b , the product water densities increase and we

arrive at a mean value of 27.85 kg my3. Here, thelower core is clearly dominant, indicating a final

Ž .depth in the Atlantic somewhat deeper about 200 mcompared with the present-day situation. The total


Fig. 17. Westward transport of the Mediterranean outflow nearX Ž . Ž . Ž7820 W; a the standard experiment, b using a higher Experi-. Ž . Ž .ment 2 , and c a lower initial density contrast Experiment 3 at

the inflow near Gibraltar.

transports have increased dramatically to 3.81 Sv. AŽ .less saline source water Experiment 3, Fig. 17c

gives an averaged output density of 27.56 kg my3

and a total transport of 2.2 Sv. In this simulation,there is an absolute transport maximum at 27.7 kgmy3 but also a secondary one at 27.4 kg my3,indicating again two cores with rather similar trans-port rates. Their potential density suggests that theyare located slightly upslope compared with the stan-dard case. The results corroborate Price andBaringer’s finding that the changes in output densitycontrast are only a fraction of those stipulated at thesource. The 20%–25% we derive from our is higher

Ž .than the 15% calculated by Price and Baringer 1994for a similar set of experiments. In their study, theyassumed that the mixing takes place only at onelocation and that the entrained ambient water proper-ties do not change. An analysis of the TS properties

Ž .along the outflow not shown indicates that theŽ .entrainment occurs more gradually cf. Fig. 8 in our

Ž .study. Additionally, the denser somewhat deeperflow of Experiment 2 entrains higher amounts ofrelatively cold NADW and the outflow of Experi-ment 3 mixes more preferentially with warmer upperlayer waters compared with the standard experiment.However, in terms of absolute output density orsalinity, the difference between the three-dimen-

Žsional and the one-point models is small 0.065kgy3 y3 .m for a 1 kg m change in source water density

and our experiments add some confidence in theŽ .simplified approach of Price and Baringer 1994 .

Both models predict that even a much denser out-flow would not reach the bottom of the deep At-lantic.

4. Summary and discussion

This model study concentrated on the simulationof the intrusion of a dense water mass into a strati-fied environment under realistic topographic con-ditions. Previous studies of the Mediterranean un-dercurrent used stationary, horizontally integratedreduced-gravity models and were not able to repro-duce certain important details of the observed flow.

The Princeton Ocean Model, which was previ-ously used mostly for estuarine and open-ocean ap-plications, simulates the flow structure in the Gulf of


Cadiz in agreement with observations. The terrain-following vertical coordinate, together with a loga-rithmic distribution of sigma-levels near the bottom,enabled us to resolve the vertical structure of thedense-bottom current remarkably well. There are twoingredients in the formation of the double-core struc-ture observed in the outflow. First, the saltiest water

Žsupplied by the Mediterranean Sea with consider-.able amounts of WMDW forms a dense layer in the

channel west of Gibraltar, which is partly isolatedfrom the AWs by a layer of slightly fresher outflowwater. It, therefore, retains a higher density andshows a slightly stronger downslope movement. Sec-ond, a steep canyon that cuts into the continentalslope at about 6845X W taps into this relatively salinewater and drives the bottom water directly downs-lope whereas the upper core continues to follow theisobaths while slowly sinking owing to Ekman veer-ing.

A sensitivity study on the response of the outflowto changes in source water properties confirmed

Ž .earlier results of Price and Baringer 1994 . The finalwater mass properties of the outflow are rather in-sensitive to changes in source water density but thetransports are. It is especially interesting that theresults of the one-point entrainment model are robustwhen compared with the respective one of the moresophisticated three-dimensional model. The simpli-fied approach could be considered as an overflowsubmodel to be plugged into a large-scale climatemodel.

The experiments demonstrate that the Mediter-ranean undercurrent becomes hydrodynamically un-stable and the instability resembles the baroclinicinstability of a dense filament described by SwatersŽ .1991 . An important difference between the latterand the Mediterranean undercurrent is that anomaliesat the downslope edge of the flow cannot slumpdownslope but are injected laterally into the ambientwater where they undergo an adjustment process andform submesoscale lenses of relatively high MW

Ž .content Meddies . The baroclinic instability stronglyinfluences the detachment of the lower core of theoutflow that has become neutrally buoyant to thesouth of Portugal. The details of this process, e.g.,the role of the local bottom topography and theimportance of time depending forcing will be inves-tigated in an upcoming study.

Acknowledgements

We thank Tal Ezer, Jim Price and two anonymousreviewers for comments which helped improve thepaper. J.H.J. was supported by a grant from theNational Oceanic and Atmospheric AdministrationŽ .NOAA, grant no. NA67RJO120 . The views ex-pressed herein are those of the authors and do notreflect the views of NOAA or any of its subagencies.

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