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Dynamics of Atmospheres and Oceans 45 (2008) 208–228

Contents lists available at ScienceDirect

Dynamics of Atmospheresand Oceans

journal homepage: www.elsevier.com/locate/dynatmoce

The effect of Antarctic Circumpolar Current transport onthe frontal variability in Drake Passage

Bin Zhanga,∗, John M. Klinckb

a Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, NJ, USAb Center for Coastal Physical Oceanography, Department of Ocean, Earth and Atmospheric Sciences,Old Dominion University, Norfolk, VA, USA

a r t i c l e i n f o

Article history:Available online 3 July 2008

Keywords:FrontsAntarctic Circumpolar CurrentNumerical modelingDrake PassageSouthern Ocean

a b s t r a c t

The Antarctic Circumpolar Current (ACC) is composed of threemajor fronts: the Sub-Antarctic Front (SAF), the Polar Front (PF),the Southern ACC Front (SACCF). The locations of these fronts arevariable. The PF can shift away from its historical (mean) locationby as much as 100 km. The transport of the ACC in Drake Passagevaries from its mean (134 Sv) by as much as 60 Sv. A regional numer-ical circulation model is used to study frontal variability in DrakePassage as affected by a range of volume transports (from 95 Sv to155 Sv with an interval of 10 Sv). Large transport shifts the frontsnorthward while the smaller transport causes a southward shift.The mean shifting distance of the PF from the historical mean loca-tion is minimum with 135 Sv transport. The SAF and the SACCF areconfined by northern and southern walls, respectively, while thePF is loosely controlled by the topography. Due to impact of theeddies and meanders on the PF at several regions in Drake Passage,the PF may move northward to join the SAF or move southwardto combine with the SACCF, especially in central Scotia Sea. TheSAF and PF are more stable with higher transport. The SAF behavesas a narrow, strong frontal jet with large transport while display-ing meanders with smaller transport. In the model simulations, theErtel Potential Vorticity (EPV) is strongly correlated with the vol-ume transport stream function. EPV at depths between 1000 and2500 m is correlated with the transport stream function with a coef-ficient above 0.9. Near the bottom, the correlation is about 0.6 due tothe disruptive influence of bottom topography. Within 750 m of the

∗ Corresponding author. Tel.: +1 732 932 6555x253; fax: +1 732 932 8578.E-mail address: [email protected] (B. Zhang).

0377-0265/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.dynatmoce.2008.05.002


B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) 208–228 209

surface, the correlation is much reduced due to the effect of K-ProfileParameterization (KPP) mixing and eddy mixing.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

The Antarctic Circumpolar Current (ACC) is composed of three continuous jets associated with threemajor fronts, which from south to north are the Southern ACC front (SACCF), the Polar Front (PF) andthe Sub-Antarctic Front (SAF).

All three fronts appear as maxima in geostrophic volume transport (Orsi et al., 1995). The meanLagrangian speed from surface drifters for the SAF and the PF are above 0.4 m s−1(Hofmann, 1985).The surface geostrophic velocity is around 0.4–0.5 m s−1 for both SAF and PF (Whitworth et al.,1982). The surface elevation change across the front is 0.7 m for SAF and 0.6 m for PF (Gille, 1994).Accordingly, temperature, salinity, oxygen concentration or biological properties across the fronts alsochange rapidly. Across the PF, the sea surface temperature (SST) change is around 1.35 ◦ C over a dis-tance less than 60 km distance (Moore et al., 1997). This large gradient of SST is often associatedwith large concentration of chlorophyll (Moore and Abbott, 2002). All these properties of the rapidjump of physics across front can be used to locate the front and its width at specific time. Goodsummary of the criterion for each front can be found in Orsi et al. (1995) and Belkin and Gordon(1996).

The location and width of each front have been looked through various methods from hydrographydata, satellite altimetry data or SST data (Nowlin and Clifford, 1982; Belkin, 1993; Gille, 1994; Orsiet al., 1995; Belkin and Gordon, 1996; Moore et al., 1999; Dong et al., 2006). The mean width of thePF and the SAF are approximately between 40 km and 60 km (Nowlin and Clifford, 1982; Gille, 1994;Moore et al., 1997). The width of SACCF is usually less than 30 km. Orsi et al. (1995) estimated the meanlocations of the SAF, the PF and the SACCF from historical hydrographic measurements (Fig. 1). Gille(1994) mapped the location of the SAF and the PF from satellite surface elevation using the Gaussiancumulative probability function. Belkin and Gordon (1996) gave the location of the SAF and the PFfrom hydrography data. Moore et al. (1997) used SST gradient to estimate the path of the PF. Dong et al.(2006) used the absolute surface temperature gradient to locate the PF. The resulting mean locationsare mostly similar but differences at some places are clear (Moore et al., 1999; Dong et al., 2006). Thedifferences might come from the errors in different methods. However, the variability of the frontsalso brings uncertainty in determining the frontal locations.

Gille and Kelly (1996) estimated the mean shifting distance of the PF from its mean location to be70 km. The time scale of this variability is 3 months and the zonal decorrelation scale is 80 km. Hofmannand Whitworth (1985) used the 2 ◦ C isotherm at 500 m from the ISOS mooring array measurementsto locate the PF. Cold core eddies were seen to impact the PF from the south resulting in shifts of upto 90 km. Eddy shedding from the PF resulted in similar location changes. All the estimates of thePF location from different methods (Gille, 1994; Orsi et al., 1995; Belkin and Gordon, 1996; Moore etal., 1999; Dong et al., 2006) show strong frontal location steering by topography. The PF meanderingintensity is weaker where the bathymetry is steeply sloped and stronger where the bottom is relativelyflat (Moore et al., 1999).

Variations within the ACC make it difficult to measure its total transport. The ACC transport can beseparated to two parts: the baroclinic and barotropic transports. The baroclinic transport remains rel-ative steady (Cunningham et al., 2003), while the barotropic transport can change rapidly. Whitworthand Peterson (1985) estimated the ACC transport in Drake Passage from moored current sensors tobe 134 Sv with a range of 95 Sv to 158 Sv. Monthly changes in transport can be more than 50 Sv.Whitworth and Peterson (1985) pointed out the fluctuations in ACC transport in Drake Passage aremainly barotropic.

Sprintall (2003) used XBT measurements in Drake Passage during 1996–2002 to show that theDrake Passage seasonal variation occurs only in the upper 200 m. Geostrophic transport mapped frommeasured temperature shows that the transport variation is interannual with no clear seasonal signal.Cold slope water and icebergs in the southern Drake Passage could impact the local hydrographic


210 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) 208–228

Fig. 1. The model domain is the 1200 km by 1200 km box in the middle of the map. The historical front locations are indicatedas heavy lines. Shading shows bathymetry shallower than 3500 m indicating the seamounts in the middle of Drake Passage andthe Shackleton Fracture Zone. Circles are the ISOS mooring locations. OI is the Orkney Island and WAP is the Western AntarcticPeninsula.

variation over short time scales (weekly to monthly) which would affect transport estimates frombottom pressure measurements.

The repeat hydrography along WOCE line SR-1 shows that the PF has two common locations and thatthe SAF and the PF sometime merge to form one front (Cunningham et al., 2003). This joining makes itdifficult to separate the contribution of each frontal jet to the transport. In addition, the hydrographyalong this section is difficult to interpret due to S-shaped meanders. Thus, understanding of frontalvariability in Drake Passage requires a 2D synoptic view of the hydrography.

The SACCF is located very near the shelf break along the western side of the Antarctic Peninsula andthus plays an important role in the transport of krill larvae to South George Island (Fach and Klinck,2006). A remarkable feature of the SACCF is the strong northward deflection in the vicinity of theShackleton Fracture Zone in southern Drake Passage (Fig. 1). This deflection is not permanent and theSACCF displays considerable meandering in this location.

There are a number of numerical models of the ACC, but most do not produce realistic paths, widthsor variability for the fronts in Drake Passage. The Fine Resolution Antarctic Model (FRAM) (FRAM Group,1991), which had a grid spacing of 27 km, produced an unrealistic partition of the transport among theACC fronts (Grose et al., 1995). The total transport in Drake Passage from FRAM is about 180 Sv withthe SAF transport being about 130 Sv. Both of these transports are well above observations. The PF inFRAM seems to have split and attached to either the SAF or the SACCF (called the Continental WaterBoundary at that time). This difficulty with the FRAM solution is believed to be caused by the coarsegrid resolution which causes unrealistic bottom topography in the model.



Thorpe et al. (2005) found different circulation in the Scotia Sea in two global ocean circulation mod-els (with 0.25◦ horizontal resolution) and proposed that different representation of the bathymetry isthe likely reason, from among many, to force the SAF and PF to merge together against the tip of SouthAmerica.

In this study, we use a high resolution regional ocean circulation model to study therelationship between the volume transport of the ACC and frontal variability. By specifying dif-ferent transport along the western boundary, we look at how each ACC front in Drake Passageresponds.

The next section describes the model that we use along with details of initial and boundary con-ditions. The following section presents the diagnostics that we use to analyze the model. Section 4presents results from the various simulations that we run. Section 5 discusses the implications ofthese results, followed by Section 6 which recaps the main conclusions.

2. Model description

The Regional Ocean Modeling System (ROMS) is used in this study. ROMS is a terrain-following,three-dimensional primitive ocean model with Boussinesq and hydrostatic pressure approximations(Shchepetkin and McWilliams, 2003). It adopts a terrain-following vertical (S) coordinate system,which allows non-uniform vertical resolution. Details of these and other features of ROMS can befound at http://www.myroms.org/index.php.

The model domain (Fig. 1) covers the major topography features in Drake Passage. A stereographic(azimuthal) projection centered at 62◦W, 58◦S, with a 30◦ clockwise rotation defines the basic coordi-nate system. The domain size is 1200 km by 1200 km. The grid spacing is approximately 6 km, whichresults in a grid size of 200 by 200. The grid rotation allows the ACC to enter the western boundaryof the model domain at approximately normal incidence, making the open boundary condition therebetter behaved.

The bottom topography was linearly interpolated to the model grid from ETOPO2 (a 2-min res-olution bathymetry) from National Geophysical Data Center (Smith and Sandwell, 1997). The mainfeatures of the Drake Passage topography, such as the seamounts and ridges are well represented inthe model (Fig. 1).

Initial distributions of temperature and salinity are taken from the World Ocean Atlas (Boyer andLevitus, 1998). However, time and space averages of sparse observations in this region with frontalvariability produces weak property gradients in place of sharp, narrow frontal features. We use a featuremodel (similar to that of Gangopadhyay et al., 2002) to recover the fronts at their mean locations. Weassume that properties in the fronts follow a Gaussian cumulative distribution function consistentwith a Gaussian frontal jet as described in Gille (1994).

The feature model is constructed as follows. The temperature and salinity from the World OceanAtlas (WOA) within each frontal zone is averaged along the front. The Gaussian cumulative distribu-tion function is used to construct the fronts as: T(�r) = T1 + (T2 − T1) ((�r − �r0)/�), where T(�r) is thetemperature or salinity at �r, Ti represents the mean temperature or salinity from WOA in each side ofthe front, is the Gaussian cumulative distribution function. The frontal width is chosen to be 51 kmfor the SAF, 61 km for the PF, 39 km for the SACCF to be consistent with hydrographic measurementsby Nowlin and Clifford (1982).

Along the open boundaries, the temperature and salinity are relaxed to the initial conditions forthese variables. The nudging time scale is 5 days. Nudging is imposed over a zone of about 30 kmthickness over most of the model grid next to the open boundary. A 60 km (10 grid intervals) zone isimposed at the eastern boundary to improve model stability. The free surface condition at boundariesis no-gradient. The total volume transport at the model boundary is controlled to keep a balancedinflow and outflow.

The geostrophic velocity �ubc is calculated along each boundary from the initial temperature andsalinity referred to 2500 db. Vertically integrating the geostrophic velocity, we obtain the 2D integratedbaroclinic flow along the boundary and the baroclinic transport �bc . We add the barotropic flow �ubtwith the same shape as the baroclinic flow to match the desired total transport �t . The barotropicvelocity is determined by this: �ubt = �ubc ∗ (1.0 − �bc/�t). The combination of the baroclinic and the



barotropic flow is imposed along each boundary. The imposed incoming volume transport representsthe effect of the Southern Hemisphere winds on the transport through Drake Passage.

No wind stress is applied within the model domain. Experiments with local wind forcing havesolutions very similar to those presented here. Bottom stress is applied as the linear function of thebottom velocity with a drag coefficient of 0.0025. The horizontal viscosity is 50 m2 s−1, and the tracerdiffusion coefficient is 5 m2 s−1. A K-Profile Parameterization (KPP) vertical mixing scheme is used.

Seven model simulations are run for different imposed transport which range from 95 Sv to 155 Svwith an interval of 10 Sv. In each transport case, the model begins in a static state with the samefeatured initial conditions and runs for 400 days. The model state is saved every 5 days.

3. Model diagnostics

3.1. Kinetic energy and potential energy

The volume averaged total energy is an important indicator of the model state. These simulationsare driven largely by kinetic energy input through the western boundary and kinetic energy dissipationdue to bottom and interior frictional losses. Energy converts between kinetic and potential due to avariety of mixing, geostrophic adjustment and dynamic instability mechanisms. The volume averagedmodel energetics are analyzed by calculating the volume averaged kinetic energy (VAKE) and volumeaveraged potential energy (VAPE) at each time the model state is saved. The specific calculationsare

KE =0.5 · ∑∑∑

�i,j,k(2ui,j,k

+ 2u

i+1,j,k+ 2vi,j,k

+ 2v

i,j+1,k)�z�x�y

∑∑∑�x�y�z

(1)

PE =∑∑∑

�i,j,kgzr i,j,k�z�x�y∑∑∑�x�y�z

(2)

3.2. Frontal kinetic energy

The volume averaged energetic quantities provide general information on the model state, but thetransport and kinetic energy are mainly found in the fronts so it is necessary to delineate each frontalarea and calculate quantities within the frontal areas.

We define each front by two sea surface elevation isolines. Since we used the strong nudg-ing/clamped boundary conditions on the western boundary, the surface elevation and temperatureon the surface maintain through the domain the step-like structure imposed at the boundary. Thepeaks in the surface elevation gradient along the western boundary are consistent with the location ofthe fronts. Centered at this point, we locate two grid points at the boundary whose distance is approxi-mately equal to the frontal width. Contour lines corresponding to these surface elevation values denotethe front. A flood-fill method is used to mark the area between these two bounding lines. The frontalsurface area, total volume, total kinetic energy and volume averaged kinetic energy is calculated foreach frontal area.

The PF and SAF are easily demarked by this method. However, the SACCF is more difficult to delin-eate. In addition. it makes a smaller contribution to the transport and energy, so the calculation is notdone for the SACCF.

3.3. Tracking fronts from surface elevation and temperature at 500 m

Over the Southern Ocean, the surface elevation and temperature may change along a frontal axis(Dong et al., 2006). However, over short distances the surface elevation is a good indicator of front.Fitting elevation to the Gaussian cumulative probability function is used to track the location of fronts(Gille, 1994). Each of the ACC fronts is associated with a very narrow range of SSH values correspondingto large lateral gradient of SSH (Sokolov and Rintoul, 2002). The surface density (imposed at the western



Table 1Mean SSH value and its standard deviation for each front and transport

95 Sv 105 Sv 115 Sv 125 Sv 135 Sv 145 Sv 155 Sv

SAF 29 ± 2 30 ± 2 31 ± 2 34 ± 2 36 ± 1 38 ± 1 41 ± 1PF −4 ± 3 −3 ± 3 −2 ± 3 −1 ± 3 2 ± 1 4 ± 1 6 ± 1SACCF −37 ± 3 −37 ± 2 −38 ± 3 −38 ± 2 −38 ± 2 −38 ± 2 −37 ± 2

These values are used to track each front with each transport. Unit: cm.

boundary) in the model solutions remains approximately fixed along streamlines. Surface elevation isa close proxy for the circulation.

Because of this relationship, the frontal axis can be tracked using the surface elevation isolinedefined by the surface elevation value on the western boundary. Different transport cases have thedifferent surface elevation values for the fronts. Due to the no-gradient boundary condition, the definedsurface elevation for a front changes slightly with time. The mean SSH values and their standarddeviations with different fronts and transports are listed in Table 1. We define the fronts for eachmodel state (starting with the second simulation month) and calculate the average and variance forthe frontal position along y-axis (typically using more than 70 values for each simulation). The frontallocations are assumed to be single valued functions of the model x coordinate, so strong meanders arenot well represented. If there is a S-shape meander in the front, the southern most point taken as thefront location as in Dong et al. (2006).

There is little seasonal temperature variation below 200 m (Sprintall, 2003). The ACC fronts areknown to have signature through the water column (Cunningham et al., 2003; Orsi et al., 1995). Thetemperature at 500 m is a good way to locate fronts over time. The 500 m temperature from the ISOSmoorings was used to track the PF (Hofmann and Whitworth, 1985) over a 14-month period. Similarly,in the model 500 m temperature is used to track the PF using a target temperature associated with thefront defined on the western boundary. The same temperature was used for a given front for differenttransport cases. As with surface elevation, the target isotherm was assumed to be a single valuedfunction of the model x coordinate.

3.4. Calculation of the PF shifting distance

The PF shifting distance is the difference of the model location compared to the historical location(Orsi et al., 1995), or SD = ∑

|�r − �r0|/N, where �r is the PF location for each x grid index I, �r0 is thehistorical PF location at the same index, and N is total x direction grid points (excluding nudgingand sponge layers). The model solution in the first month is not used due to model adjustment. Thisdiagnostic is used to estimate the effect of imposed ACC transport on frontal location and variability.

3.5. Calculation of the Ertel Potential Vorticity

Ertel Potential Vorticity (EPV) is an important physical variable which under the adiabatic con-ditions and without external forcing is a conserved quantity following the flow (Gill, 1982). In deepwater, these conditions apply and EPV can be regarded as conserved. In these simulations, EPV is usedto distinguish waters of different origin, such as those found between each front.

EPV is defined as q = ((�f + ��) · ∇�/�), where q is Ertel Potential Vorticity, �f is the planetary vorticity,�� is the relative vorticity, � is the conserved quantity, here chosen as the potential density, � is thedensity. Conserved EPV is a function of the stream function ( ), which in this case is deduced from the2D vertically averaged velocity and the total water depth. A relationship between q and� is determinedby least square methods from the model solution.

4. Model results

Model simulations are run for 1 month to allow the initial fronts, specified by the feature model, tocome to a geostrophic balance. Model results from the end of the first month to day 400 are analyzed.



For each of the simulations with different imposed transport, we analyze the integrated energy, com-pare the frontal locations to historical ones and compare surface elevation to satellite observationsand analyze EPV.

4.1. Kinetic and potential energy analysis

VAKE behaves differently for different transport cases (Fig. 2a). For all cases, VAKE increaseswith time and oscillates but there is no tendency for VAKE to increase with increasing trans-

Fig. 2. Volume averaged kinetic and potential energy over the whole model domain. The units of VAKE in the plot are1000 kg m2 s−2 and a constant number is subtracted to better see the variability. (a) Volume averaged kinetic energy, (b) volumeaveraged potential energy.



port (although the case with the largest transport has a much larger excursions of VAKE than theother cases). VAKE increases over time as the frontal jets become unstable and develop meso-scalevariability.

The total input kinetic energy for these different transport cases must be balanced by some othermechanisms besides the geophysical adjustment to frontal kinetic energy, such as transferring theVAKE to the potential energy, increasing of dissipation rate due to increased vertical shear or an increasein bottom form drag. The oscillation of VAKE with time is partially due to the open boundary conditions(see the discussion by Marchesiello et al., 2001).

VAPE decreases with time for all transport cases with the smaller transport cases declining morethan the higher transport. The amount of VAPE reduced with time ranges from 100 kg m2 s−2 with155 Sv transport to 600 kg m2 s−2 with 95 Sv. These numbers are much higher than the amount ofincrease in VAKE (order of 10 kg m2 s−2). This reduction in VAPE is associated with reduced pycnoclineslope, which is due mainly to active mixing process.

The VAKE in each front is relatively steady (Figs. 3 and 4) and different compared to the wholedomain VAKE (Fig. 2). This steadiness indicates that the PF and SAF have adjusted to a geostrophicbalance during the first month. Thus, the VAKE in zones between fronts must increase to accountfor this difference. This increase must be caused by transfer of kinetic energy from the fronts due toshedding of meso-scale eddies. These processes mix waters across the fronts which tend to diminishthe isopycnal slope in the fronts.

The area of the PF increases over time for all transport cases. This increase is due to meso-scaleeddies, which are clear from model snapshots except close to the nudging and sponge layer whereit converges to the specified location on the eastern boundary. Longer running cases (up to 4 years)develop an increasingly wide PF due to eddy shedding to the point that the PF is difficult to detect(figures not shown). Over these long simulations, the PF in the model reappears as a frontal jet butremains weaker than the SAF.

The VAKE for the SAF increases with increasing transport implying that the velocity of the SAFjet increases. The area of the SAF stays relatively steady. The highest transport case (155 Sv) shows areduction of the SAF area compared to other transport cases in spite of the higher VAKE, indicatingthat the eddy shedding must decrease.

Unlike the PF, the SAF can not shed its additional KE through shedding of rings due to the closeproximity of the continental slope at the north side of Drake Passage. This tendency is indicated by therelatively constant frontal area for the SAF (Fig. 4).

4.2. Surface elevation comparison with satellite data

The observed surface elevation is obtained from AVISO Ssalto/Duacs which provides weeklyglobal gridded (1/3◦ × 1/3◦) absolute surface dynamic topography (http://www.aviso.oceanobs.com/html/donnees/welcome uk.html). This field is constructed from data from all altimeter missions(Jason-1, Topex/Poseidon, Envisat, GFO, ERS-1 & 2 and even Geosat).

The AVISO data is extracted over the model domain and averaged for 5 years (Fig. 5a). Frontallocations are not clearly evident due to averaging, but some basic features remain. The separation ofthe SAF and the PF in the middle of Drake Passage can be seen. The remarkable northward excur-sion of the SACCF occurs after passing the Shackleton Fracture Zone (around 58◦W, 60◦S). In thewest, fronts are not distinguished clearly by the mean SSH fields due to the high spatial variabilitythere.

The surface elevation from the model solutions are averaged for 1 year (Fig. 5). We label each frontin the mean fields with the mean SSH isoline in Table 1 to roughly indicate each frontal location inthe mean field. The strongest frontal jet is associated with the SAF for cases with transport higherthan 115 Sv. The SACCF jet is the weakest with these transports. The PF shows clear differences incases with different transport. With higher transport, the PF is narrower than with smaller transport.Large meanders occur in the SAF and the PF near the western boundary for the smaller transportcases (95–125 Sv). For the higher transport (135–155 Sv), these meanders become weaker or disap-pear. The SACCF shifts more northward with higher transport (along the longitude line 65◦W) in themodel.



Fig. 3. The volume averaged kinetic energy (solid line) and area (dashed line) of the Polar Front. The straight solid line is thetime mean VAKE.

One notable feature in AVISO altimetry (not evident in the mean field) is the splitting and rejoiningof fronts. In the satellite field, sometimes the PF enters Drake Passage and splits into several filamentswhen passing the seamounts in the center of the passage. These filaments rejoin downstream. In themodel, the PF occurs as a very strong jet upstream and does not split over the seamounts. However,eddies are generated downstream of the seamounts in the model.

The observed SACCF shifts northward after passing the Shackleton Fracture Zone Ridge to formthe S meander as indicated by the 25 cm isoline of the surface elevation at (58◦W, 59.7◦S) inFig. 5(a). The model SACCF loses this excursion. This feature is also missed in other GCM solu-tions (Thorpe et al., 2005), which is believed to be caused by smoothing bottom topography in themodels.



Fig. 4. The volume averaged kinetic energy (solid line) and area (dashed line) for the Sub-Antarctic Front. The straight solid lineis the time mean VAKE.

4.3. Surface elevation tracked fronts

The mean location for each front with different transport cases are compared to its historical meanlocations (Fig. 6a–c). The basic tendency is that the mean frontal axis stays northward with highertransport while southward with smaller transport in the middle region of the Drake Passage. Thedistance of the mean location from its historical location is not the same for the three fronts in thesame transport cases. We see the largest shifting distance occurs for the PF, which is the most unstablefront in the model.

The PF largest shifting distance occurs in the middle of Drake Passage where the topography isrelatively flat. The mean location difference for 95 Sv and 155 Sv can be as large as 300 km. With 145 Svand 155 Sv transport cases, the mean PF location are to the north of the historical location. For the



Fig. 5. Time mean sea surface height from observations (AVISO) and model results (95–155 Sv). The weekly observed altimetrydata is averaged over the time from 09/2001 to 07/2006. Model results are averaged from day 31 to day 400. The bold lineindicates each front approximately. (a) AVISO Mean SSH, (b) SSH for 095 Sv, (c) SSH for 105 Sv, (d) SSH for 115 Sv, (e) SSH for125 Sv, (f) SSH for 135 Sv, (g) SSH for 145 Sv, (h) SSH for 155 Sv.

135 Sv transport case, the mean PF location is north of the historical location in the west part of themodel domain (I index less than 95), and is slightly south of the historical location in the east part ofthe domain. Other transport cases stay to the south of the historical location; though, with the 125 Svtransport case the mean location is very close to the historical location in the west model domain. Itshould keep in mind we average the frontal location along the longitudinal line (constant x), so thelarge fluctuations of the front could not be detect in these mean locations (for example, an S meanderof the front).

The SAF moves northward a small distance for transport larger than 135 Sv, while with smalltransport stays southward. It is likely that the northern wall blocks northward shifting with larger



Fig. 6. Frontal location based on sea surface height. The thick dashed lines are the historical locations of the fronts from Orsi etal. (1995). (a) Sub-Antarctic Front, (b) Polar Front, (c) Southern ACC Front.

transport. The size of the upstream southward meander is also related to transport, being small forlarger transport and larger for smaller transport. This feature can also be seen in the mean SSH fields(Fig. 5).

In the western region, the SACCF moves northward after passing the seamounts area (approxi-mately along the longitude line 64◦W) with transport larger than 135 Sv. The front then goes backto south against the southern wall at the Shackleton Fracture Zone. While on the eastern side of themodel domain, the SACCF goes against the southern wall and has little meandering; it does not appearconsistent with the northward excursion observed in the historical hydrographic measurements. Wedid not observe in the model the northward excursion of the SACCF at Shackleton Fracture Zone asstated in Orsi et al. (1995).

The PF locations from Orsi et al. (1995), Moore et al. (1999) and Belkin and Gordon (1996) arecompared with the modeled 135 Sv surface front (Fig. 7). The differences from various methods areclear. The modeled PF location is more close to that from Orsi et al. (1995) than those from the others.The PF location from Moore et al. (1999) agrees better with that from Orsi et al. (1995). At most ofthe locations, the PF from Belkin and Gordon (1996) lies to the north of the modeled PF and those



Fig. 7. The PF locations from model results with 135 Sv (solid line), Belkin and Gordon (1996) (dash-dotted line), Orsi et al.(1995) (dotted line) and Moore et al. (1999) (dashed line). The vertical bar represents RMS displacement of the modeled PF toits mean location.

from Orsi et al. (1995) and Moore et al. (1999) except at around (66◦W, 59◦S) and eastern side of themodeling region. However, we noticed that the PF from Belkin and Gordon (1996) is closer to the PFfrom Gille (1994) in Dong et al. (2006) (Fig. 4a) in Drake Passage. The Root Mean Square (RMS) ofthe PF displacement ranges between 44 km and 85 km for different transport cases in the model. TheRMS of the PF displacement from Moore et al. (1999) and Dong et al. (2006) in Drake Passage bothexceeds 50 km. Though the error from data and methods used to determine the front can account forthe difference, the interannual frontal variability also affects the RMS value since the data used in eachstudy are from different periods.

4.4. 500 m isotherm tracked fronts

Frontal locations based on the temperature at 500 m (Fig. 8) are similar to those from surfaceelevation. The pattern of changes with different transport are the same as above. The fronts in themiddle of Drake Passage tend to move northward with higher transport. The PF and SACCF deflectnorthward after passing the seamounts in the center of the passage. However, the frontal locationbased on temperature were more variable near the eastern boundary, especially for SACCF and SAF.These differences are due to eddy-induced spreading of the temperature. On the whole, for the SAFand SACCF, there is a little difference between the frontal location determined by SSH or temperatureat 500 m, indicating little difference between the surface and subsurface expression of these frontsin the model. For the PF, the locations at 500 m are a little bit to the south of those from the surfaceelevation. Dong et al. (2006) point out that the PF surface locations are a bit to the southward of thesubsurface location. This discrepancy might be due to the error of temperature used to determine thefront. The lack of the surface heating flux in the model might also affect the upper layer temperature,and the frontal locations determined from the temperature.



Fig. 8. Frontal location based on temperature at 500 m. The thick dashed line is the historical location of the fronts. (a) Sub-Antarctic Front, (b) Polar Front, (c) Southern ACC Front.

The SAF location is less variable and tends to shift northward with larger transport. In the smallertransport cases, the SAF forms several meanders west of the tip of South America and remains southof its historical location.

4.5. Time series of isotherm locations from the ISOS moorings

Analysis of the ISOS moored temperature data indicated that the 2.0 ◦ C isotherm at 500 m wasassociated with the PF (Hofmann and Whitworth, 1985). In the model, the 2.3 ◦ C isotherm is associatedwith the axis of the PF at the western model boundary. This small temperature difference is due to theGaussian fronts in the model being based on averaged temperature and salinity in the zones betweenfronts. Though the 2 ◦ C isotherm was used as the indicator of the fronts at 500 m, it may not beconsistent with the exact PF locations (maximum temperature gradient at the same depth).

The meridional location of the 2.3 ◦ C isotherm at 500 m in the model across the ISOS main linealong with the 2.0 ◦ C isotherm from observations (Hofmann and Whitworth, 1985) are shown inFig. 9. The model PF shifts northward with increasing transport which is consistent with the otherindicators of PF location. For the smaller transport cases, the PF tends to move southward with time.



Fig. 9. Location of the Polar Front along model index i = 80, which is close to the ISOS mooring main line, based on temperatureat 500 m. The 2.3 ◦ C isotherm locates the PF in the model solution. The Orsi et al. (1995) PF is located at model index j = 118.The 2 ◦ C isotherm (dashed line to the south, lines are isotherms) is used in Hofmann and Whitworth (1985) to locate the PF. (a)095 Sv, (b) 105 Sv, (c) 115 Sv, (d) 125 Sv, (e) 135 Sv, (f) 145 Sv, (g) 155 Sv, (h) Hofmann and Whitworth (1985) PF location.

For 135 Sv transport case, the PF remains close to its initial position. At this location, the model PF isassociated with meso-scale eddies, although the number of eddies declines as the transport increases.The observed location of the PF at the ISOS main line (Fig. 9h) is variable with no trend or seasonalpattern. Two PF eddies are observed in the 14 months of this record.



The model results have a somewhat different character from the observations. Each case displaysa few small eddies along with large meanders of the PF. In the larger transport cases, the number ofeddies is reduced over the smaller transport cases.

There are some eddies occurring with time scale of 1–2 months. These eddies may not be fullyresolved since the grid spacing is close to the radius of deformation in southern Drake Passage. Wefind that the meandering of the SACCF did affect the path of the PF in Drake Passage. This northwardmeandering of the SACCF pushes the PF northward for the larger transport cases. The northward mean-der of the PF pushes the SAF further north. Thus, eddy generation from SACCF may be important forthe overall character of the flow in Drake Passage. The eddies are seen in the seamount area (along theISOS main line) in the west of Drake Passage. However, the errors in representation of the topographyand distribution of transport to the SACCF might affect the eddy generation.

4.6. The shifting distance of the PF and the transport

Different total transport affects frontal variability as well as the mean location of the fronts. Themean absolute shifting distance of the fronts from their historical location is a good diagnostic of thefrontal variability. Among all the transport cases, the shifting distance for the PF is smallest (Fig. 10)with 135 Sv. This means that the PF is closest to its observed location for this transport. The PF shiftsnorthward for increasing transport, and southward for decreased transport (Fig. 6). The mean transportof ACC calculated from the extensive ISOS current meter array is 134 Sv (Whitworth and Peterson,1985). So the transport with smallest PF shifting distance coincides with the observed mean transport.

There is a fine balance between the baroclinic transport based on the model density structure(which is specific from WOA98 climatology) and the imposed speed at the western boundary (whichsets the total volume transport), which controls the dynamic stability of the frontal jets. For the case

Fig. 10. Mean displacement of the Polar Front from its historical location for different values of imposed transport. The verticalbar represents the standard deviation of the displacement to the historical locations.



with 135 Sv, the model deviates the least from the observed frontal locations and has the least meanderrate. This case has the least conversion between the potential energy of the initial density structureand the imposed kinetic energy due to geostrophic adjustment and imposed frontal transport. For animposed transport of 135 Sv, the model result is closest to the observed conditions.

4.7. Ertel Potential Vorticity analysis

We choose the most realistic (135 Sv) case to calculate the EPV and transport stream function. Theanalysis time is day 390 which is close to the end of the simulation and the model seems to be adjustedto the initial and imposed conditions (other times late in the simulation yield comparable results). EPVis calculated at a variety of depths.

The relationship between EPV at all model grids with depth greater than 1500 m and the transportstream function (Fig. 11a) is clearly linear at most points. The correlation between EPV at differentdepths and the stream function (Fig. 11b) indicates that away from the surface and bottom, there isclear relationship to be expected of a quantity (EPV) which should be conserved along streamlines.The maximum coefficient (more than 0.90) occurs for depths from 1000 m to 2500 m.

Between the surface and 750 m, the correlation changes from −1 to +1. Surface processes associatedwith strong flow shear and mixing (the effect of the KPP scheme) near the surface change the relation-ship between EPV and stream function. Similarly, within 500 m of the bottom, there is a reduction in thiscorrelation which is due to the influence of variability created by bottom topography. Flow distortionby bottom topography and increased mixing reduce the conservation of EPV along streamlines.

5. Discussion

5.1. Model realism

Sea surface elevation from satellite altimeters (provide by AVISO) provides a good test for thesemodel solutions. The SAF is portrayed the most realistically in the model compared to other fronts.The PF and SACCF shift northward in the model after passing the seamount area; a behavior that isobserved on occasion. The model PF is wider downstream of the seamounts, which indicates greatervariability in response to the variable bottom topography. Satellite observations portray the PF asseveral filaments rather than a single jet in the snapshots. In any case the averaged PF is wide and noteasily distinguished in the mean SSH fields.

The SACCF in the model lacks the strong S meander when encountering the Shackleton Ridge. Thereare several possible causes for this inconsistency. First, the model resolution may not be fine enoughto represent all of the features of this bottom topography. The ridge is much deeper than its real depth.In addition, in the southern Drake Passage the grid spacing is about equal to the internal deformationradius, so the dynamics may not be fully resolved. Second, there is no source of cold water from thewestern Weddell Sea which would have some influence on the meander near the tip of the AntarcticPeninsula. Finally, the southward deflection of the PF in some simulations can limit the northwardexcursion of the SACCF, reducing the effect of the topographically induced meander.

The PF location correspondence to the net baroclinic transport is reported in the SR-1 hydrographyby Cunningham et al. (2003). Along the SR-1 hydrography section, the PF is in its southerly location foryears 1993 and 1996 with the small net baroclinic transport (132 Sv); the PF is in its northerly positionat years 1994, 1997 and 1999 with the large transport (142 Sv). Though this relation does not hold foryear 2000 and this section is downstream of our model domain, it partially supports our results thatthe total ACC transport affects the frontal locations.

There are several factors responsible for the different frontal locations for different imposed trans-port. The partition of the total transport among the frontal jets is proportional to the verticallyintegrated baroclinic transport. Thus, the changing transport is proportionally distributed among thethree jets and the intervening zones. The mechanism for transport changes of the ACC in Drake Passagehave not been identified, other than the commonly held opinion that the barotropic transport is thepart that changes. The amount of transport change for the different jets has not been analyzed. Allow-ing the transport change to be accommodated by the SAF or PF alone is likely to lead to different results



Fig. 11. The Relationship between Ertel Potential Vorticity and stream function for 135 Sv at Day 390. The EPV is calculatedfor all the model grids with a depth greater than 1500 m. (a) Scatter plotting of EPV and stream function, (b) EPV and streamfunction correlation coefficient with depth.

due to the stability of the SAF and the instability of the PF. These variation are beyond the scope of thepresent study, in particular because there is no observational evidence to guide these experiments.

5.2. Potential vorticity

Conservation of potential vorticity is used to explain the shifting of frontal locations with changingtransport. For this analysis, the barotropic form of potential vorticity is used, or q = (� + f/h), where �is the vertical component of relative vorticity, and h is the water depth. Due to the weak stratification



of the Southern Ocean, bottom topography has a strong effect on the flow. While vertical structure offrontal jets does exist (Klinck and Hofmann, 1985), the surface elevation and the 500 m temperaturefronts both give consistent locations for the fronts. For simplicity, the discussion considers the frontaljets to be barotropic.

The frontal jet is symmetric about its axis, so (∂u/∂y)|x=0∼0 in the core of the jet. For a jet withouta meander, which is the initial state, �∼0. Thus, the initial potential vorticity q = f/h, and the flow willfollow planetary vorticity contours. The value for q to be conserved for each streamline is set at thewestern model boundary, where the water is deep. Assuming conservation of q, the relative vorticityin the model interior is � = q · h− f . In the Southern Ocean f and q are negative, so a decrease in depthleads to an increase in �.

Central Drake Passage has a depth around 3000 m and is shallower than the eastern Pacific Oceanwith depths around 4500 m (in the model domain). This shallowing will generate positive relativevorticity which is consistent with a northward curvature of the frontal axis. The shallowing of DrakePassage makes the frontal jets shift to the north.

An alternative explanation for the northward frontal shifts is seen in the surface elevation (Fig. 5).The SACCF deflects northward (as meanders or eddies) after passing the seamount area in the southernPassage leading to a northward shift of the PF. Eddies from the SACCF into the Polar Frontal Zone (Zonebetween the PF and the SAF) may have the same influence. Similarly, the PF may shift to the northaffecting the SAF.

Fronts located by surface elevation or the 500 m temperature are consistent. Without local surfaceforcing in this regional model or variations of the boundary input, the surface temperature and salinityare conserved following the flow. The strong gradient in density and the along-front velocity maximumcoincide in the vicinity of a developed front, so do the density and along-front velocity contours (Gill,1982).

5.3. Model adjustment

The development of the PF jet occurs in two parts. First, the imposed jet assumes a quasi-geostrophicbalance with the initial density with a time scale of 1/f (about a day). For a mean surface velocity ofabout 0.5 m/s, information at the western boundary will take about 1 month to cross the whole modeldomain (1200 km).

The second adjustment is due to diffusion caused by eddies and sub-grid scale mixing; generally,slow processes. The geostrophic frontal jet can become dynamically unstable (depending on flow speedand density structure). For large transport cases (bigger than 135 Sv), the developing meso-scale eddiesis inhibited. The vertically integrated horizontal density gradient provides the necessary balance tothe Coriolis force created by the strong current. It is less likely that potential energy is released throughspawning eddies, which is a baroclinic process that tends to diminish the tilting of the isopycnal. Withsmaller transport, the baroclinic instability is effective in releasing potential energy to form eddies andmeanders. The observed PF location along the ISOS mooring line (Fig. 9h) appears less variable withhigh measured transport.

Stability of the SAF seems a different matter, which is changed fundamentally by the continentalslope along the northern Drake Passage. Topography can stabilize flow or it can limit the size of thedeveloping instability and halt its development. The SAF is influenced by the topographic ridge justwest of Cape Horn which allows the development of lee eddies under appropriate inflow conditions(Dong et al., 2007). A hint of this influence is seen in the historical front locations (Fig. 1) and to someextent in the mean surface elevation (Fig. 5a).

5.4. Transport and frontal stability

Given the balance of kinetic and potential energy in the frontal jets, each front may only have anarrow range of imposed transport that is associated with realistic behavior. The SAF is narrow andstrong with 155 Sv transport, while the PF is closest to its historical location at a transport of 135 Sv.The SACCF shifts unrealistically to the south and is less variable with large imposed transport.



The strength of the imposed transport and velocity structure are important for a short-term (severalmonths) forecasting with regional meso-scale models. Furthermore, the flow paths of some frontal jetsin the interior of this model have unrealistic meanders. This effect is most clearly seen in the surfaceelevation for smaller transport cases (Fig. 5) where a southward meander develops in the SAF and thePF close to the west boundary. This meander is not evident as the transport increases.

5.5. Model initial condition effects

The model is initialized with the same fronts for all transport cases. The frontal displacement isonly determined by the transport imposed on the boundary. This is a sensitivity study of the frontallocation and transport only. The parameterizing of the initial front is carefully chosen to represent therealistic front.

The initialization of the model does not provide a geostrophic balance between the density and thevelocity. Since the T/S has been set up, we leave the model to adjust itself to the transport along theboundary instead prescribing initial velocity above complex topography. As mentioned in Section 5.3,the adjustment of the velocity field to the T/S front can be taken in a short time of the scale 1/f . Thenthe model results are analyzed from the second month.

Strong velocity shear from the imposed transport might trigger the instability of the front. Only onemean frontal width is used in construction each of the fronts. If different width is used, the instabilitycondition will be changed and the frontal displacement pattern might be affected a little bit too. Thiseffect will be minor since the front will adjust itself lately according to the transport distributed on itby tilting or shrinking the isopycnals.

6. Conclusions

These model results show a number of effects with different imposed volume transport. The vari-ability of ACC fronts in Drake Passage is clearly related to the volume transport of the ACC. With largetransport, the SAF and PF are more stable. The PF and SAF spawn fewer eddies. The SAF, PF and SACCFshift northward with large transport while they remain to the south with smaller transport. Withsmaller transport, the SAF develops large meanders. The transport and the frontal variability reflectthe competition between the frontal available potential energy and the kinetic energy. Consistency ofinput transport and the density fields is important for regional meso-scale circulation models.

In all the transport cases, the mean shifting distance of PF to its historical locations is from 50 km to90 km, which is close to the Gille (1994) estimate of 70 km. The minimum shifting distance occurs ata transport of 135 Sv, which is consistent with the ISOS estimation to the total ACC transport of 134 Sv.

The SAF and SACCF are confined by northern and southern walls, respectively. The path of the PFis loosely controlled by the topography. After passing the seamounts in the Central Drake Passage, thePF meanders strongly and becomes a wider flow.

The Ertel Potential Vorticity is linearly correlated to the transport stream function between depthsof 1500 m to 2500 m with a correlation of more than 0.9. Near-bottom flow has a weaker correlationbetween EPV and stream function. Near the surface, the correlation is weaker and even reverses sign.

Acknowledgments

The altimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support fromCnes. Computer facilities and support were provided by the Commonwealth Center for Coastal PhysicalOceanography at Old Dominion University. We appreciate this support. We thank Dr. Alejandro Orsi,Dr. Igor Belkin and Dr. Keith Moore for providing their digital PF locations.

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