This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Dynamics of Atmospheres and Oceans 45 (2008) Contents lists available at ScienceDirect Dynamics of Atmospheres and Oceans journal homepage: The effect of Antarctic Circumpolar Current transport on the frontal variability in Drake Passage Bin Zhang a,, John M. Klinck b a Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, NJ, USA b Center for Coastal Physical Oceanography, Department of Ocean, Earth and Atmospheric Sciences, Old Dominion University, Norfolk, VA, USA article info abstract Article history: Available online 3 July 2008 Keywords: Fronts Antarctic Circumpolar Current Numerical modeling Drake Passage Southern Ocean The Antarctic Circumpolar Current (ACC) is composed of three major fronts: the Sub-Antarctic Front (SAF), the Polar Front (PF), the Southern ACC Front (SACCF). The locations of these fronts are variable. The PF can shift away from its historical (mean) location by as much as 100 km. The transport of the ACC in Drake Passage varies from its mean (134 Sv) by as much as 60 Sv. A regional numerical circulation model is used to study frontal variability in Drake Passage as affected by a range of volume transports (from 95 Sv to 155 Sv with an interval of 10 Sv). Large transport shifts the fronts northward while the smaller transport causes a southward shift. The mean shifting distance of the PF from the historical mean location is minimum with 135 Sv transport. The SAF and the SACCF are confined by northern and southern walls, respectively, while the PF is loosely controlled by the topography. Due to impact of the eddies and meanders on the PF at several regions in Drake Passage, the PF may move northward to join the SAF or move southward to combine with the SACCF, especially in central Scotia Sea. The SAF and PF are more stable with higher transport. The SAF behaves as a narrow, strong frontal jet with large transport while displaying meanders with smaller transport. In the model simulations, the Ertel Potential Vorticity (EPV) is strongly correlated with the volume transport stream function. EPV at depths between 1000 and 2500 m is correlated with the transport stream function with a coefficient above 0.9. Near the bottom, the correlation is about 0.6 due to the disruptive influence of bottom topography. Within 750 m of the Corresponding author. Tel.: x253; fax: address: bzhang@marine.rutgers.edu (B. Zhang) /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.dynatmoce

3 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) surface, the correlation is much reduced due to the effect of K-Profile Parameterization (KPP) mixing and eddy mixing Elsevier B.V. All rights reserved. 1. Introduction The Antarctic Circumpolar Current (ACC) is composed of three continuous jets associated with three major fronts, which from south to north are the Southern ACC front (SACCF), the Polar Front (PF) and the Sub-Antarctic Front (SAF). All three fronts appear as maxima in geostrophic volume transport (Orsi et al., 1995). The mean Lagrangian 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 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 also change rapidly. Across the PF, the sea surface temperature (SST) change is around 1.35 C over a distance less than 60 km distance (Moore et al., 1997). This large gradient of SST is often associated with large concentration of chlorophyll (Moore and Abbott, 2002). All these properties of the rapid jump of physics across front can be used to locate the front and its width at specific time. Good summary 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 hydrography data, satellite altimetry data or SST data (Nowlin and Clifford, 1982; Belkin, 1993; Gille, 1994; Orsi et al., 1995; Belkin and Gordon, 1996; Moore et al., 1999; Dong et al., 2006). The mean width of the PF 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 mean locations 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 Gaussian cumulative probability function. Belkin and Gordon (1996) gave the location of the SAF and the PF from 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 locations are mostly similar but differences at some places are clear (Moore et al., 1999; Dong et al., 2006). The differences might come from the errors in different methods. However, the variability of the fronts also brings uncertainty in determining the frontal locations. Gille and Kelly (1996) estimated the mean shifting distance of the PF from its mean location to be 70 km. The time scale of this variability is 3 months and the zonal decorrelation scale is 80 km. Hofmann and Whitworth (1985) used the 2 C isotherm at 500 m from the ISOS mooring array measurements to locate the PF. Cold core eddies were seen to impact the PF from the south resulting in shifts of up to 90 km. Eddy shedding from the PF resulted in similar location changes. All the estimates of the PF location from different methods (Gille, 1994; Orsi et al., 1995; Belkin and Gordon, 1996; Moore et al., 1999; Dong et al., 2006) show strong frontal location steering by topography. The PF meandering intensity is weaker where the bathymetry is steeply sloped and stronger where the bottom is relatively flat (Moore et al., 1999). Variations within the ACC make it difficult to measure its total transport. The ACC transport can be separated to two parts: the baroclinic and barotropic transports. The baroclinic transport remains relative steady (Cunningham et al., 2003), while the barotropic transport can change rapidly. Whitworth and Peterson (1985) estimated the ACC transport in Drake Passage from moored current sensors to be 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 are mainly barotropic. Sprintall (2003) used XBT measurements in Drake Passage during to show that the Drake Passage seasonal variation occurs only in the upper 200 m. Geostrophic transport mapped from measured 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

4 210 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 1. The model domain is the 1200 km by 1200 km box in the middle of the map. The historical front locations are indicated as heavy lines. Shading shows bathymetry shallower than 3500 m indicating the seamounts in the middle of Drake Passage and the Shackleton Fracture Zone. Circles are the ISOS mooring locations. OI is the Orkney Island and WAP is the Western Antarctic Peninsula. variation over short time scales (weekly to monthly) which would affect transport estimates from bottom pressure measurements. The repeat hydrography along WOCE line SR-1 shows that the PF has two common locations and that the SAF and the PF sometime merge to form one front (Cunningham et al., 2003). This joining makes it difficult to separate the contribution of each frontal jet to the transport. In addition, the hydrography along this section is difficult to interpret due to S-shaped meanders. Thus, understanding of frontal variability 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 and thus 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 the Shackleton Fracture Zone in southern Drake Passage (Fig. 1). This deflection is not permanent and the SACCF displays considerable meandering in this location. There are a number of numerical models of the ACC, but most do not produce realistic paths, widths or 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 the ACC fronts (Grose et al., 1995). The total transport in Drake Passage from FRAM is about 180 Sv with the SAF transport being about 130 Sv. Both of these transports are well above observations. The PF in FRAM seems to have split and attached to either the SAF or the SACCF (called the Continental Water Boundary at that time). This difficulty with the FRAM solution is believed to be caused by the coarse grid resolution which causes unrealistic bottom topography in the model.

5 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Thorpe et al. (2005) found different circulation in the Scotia Sea in two global ocean circulation models (with 0.25 horizontal resolution) and proposed that different representation of the bathymetry is the likely reason, from among many, to force the SAF and PF to merge together against the tip of South America. In this study, we use a high resolution regional ocean circulation model to study the relationship between the volume transport of the ACC and frontal variability. By specifying different transport along the western boundary, we look at how each ACC front in Drake Passage responds. The next section describes the model that we use along with details of initial and boundary conditions. The following section presents the diagnostics that we use to analyze the model. Section 4 presents results from the various simulations that we run. Section 5 discusses the implications of these 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 be found at 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 coordinate system. The domain size is 1200 km by 1200 km. The grid spacing is approximately 6 km, which results in a grid size of 200 by 200. The grid rotation allows the ACC to enter the western boundary of the model domain at approximately normal incidence, making the open boundary condition there better behaved. The bottom topography was linearly interpolated to the model grid from ETOPO2 (a 2-min resolution bathymetry) from National Geophysical Data Center (Smith and Sandwell, 1997). The main features of the Drake Passage topography, such as the seamounts and ridges are well represented in the model (Fig. 1). Initial distributions of temperature and salinity are taken from the World Ocean Atlas (Boyer and Levitus, 1998). However, time and space averages of sparse observations in this region with frontal variability produces weak property gradients in place of sharp, narrow frontal features. We use a feature model (similar to that of Gangopadhyay et al., 2002) to recover the fronts at their mean locations. We assume that properties in the fronts follow a Gaussian cumulative distribution function consistent with a Gaussian frontal jet as described in Gille (1994). The feature model is constructed as follows. The temperature and salinity from the World Ocean Atlas (WOA) within each frontal zone is averaged along the front. The Gaussian cumulative distribution function is used to construct the fronts as: T( r) = T 1 + (T 2 T 1 ) (( r r 0 )/), where T( r) isthe temperature or salinity at r, T i represents the mean temperature or salinity from WOA in each side of the front, is the Gaussian cumulative distribution function. The frontal width is chosen to be 51 km for the SAF, 61 km for the PF, 39 km for the SACCF to be consistent with hydrographic measurements by Nowlin and Clifford (1982). Along the open boundaries, the temperature and salinity are relaxed to the initial conditions for these variables. The nudging time scale is 5 days. Nudging is imposed over a zone of about 30 km thickness over most of the model grid next to the open boundary. A 60 km (10 grid intervals) zone is imposed at the eastern boundary to improve model stability. The free surface condition at boundaries is no-gradient. The total volume transport at the model boundary is controlled to keep a balanced inflow and outflow. The geostrophic velocity u bc is calculated along each boundary from the initial temperature and salinity referred to 2500 db. Vertically integrating the geostrophic velocity, we obtain the 2D integrated baroclinic flow along the boundary and the baroclinic transport bc. We add the barotropic flow u bt with the same shape as the baroclinic flow to match the desired total transport t. The barotropic velocity is determined by this: u bt = u bc (1.0 bc / t ). The combination of the baroclinic and the

6 212 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) barotropic flow is imposed along each boundary. The imposed incoming volume transport represents the 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 have solutions very similar to those presented here. Bottom stress is applied as the linear function of the bottom velocity with a drag coefficient of The horizontal viscosity is 50 m 2 s 1, and the tracer diffusion coefficient is 5 m 2 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 Sv with an interval of 10 Sv. In each transport case, the model begins in a static state with the same featured 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 simulations are driven largely by kinetic energy input through the western boundary and kinetic energy dissipation due to bottom and interior frictional losses. Energy converts between kinetic and potential due to a variety of mixing, geostrophic adjustment and dynamic instability mechanisms. The volume averaged model energetics are analyzed by calculating the volume averaged kinetic energy (VAKE) and volume averaged potential energy (VAPE) at each time the model state is saved. The specific calculations are KE = 0.5 i,j,k ( 2 u + u 2 + v 2 + v 2 ) z x y i,j,k i+1,j,k i,j,k i,j+1,k (1) x y z PE = i,j,k gz r 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 the transport and kinetic energy are mainly found in the fronts so it is necessary to delineate each frontal area and calculate quantities within the frontal areas. We define each front by two sea surface elevation isolines. Since we used the strong nudging/clamped boundary conditions on the western boundary, the surface elevation and temperature on the surface maintain through the domain the step-like structure imposed at the boundary. The peaks in the surface elevation gradient along the western boundary are consistent with the location of the fronts. Centered at this point, we locate two grid points at the boundary whose distance is approximately equal to the frontal width. Contour lines corresponding to these surface elevation values denote the front. A flood-fill method is used to mark the area between these two bounding lines. The frontal surface area, total volume, total kinetic energy and volume averaged kinetic energy is calculated for each frontal area. The PF and SAF are easily demarked by this method. However, the SACCF is more difficult to delineate. In addition. it makes a smaller contribution to the transport and energy, so the calculation is not done for the SACCF 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 corresponding to large lateral gradient of SSH (Sokolov and Rintoul, 2002). The surface density (imposed at the western

7 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Table 1 Mean 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± 1 PF 4 ± 3 3 ± 3 2 ± 3 1 ± 3 2± 1 4± 1 6± 1 SACCF 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 is a close proxy for the circulation. Because of this relationship, the frontal axis can be tracked using the surface elevation isoline defined by the surface elevation value on the western boundary. Different transport cases have the different surface elevation values for the fronts. Due to the no-gradient boundary condition, the defined surface elevation for a front changes slightly with time. The mean SSH values and their standard deviations with different fronts and transports are listed in Table 1. We define the fronts for each model state (starting with the second simulation month) and calculate the average and variance for the frontal position along y-axis (typically using more than 70 values for each simulation). The frontal locations are assumed to be single valued functions of the model x coordinate, so strong meanders are not well represented. If there is a S-shape meander in the front, the southern most point taken as the front location as in Dong et al. (2006). There is little seasonal temperature variation below 200 m (Sprintall, 2003). The ACC fronts are known to have signature through the water column (Cunningham et al., 2003; Orsi et al., 1995). The temperature at 500 m is a good way to locate fronts over time. The 500 m temperature from the ISOS moorings 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 the front defined on the western boundary. The same temperature was used for a given front for different transport cases. As with surface elevation, the target isotherm was assumed to be a single valued function of the model x coordinate 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), orsd = r r 0 /N, where r is the PF location for each x grid index I, r 0 is the historical PF location at the same index, and N is total x direction grid points (excluding nudging and sponge layers). The model solution in the first month is not used due to model adjustment. This diagnostic is used to estimate the effect of imposed ACC transport on frontal location and variability Calculation of the Ertel Potential Vorticity Ertel Potential Vorticity (EPV) is an important physical variable which under the adiabatic conditions and without external forcing is a conserved quantity following the flow (Gill, 1982). In deep water, these conditions apply and EPV can be regarded as conserved. In these simulations, EPV is used to 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 the density. Conserved EPV is a function of the stream function ( ), which in this case is deduced from the 2D vertically averaged velocity and the total water depth. A relationship between q and is determined by 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, to come to a geostrophic balance. Model results from the end of the first month to day 400 are analyzed.

8 214 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) For each of the simulations with different imposed transport, we analyze the integrated energy, compare the frontal locations to historical ones and compare surface elevation to satellite observations and analyze EPV Kinetic and potential energy analysis VAKE behaves differently for different transport cases (Fig. 2a). For all cases, VAKE increases with 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 are 1000 kg m 2 s 2 and a constant number is subtracted to better see the variability. (a) Volume averaged kinetic energy, (b) volume averaged potential energy.

9 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) port (although the case with the largest transport has a much larger excursions of VAKE than the other cases). VAKE increases over time as the frontal jets become unstable and develop meso-scale variability. The total input kinetic energy for these different transport cases must be balanced by some other mechanisms besides the geophysical adjustment to frontal kinetic energy, such as transferring the VAKE to the potential energy, increasing of dissipation rate due to increased vertical shear or an increase in 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 more than the higher transport. The amount of VAPE reduced with time ranges from 100 kg m 2 s 2 with 155 Sv transport to 600 kg m 2 s 2 with 95 Sv. These numbers are much higher than the amount of increase in VAKE (order of 10 kg m 2 s 2 ). This reduction in VAPE is associated with reduced pycnocline slope, 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 whole domain VAKE (Fig. 2). This steadiness indicates that the PF and SAF have adjusted to a geostrophic balance during the first month. Thus, the VAKE in zones between fronts must increase to account for this difference. This increase must be caused by transfer of kinetic energy from the fronts due to shedding of meso-scale eddies. These processes mix waters across the fronts which tend to diminish the isopycnal slope in the fronts. The area of the PF increases over time for all transport cases. This increase is due to meso-scale eddies, which are clear from model snapshots except close to the nudging and sponge layer where it 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 but remains weaker than the SAF. The VAKE for the SAF increases with increasing transport implying that the velocity of the SAF jet increases. The area of the SAF stays relatively steady. The highest transport case (155 Sv) shows a reduction of the SAF area compared to other transport cases in spite of the higher VAKE, indicating that the eddy shedding must decrease. Unlike the PF, the SAF can not shed its additional KE through shedding of rings due to the close proximity of the continental slope at the north side of Drake Passage. This tendency is indicated by the relatively constant frontal area for the SAF (Fig. 4) Surface elevation comparison with satellite data The observed surface elevation is obtained from AVISO Ssalto/Duacs which provides weekly global gridded (1/3 1/3 ) absolute surface dynamic topography ( 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). Frontal locations are not clearly evident due to averaging, but some basic features remain. The separation of the SAF and the PF in the middle of Drake Passage can be seen. The remarkable northward excursion of the SACCF occurs after passing the Shackleton Fracture Zone (around 58 W, 60 S). In the west, fronts are not distinguished clearly by the mean SSH fields due to the high spatial variability there. The surface elevation from the model solutions are averaged for 1 year (Fig. 5). We label each front in the mean fields with the mean SSH isoline in Table 1 to roughly indicate each frontal location in the mean field. The strongest frontal jet is associated with the SAF for cases with transport higher than 115 Sv. The SACCF jet is the weakest with these transports. The PF shows clear differences in cases 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 transport cases ( Sv). For the higher transport ( Sv), these meanders become weaker or disappear. The SACCF shifts more northward with higher transport (along the longitude line 65 W) in the model.

10 216 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 3. The volume averaged kinetic energy (solid line) and area (dashed line) of the Polar Front. The straight solid line is the time mean VAKE. One notable feature in AVISO altimetry (not evident in the mean field) is the splitting and rejoining of fronts. In the satellite field, sometimes the PF enters Drake Passage and splits into several filaments when passing the seamounts in the center of the passage. These filaments rejoin downstream. In the model, 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 form the S meander as indicated by the 25 cm isoline of the surface elevation at (58 W, 59.7 S) in Fig. 5(a). The model SACCF loses this excursion. This feature is also missed in other GCM solutions (Thorpe et al., 2005), which is believed to be caused by smoothing bottom topography in the models.

11 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 4. The volume averaged kinetic energy (solid line) and area (dashed line) for the Sub-Antarctic Front. The straight solid line is the time mean VAKE Surface elevation tracked fronts The mean location for each front with different transport cases are compared to its historical mean locations (Fig. 6a c). The basic tendency is that the mean frontal axis stays northward with higher transport while southward with smaller transport in the middle region of the Drake Passage. The distance of the mean location from its historical location is not the same for the three fronts in the same transport cases. We see the largest shifting distance occurs for the PF, which is the most unstable front in the model. The PF largest shifting distance occurs in the middle of Drake Passage where the topography is relatively flat. The mean location difference for 95 Sv and 155 Sv can be as large as 300 km. With 145 Sv and 155 Sv transport cases, the mean PF location are to the north of the historical location. For the

12 218 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 5. Time mean sea surface height from observations (AVISO) and model results ( Sv). The weekly observed altimetry data is averaged over the time from 09/2001 to 07/2006. Model results are averaged from day 31 to day 400. The bold line indicates each front approximately. (a) AVISO Mean SSH, (b) SSH for 095 Sv, (c) SSH for 105 Sv, (d) SSH for 115 Sv, (e) SSH for 125 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 the model domain (I index less than 95), and is slightly south of the historical location in the east part of the domain. Other transport cases stay to the south of the historical location; though, with the 125 Sv transport case the mean location is very close to the historical location in the west model domain. It should keep in mind we average the frontal location along the longitudinal line (constant x), so the large fluctuations of the front could not be detect in these mean locations (for example, an S meander of the front). The SAF moves northward a small distance for transport larger than 135 Sv, while with small transport stays southward. It is likely that the northern wall blocks northward shifting with larger

13 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 6. Frontal location based on sea surface height. The thick dashed lines are the historical locations of the fronts from Orsi et al. (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 for larger 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 (approximately along the longitude line 64 W) with transport larger than 135 Sv. The front then goes back to south against the southern wall at the Shackleton Fracture Zone. While on the eastern side of the model domain, the SACCF goes against the southern wall and has little meandering; it does not appear consistent with the northward excursion observed in the historical hydrographic measurements. We did not observe in the model the northward excursion of the SACCF at Shackleton Fracture Zone as stated in Orsi et al. (1995). The PF locations from Orsi et al. (1995), Moore et al. (1999) and Belkin and Gordon (1996) are compared with the modeled 135 Sv surface front (Fig. 7). The differences from various methods are clear. 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). Atmostof the locations, the PF from Belkin and Gordon (1996) lies to the north of the modeled PF and those

14 220 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) 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 to its mean location. from Orsi et al. (1995) and Moore et al. (1999) except at around (66 W, 59 S) and eastern side of the modeling region. However, we noticed that the PF from Belkin and Gordon (1996) is closer to the PF from Gille (1994) in Dong et al. (2006) (Fig. 4a) in Drake Passage. The Root Mean Square (RMS) of the PF displacement ranges between 44 km and 85 km for different transport cases in the model. The RMS of the PF displacement from Moore et al. (1999) and Dong et al. (2006) in Drake Passage both exceeds 50 km. Though the error from data and methods used to determine the front can account for the difference, the interannual frontal variability also affects the RMS value since the data used in each study are from different periods m isotherm tracked fronts Frontal locations based on the temperature at 500 m (Fig. 8) are similar to those from surface elevation. The pattern of changes with different transport are the same as above. The fronts in the middle of Drake Passage tend to move northward with higher transport. The PF and SACCF deflect northward after passing the seamounts in the center of the passage. However, the frontal location based 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 SAF and SACCF, there is a little difference between the frontal location determined by SSH or temperature at 500 m, indicating little difference between the surface and subsurface expression of these fronts in the model. For the PF, the locations at 500 m are a little bit to the south of those from the surface elevation. Dong et al. (2006) point out that the PF surface locations are a bit to the southward of the subsurface location. This discrepancy might be due to the error of temperature used to determine the front. 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.

15 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) 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 smaller transport cases, the SAF forms several meanders west of the tip of South America and remains south of its historical location 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 was associated with the PF (Hofmann and Whitworth, 1985). In the model, the 2.3 C isotherm is associated with the axis of the PF at the western model boundary. This small temperature difference is due to the Gaussian fronts in the model being based on averaged temperature and salinity in the zones between fronts. Though the 2 C isotherm was used as the indicator of the fronts at 500 m, it may not be consistent 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 line along with the 2.0 C isotherm from observations (Hofmann and Whitworth, 1985) are shown in Fig. 9. The model PF shifts northward with increasing transport which is consistent with the other indicators of PF location. For the smaller transport cases, the PF tends to move southward with time.

16 222 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 9. Location of the Polar Front along model index i = 80, which is close to the ISOS mooring main line, based on temperature at 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 is associated 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 seasonal pattern. Two PF eddies are observed in the 14 months of this record.

17 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) The model results have a somewhat different character from the observations. Each case displays a few small eddies along with large meanders of the PF. In the larger transport cases, the number of eddies is reduced over the smaller transport cases. There are some eddies occurring with time scale of 1 2 months. These eddies may not be fully resolved since the grid spacing is close to the radius of deformation in southern Drake Passage. We find that the meandering of the SACCF did affect the path of the PF in Drake Passage. This northward meandering of the SACCF pushes the PF northward for the larger transport cases. The northward meander of the PF pushes the SAF further north. Thus, eddy generation from SACCF may be important for the overall character of the flow in Drake Passage. The eddies are seen in the seamount area (along the ISOS main line) in the west of Drake Passage. However, the errors in representation of the topography and distribution of transport to the SACCF might affect the eddy generation The shifting distance of the PF and the transport Different total transport affects frontal variability as well as the mean location of the fronts. The mean absolute shifting distance of the fronts from their historical location is a good diagnostic of the frontal 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 shifts northward for increasing transport, and southward for decreased transport (Fig. 6). The mean transport of 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 (which sets 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 vertical bar represents the standard deviation of the displacement to the historical locations.

18 224 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) with 135 Sv, the model deviates the least from the observed frontal locations and has the least meander rate. This case has the least conversion between the potential energy of the initial density structure and the imposed kinetic energy due to geostrophic adjustment and imposed frontal transport. For an imposed transport of 135 Sv, the model result is closest to the observed conditions Ertel Potential Vorticity analysis We choose the most realistic (135 Sv) case to calculate the EPV and transport stream function. The analysis time is day 390 which is close to the end of the simulation and the model seems to be adjusted to the initial and imposed conditions (other times late in the simulation yield comparable results). EPV is calculated at a variety of depths. The relationship between EPV at all model grids with depth greater than 1500 m and the transport stream function (Fig. 11a) is clearly linear at most points. The correlation between EPV at different depths and the stream function (Fig. 11b) indicates that away from the surface and bottom, there is clear 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 750m, the correlation changes from 1 to +1. Surface processes associated with strong flow shear and mixing (the effect of the KPP scheme) near the surface change the relationship between EPV and stream function. Similarly, within 500 m of the bottom, there is a reduction in this correlation which is due to the influence of variability created by bottom topography. Flow distortion by 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 these model 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 is observed on occasion. The model PF is wider downstream of the seamounts, which indicates greater variability in response to the variable bottom topography. Satellite observations portray the PF as several filaments rather than a single jet in the snapshots. In any case the averaged PF is wide and not easily distinguished in the mean SSH fields. The SACCF in the model lacks the strong S meander when encountering the Shackleton Ridge. There are several possible causes for this inconsistency. First, the model resolution may not be fine enough to 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 deformation radius, so the dynamics may not be fully resolved. Second, there is no source of cold water from the western Weddell Sea which would have some influence on the meander near the tip of the Antarctic Peninsula. Finally, the southward deflection of the PF in some simulations can limit the northward excursion 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 hydrography by Cunningham et al. (2003). Along the SR-1 hydrography section, the PF is in its southerly location for years 1993 and 1996 with the small net baroclinic transport (132 Sv); the PF is in its northerly position at years 1994, 1997 and 1999 with the large transport (142 Sv). Though this relation does not hold for year 2000 and this section is downstream of our model domain, it partially supports our results that the total ACC transport affects the frontal locations. There are several factors responsible for the different frontal locations for different imposed transport. The partition of the total transport among the frontal jets is proportional to the vertically integrated baroclinic transport. Thus, the changing transport is proportionally distributed among the three jets and the intervening zones. The mechanism for transport changes of the ACC in Drake Passage have not been identified, other than the commonly held opinion that the barotropic transport is the part that changes. The amount of transport change for the different jets has not been analyzed. Allowing the transport change to be accommodated by the SAF or PF alone is likely to lead to different results

19 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) Fig. 11. The Relationship between Ertel Potential Vorticity and stream function for 135 Sv at Day 390. The EPV is calculated for all the model grids with a depth greater than 1500 m. (a) Scatter plotting of EPV and stream function, (b) EPV and stream function correlation coefficient with depth. due to the stability of the SAF and the instability of the PF. These variation are beyond the scope of the present study, in particular because there is no observational evidence to guide these experiments Potential vorticity Conservation of potential vorticity is used to explain the shifting of frontal locations with changing transport. 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

20 226 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) of the Southern Ocean, bottom topography has a strong effect on the flow. While vertical structure of frontal jets does exist (Klinck and Hofmann, 1985), the surface elevation and the 500 m temperature fronts both give consistent locations for the fronts. For simplicity, the discussion considers the frontal jets 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 without a meander, which is the initial state, 0. Thus, the initial potential vorticity q = f/h, and the flow will follow planetary vorticity contours. The value for q to be conserved for each streamline is set at the western model boundary, where the water is deep. Assuming conservation of q, the relative vorticity in the model interior is = q h f. In the Southern Ocean f and q are negative, so a decrease in depth leads to an increase in. Central Drake Passage has a depth around 3000 m and is shallower than the eastern Pacific Ocean with depths around 4500 m (in the model domain). This shallowing will generate positive relative vorticity which is consistent with a northward curvature of the frontal axis. The shallowing of Drake Passage 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 southern Passage leading to a northward shift of the PF. Eddies from the SACCF into the Polar Frontal Zone (Zone between the PF and the SAF) may have the same influence. Similarly, the PF may shift to the north affecting the SAF. Fronts located by surface elevation or the 500 m temperature are consistent. Without local surface forcing in this regional model or variations of the boundary input, the surface temperature and salinity are conserved following the flow. The strong gradient in density and the along-front velocity maximum coincide in the vicinity of a developed front, so do the density and along-front velocity contours (Gill, 1982) Model adjustment The development of the PF jet occurs in two parts. First, the imposed jet assumes a quasi-geostrophic balance with the initial density with a time scale of 1/f (about a day). For a mean surface velocity of about 0.5 m/s, information at the western boundary will take about 1 month to cross the whole model domain (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 speed and density structure). For large transport cases (bigger than 135 Sv), the developing meso-scale eddies is inhibited. The vertically integrated horizontal density gradient provides the necessary balance to the Coriolis force created by the strong current. It is less likely that potential energy is released through spawning eddies, which is a baroclinic process that tends to diminish the tilting of the isopycnal. With smaller transport, the baroclinic instability is effective in releasing potential energy to form eddies and meanders. The observed PF location along the ISOS mooring line (Fig. 9h) appears less variable with high measured transport. Stability of the SAF seems a different matter, which is changed fundamentally by the continental slope along the northern Drake Passage. Topography can stabilize flow or it can limit the size of the developing instability and halt its development. The SAF is influenced by the topographic ridge just west 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 some extent in the mean surface elevation (Fig. 5a) Transport and frontal stability Given the balance of kinetic and potential energy in the frontal jets, each front may only have a narrow range of imposed transport that is associated with realistic behavior. The SAF is narrow and strong 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.

21 B. Zhang, J.M. Klinck / Dynamics of Atmospheres and Oceans 45 (2008) The strength of the imposed transport and velocity structure are important for a short-term (several months) forecasting with regional meso-scale models. Furthermore, the flow paths of some frontal jets in the interior of this model have unrealistic meanders. This effect is most clearly seen in the surface elevation for smaller transport cases (Fig. 5) where a southward meander develops in the SAF and the PF close to the west boundary. This meander is not evident as the transport increases Model initial condition effects The model is initialized with the same fronts for all transport cases. The frontal displacement is only determined by the transport imposed on the boundary. This is a sensitivity study of the frontal location and transport only. The parameterizing of the initial front is carefully chosen to represent the realistic front. The initialization of the model does not provide a geostrophic balance between the density and the velocity. Since the T/S has been set up, we leave the model to adjust itself to the transport along the boundary 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. Then the model results are analyzed from the second month. Strong velocity shear from the imposed transport might trigger the instability of the front. Only one mean frontal width is used in construction each of the fronts. If different width is used, the instability condition will be changed and the frontal displacement pattern might be affected a little bit too. This effect will be minor since the front will adjust itself lately according to the transport distributed on it by tilting or shrinking the isopycnals. 6. Conclusions These model results show a number of effects with different imposed volume transport. The variability of ACC fronts in Drake Passage is clearly related to the volume transport of the ACC. With large transport, the SAF and PF are more stable. The PF and SAF spawn fewer eddies. The SAF, PF and SACCF shift northward with large transport while they remain to the south with smaller transport. With smaller transport, the SAF develops large meanders. The transport and the frontal variability reflect the competition between the frontal available potential energy and the kinetic energy. Consistency of input 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 to 90 km, which is close to the Gille (1994) estimate of 70 km. The minimum shifting distance occurs at a 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 PF is loosely controlled by the topography. After passing the seamounts in the Central Drake Passage, the PF meanders strongly and becomes a wider flow. The Ertel Potential Vorticity is linearly correlated to the transport stream function between depths of 1500 m to 2500 m with a correlation of more than 0.9. Near-bottom flow has a weaker correlation between 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 from Cnes. Computer facilities and support were provided by the Commonwealth Center for Coastal Physical Oceanography 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. References Belkin, I.M., Frontal structure of the South Atlantic. In: Voronina, N.M. (Ed.), Pelagic Ecosystems of the Southern Ocean. Nauka, Moscow, pp (in Russian). Belkin, I.M., Gordon, A.L., Southern Ocean fronts from the Greenwich meridian to Tasmania. Journal of Geophysical Research,