AUGUST 1999 HUGHES ET AL. 1971

Wind-Driven Transport Fluctuations through Drake Passage: A Southern Mode

CHRIS W. H UGHES Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside, United Kingdom

MIKE P. M EREDITH AND KAREN J. HEYWOOD School of Environmental Sciences, University of East Anglia, Norwich, United Kingdom

(Manuscript received 31 March 1997, in ®nal form 3 August 1998)

ABSTRACT It is proposed that, for periods between about 10 and 220 days, the variability in Antarctic circumpolar transport is dominated by a barotropic mode that follows f/H contours almost everywhere. Theoretical arguments are given that suggest the possible importance of this mode and show that bottom pressure to the south of the current should be a good monitor of its transport. The relevance of these arguments to eddy-resolving models is con®rmed by data from the Fine Resolution Antarctic Model and the Parallel Ocean Climate Model. The models also show that it may be impossible to distinguish the large-scale barotropic variability from local baroclinic processes, given only local measurements, although this is not generally a problem to the south of the Antarctic Circumpolar Current. Comparison of bottom pressures measured in Drake Passage and subsurface pressure on the Antarctic coast, with wind stresses derived from meteorological analyses, gives results consistent with the models, showing that wind stress to the south of Drake Passage can explain most of the observed coherence between wind stresses and circumpolar transport. There is an exception to this in a narrow band of periods near 20 days for which winds farther north seem important. It is suggested that this may be due to a sensitivity of the ``almost free'' mode to winds at particular locations, where the current crosses f/H contours.

1. Introduction the zonal coherence of those ¯uctuations. The purpose of this paper is to investigate how well the transport Since November 1988, as part of the Antarctic Cir- ¯uctuations can be measured by BPRs and to look for cumpolar Current Levels from Altimetry and Island a relationship between the transport and the wind stress Measurements (ACCLAIM) project (Spencer et al. over the Southern Ocean. This follows on from the In- 1993), the Proudman Oceanographic Laboratory (POL) ternational Southern Ocean Studies (ISOS) experiment, has been deploying bottom pressure recorders (BPRs) on either side of Drake Passage, as a contribution to the conducted in the mid-1970s and early 1980s, which es- World Ocean Circulation Experiment choke point mon- tablished that much of the transport variability was re- itoring. Instruments have been deployed in three dif- ¯ected by the bottom pressure (Whitworth 1983; Whi- ferent north±south con®gurations close to Drake Pas- tworth and Peterson 1985) and that the transport ¯uc- sage, each deployment lasting approximately one year. tuations are related to the wind ®eld (Wearn and Baker The positions and times are summarized in Fig. 1 and 1980; Chelton 1982; Peterson 1988a). Table 1. This is not a complete list of deployments in The next section of this paper revisits the theory of the area, which also include positions at intermediate wind-driven ¯uctuations in the transport through Drake latitudes (Spencer and Vassie 1997; Meredith 1995). Passage, and the following section considers the prob- The intention was to use the BPRs to monitor trans- lem of relating bottom pressure measurements to trans- port in the Antarctic Circumpolar Current (ACC) to help port ¯uctuations. These theoretical remarks are then establish the dynamics of ACC transport ¯uctuations tested by recourse to data from the Fine Resolution Ant- and, in conjunction with measurements by other groups arctic Model (FRAM), an eddy-permitting model of the at choke points south of Africa and Australia, to assess Southern Ocean, where it is shown that the concept of barotropic ¯uctuations is only relevant to large-scale currents or regions to the south of the ACC. The new BPR data are then compared with wind stresses from Corresponding author address: Dr. Chris W. Hughes, Proudman meteorological analyses, and the results of this com- Oceanographic Laboratory, Bidston Observatory, Birkenhead, Mer- seyside L43 7RA, United Kingdom. parison are discussed in the light of theory, model, and E-mail: [email protected] ISOS results. The picture that has been built up is then

᭧ 1999 American Meteorological Society

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FIG. 1. Map of the Drake Passage area showing the positions of BPRs discussed in this paper, and of the Faraday tide gauge. Also shown are the coastline and the 1000-m depth contour. tested further using model data from the Parallel Ocean due to a zonal mean wind stress can be balanced by a Climate Model (POCM), a global model with more re- pressure difference across the basin, producing a torque alistic wind stress forcing. on the solid earth via the continental boundaries. If there are no boundaries, the torque must be produced by an- 2. Dynamics of ACC transport other mechanism. The transports that would be neces- sary to allow horizontal friction or transient eddy pro- a. The mean ¯ow cesses to carry angular momentum to the blocked lat- The dynamics of the ACC are unique because of the itudes are much larger than those observed, unless very lack of meridional barriers at the latitudes of Drake large eddy friction coef®cients are assumed. Similarly, Passage. Munk and PalmeÂn (1951) were the ®rst to point vertical eddy transport is inadequate in the ¯at bottom out that this means that bottom topography must be case. A relatively small pressure difference of a few important in balancing the eastward wind stress at these centimeters of water across the major topographic fea- latitudes. In a closed basin, the angular momentum input tures of the Southern Ocean is, however, quite adequate to balance the input by wind stress. Stommel (1957) pointed out that there is no latitude TABLE 1. Details of deployments of ACCLAIM bottom pressure for which the minimum depth is greater than about 1000 recorders at northern and southern extremes of Drake Passage. m. He therefore decided on a model in which the South- Latitude Longitude Depth ern Ocean is closed at all latitudes but has a zonal gap Site Start End (ЊS) (ЊW) (m) between South America and the Antarctic Peninsula/ FS1 27 Nov 88 11 Nov 89 53.540 57.015 2803 Scotia arc region. Effectively, he was assuming that the FS1 11 Nov 89 21 Nov 90 53.539 57.031 2800 topography penetrates close enough to the surface to act FS1 21 Nov 90 09 Jan 92 53.512 56.980 2800 FS1 12 Jan 92 21 Jul 92 53.523 57.032 2800 as a continent. He then invoked a conventional (¯at ND1 22 Dec 91 06 Nov 92 56.491 52.985 3925 bottom, or no interaction with topography) Sverdrup ND2 09 Nov 92 22 Nov 93 54.942 58.393 1010 balance at latitudes north of Drake Passage, but with a ND2 22 Nov 93 15 Nov 94 54.943 58.392 1007 zonal jet to close the circulation. This zonal jet appears FS3 14 Nov 89 24 Nov 90 60.037 47.100 2180 FS3 23 Nov 90 07 Jan 92 60.052 47.085 2010 because south of Drake Passage he assumed an uncon- FS3 07 Jan 92 23 Nov 92 60.052 47.167 2267 ventional Sverdrup balance in which the streamfunction SD1 23 Dec 91 07 Nov 92 61.474 61.291 3946 is calculated by integrating wind stress curl eastward SD2 13 Nov 92 26 Nov 93 60.850 54.715 1020 from the western boundary, instead of westward from SD2 27 Nov 93 21 Nov 94 60.850 54.714 1020 the eastern boundary. There is no very good reason for

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC AUGUST 1999 HUGHES ET AL. 1973 doing this, as Stommel was aware, pointing out that do not produce Reynolds stresses strong enough to bal- these remarks ``cannot be considered to be a theory; ance the winds in this way. Lateral frictions in eddy- they are merely suggestive of one.'' By this reasoning, resolving models are typically less than 200 m2 sϪ1. the strength of the ACC is determined by the southward Given that eddies and friction are too small to balance transport due to nontopographic Sverdrup balance at the the wind stress, bottom topography must be important. northernmost latitude of Drake Passage, and hence by Johnson and Bryden (1989) proposed that eddies could the zonally integrated wind-stress curl at that latitude. provide the mechanism whereby angular momentum in- Baker (1982) used the Han and Lee (1981) winds to put by wind stress is transferred to depths where the calculate this Sverdrup transport across 55ЊS and de- ¯ow can interact with topography; however, numerical rived a value of 190 Ϯ 60 Sv (Sv ϵ 106 m3 sϪ1), com- model results (Treguier and McWilliams 1990; Wolff et parable with the contemporary estimate of 127 Ϯ 12 al. 1991; Killworth and Nanneh 1994) suggest that it is Sv for transport through Drake Passage, by Whitworth the time average ¯ow, rather than transient eddies, that et al. (1982). The zonal distribution of the implied south- produces most of the form stress. ward return ¯ow is also similar to that inferred (for the baroclinic ¯ow) from hydrography, with most of the b. Fluctuations in the ¯ow southward motion occurring in the Indian Ocean sector where the wind stress curl is strongest. There is support The above models are all of the mean ¯ow in the for these conclusions from calculations using the Hell- ACC and are described because they form an important erman and Rosenstein (1983) wind climatology (Chel- background to many investigations into the time vari- ton et al. 1990), and in FRAM, too, Wells and de Cuevas ability of the ACC. However, it will be seen that the (1995) ®nd that the net southward transport across 55ЊS, dynamical nature of the transport variability is, in fact, away from the Falklands Current, is close to an inte- profoundly different from that of the mean ¯ow. Most grated nontopographic Sverdrup balance with the wind authors agree that, for periods less than about a year, stress curl (although this does not make up the complete ¯uctuations in ACC transport are mostly barotropic (the ¯ow through Drake Passage). So the empirical basis for term is used throughout this paper to mean a ¯ow that the signi®cance of Sverdrup-type dynamics seems quite has a geostrophic componentÐand thus a horizontal persuasive. However, the question of how nontopo- pressure gradientÐindependent of depth. Thus, a wind- graphic Sverdrup dynamics can persist in a region where driven barotropic ¯ow consists of an Ekman ¯ow, a interactions with bottom topography are necessary is depth-independent geostrophic ¯ow, and possibly other yet to be explained. A zonal jet, shallower than 1000 ageostrophic components). Support for this view comes m, con®ned to the Drake Passage latitudes, can be added from the analytical and modeling study by Willebrand to the Sverdrup-type solution without altering the me- et al. (1980) (although this study was aimed at the mid- ridional currents, which are all that is speci®ed by Sver- latitudes), the analytical solution by Clarke (1982) based drup balance. In this sense, the Sverdrup solution still on a similarity solution of the time-dependent thermo- cannot be considered an explanation of the strength of cline equations for a ¯at bottom, and measurements in the ACC until a reason is given for selection of a Drake Passage reported by Whitworth and Peterson strength for the zonal jet. For more discussion of this (1985). Strong evidence for barotropic pressure ¯uc- matter, see Warren et al. (1996, 1997), Hughes (1997), tuations at the south side of Drake Passage is given by and Olbers (1998). Peterson (1988a) and Meredith et al. (1996). Physically, Another model for the mean ACC is that of Gill the reason for this is that the barotropic response to wind (1968) in which ¯at-bottomed Sverdrup regimes to the stress is mediated by relatively fast-moving barotropic north and south of Drake Passage, and a zonal jet in topographic Rossby waves, or ordinary barotropic Ross- Drake Passage, are connected by frictional boundary by waves in the ¯at bottom case (Anderson and Gill layers. Again, a reasonable shape for the ACC is ob- 1975; Anderson and Killworth 1977; Hughes 1996). tained, with a sharp northward de¯ection east of Drake Wearn and Baker (1980) refer to the even faster long Passage, and gradual southward return elsewhere. The gravity waves, which can travel around Antarctica in lack of bottom topography still means that high friction approximately one day. The role of gravity waves on coef®cients are necessary to limit the transport to rea- longer timescales can be seen as setting up the surface sonable values. Gill recommended lateral friction of 104 elevation consistent with near-geostrophic dynamics. m2 sϪ1, or vertical friction of 10Ϫ1 m2 sϪ1. With such On the timescale of barotropic gravity waves, diver- high friction, the zonal jet is reduced to carrying only gence is important, so there can be a signi®cant net 25% to 40% of the ACC transport, and the Sverdrup transport into a closed region, making the de®nition of balance is signi®cantly modi®ed by friction almost ev- transport around Antarctica a highly localized one. For erywhere. A very similar solution was produced by this reason, the analysis here concentrates on longer Klinck (1991). These values of friction are within the timescales, greater than about 10 days. range typically used as a parameterization of mesoscale Baroclinic Rossby waves move much more slowly, eddies, but it has been shown (Morrow et al. 1994; especially at high latitudes. In fact, within the ACC there Bryden and Heath 1985) that eddies in the real ocean is evidence that the mean current is strong enough to

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FIG. 2. Contours of f/H in the Southern Ocean, from the DBDB5 topography averaged onto a half-degree grid, plotted with a contour interval of 5 ϫ 10Ϫ9 mϪ1 sϪ1. The minimum value is Ϫ5 ϫ 10Ϫ8 mϪ1 sϪ1, and light gray shading is between Ϫ4 and Ϫ3 ϫ 10Ϫ8 mϪ1 sϪ1, or H/f values between Ϫ2.5 and Ϫ3.333 ϫ 107 sm. advect baroclinic waves eastward (Hughes et al. 1998), comes relatively more important as beta (the meridional so the baroclinic response is limited to much smaller gradient of f) decreases. Throughout the Southern length scales. It should however be noted that much of Ocean, the variation of f/H is dominated by topographic the ACC transport is concentrated in narrow jets with effects (Fig. 2). For barotropic ¯uctuations then, any a strong eddy ®eld, so it cannot be taken for granted Sverdrup balance must be a topographic Sverdrup bal- that there is no baroclinic response on these length ance in which the effective western boundary is deter- scales. For example, Meredith et al. (1996, 1997) give mined in relation to the gradient of f/H rather than f. very convincing evidence that ¯uctuations on small The Sverdrup balance is set up by the propagation of length scales (less than 200 km) can dominate the bot- topographic Rossby waves, with typical propagation tom pressure record at certain locations, making such speeds of several meters per second. Willebrand et al. records useless as a monitor of the large-scale ¯ow. (1980) estimate that a ¯at-bottom Sverdrup balance Since the net transport must be a large-scale ¯ow (it would take about 30 days to come into equilibrium at has to be coherent around large fractions of Antarctica), midlatitudes. At higher latitudes beta is smaller, but the we will assume that the dynamics of wind-driven trans- effective beta is dominated by topography, so 30 days port ¯uctuations are barotropic for periods shorter than is probably an upper limit on the time needed for Sver- a year. This is an assumption that is almost certainly drup balance to be set up on the largest scales, and a not entirely valid since the interaction of wind stress typical value for the smaller scales characteristic of the with narrow, intense, baroclinic jets is a complicated bottom topography (except where closed contours of matter, which may also produce transport ¯uctuations. f/H do not allow a barotropic Sverdrup balance to be However, the simpli®cation permits a more detailed ex- established). planation of this aspect of the dynamics that produces Clarke (1982) applies ¯at-bottom barotropic dynam- a useful framework within which the observations and ics to ACC ¯uctuations, although he attempts to include model results may be examined. Even assuming a bar- topographic effects by employing a large drag to rep- otropic response on the large scale does not guarantee resent topographic form stress. Wearn and Baker (1980) that this response will be detectable in local measure- assume a similar model to that derived by Clarke (1982), ments, as the signal at any one place may be dominated in which a zonal jet is accelerated by winds and retarded by baroclinic ¯uctuations at small scales. by friction (or form drag) with a time constant, based As Willebrand et al. (1980) pointed out, for a baro- on correlations between zonal average winds and mea- tropic response it is vitally important to take account of sured bottom pressure difference across Drake Passage, the bottom topography. The characteristics along which of between 5.5 and 9.5 days. The models implicit in barotropic Rossby waves propagate are not lines of con- Peterson (1988a) also use ¯at bottom dynamics, con- stant latitude, but lines of constant f/H, where f is the centrating on the importance of zonally averaged wind Coriolis parameter and H the ocean depth. At midlati- stress over the ACC region, and wind stress curl north tudes, gradients of f/H are dominated by variations in and south of this region, although in this case the models H if the slope is large enough to produce an order-1 were simply used as scenarios to compare with obser- difference in ocean depth over horizontal distances less vations, without advocating the use of ¯at bottom dy- than one earth radius. At high latitudes, topography be- namics (indeed, it was concluded that other dynamics

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC AUGUST 1999 HUGHES ET AL. 1975 must be involved). None of these models take adequate (1973)]. Of course, E can also change as a consequence account of the dramatic change in barotropic dynamics of convection-driven ¯ows, and this might be expected when topography is included. This change is illustrated to be a signi®cant process close to Antarctica, especially by the results of Klinck (1991) in which the mean trans- at the annual period. It can also change because of ad- port of a barotropic ACC drops from 180 Sv without vection of small-scale features such as intense jets (for topography (but with large friction, with a spindown which the linear vorticity dynamics assumed by Gill and time of less than 6 days) to 10±25 Sv with topography. Niiler would be inappropriate) but, for the purposes of The reason for this, as explained below, is probably that this investigation, we are assuming that these processes there is a much smaller cross-sectional area over the do not dominate the dynamics. region of f/H contours that pass around Antarctica than The remaining balance of terms is between a time- the area of the whole Drake Passage region without dependent term that permits topographic Rossby waves bottom topography. This result emphasizes that baro- (and can be ignored in most regions once the Sverdrup tropic dynamics, which can reasonably be applied to balance has been set up), the ¯ow across contours of relatively short period ¯uctuations, produce quite dif- f/H, and the curl of ␶/H, so water can get through Drake ferent results from either the ¯at-bottom case or the Passage by means of a forced ¯ow across f/H contours. baroclinic case with topography, which is needed to At ®rst glance, it might seem that this forced ¯ow would explain the mean ¯ow. be smaller than the ¯at bottom equivalent, since gra- If the linear momentum equations are integrated over dients of f/H, suitably normalized, are larger than beta, the depth of the ocean, the result can be written as but in fact the two are exactly the same in an integrated sense. As pointed out by Hughes and Killworth (1995), -١E ϩ ␶, (1) if (1) is integrated around a closed contour of H (ig ١⌿t Ϫ ␳ 0f١⌿ϭϪH١pb Ϫ ␳ 0k ϫ where ⌿ is the vertically integrated streamfunction (the noring time dependence), then the effects of strati®ca- rigid-lid approximation has been made, and subscript t tion and bottom topography both drop out, leaving represents differentiation with respect to time), H is depth, ␳ 0 is a reference density, pb is the bottom pres- (١⌿ ´ ds ϭ ␶ ´ ds. (4 Ϫ␳0 f sure, ␶ the surface wind stress (it can also be taken to ͶͶconst const include the other neglected quantities), and E is potential HH energy, Applying Stokes theorem then gives

0 (ϫ ␶ dS, (5 ١ E ϭ gz␳ dz, (2) ␳␤0 ⌿x dS ϭ ␳0 ͵ ͵const͵ const ϪH HH measured relative to the surface. Dividing by H and which is the Sverdrup balance integrated over the en- then taking the curl gives closed area (the physical reason for this balance is that the bottom pressure torque vanishes over areas enclosed ١⌿ ␶ by contours of constant depth). This could be the basis (ϫ . (3 ١ ´ t ϩ ␳ J(⌿, f /H) ϭ J(E, 1/H) ϩ k ´ ١ HH0 for a relationship between wind stress curl and ACC ΂΃ transport, although it is clearly not the curl along a If H is set to a constant, this reduces to the conven- particular latitude that is important; frictional effects tional Sverdrup balance in the steady state. With variable may be relevant (especially near the coast), and the re- bottom topography, the ®rst term on the right-hand side lationship between the meridional transport in (5) and represents the effect of strati®cation. Although this is the zonal transport through Drake Passage is far from very important in the time mean ¯ow, providing a mech- transparent. Although time dependence has been ig- anism that insulates the ¯ow from effects of the bottom nored, this argument would also apply to variations in topography, it is less important at seasonal timescales the topographic Sverdrup mode on timescales long and large length scales. This was demonstrated by Gill enough for this mode to come into equilibrium since and Niiler (1973) who considered barotropic dynamics the time-dependent term is much smaller than the other assuming length scales of 3000 km zonally and 1000 terms in this situation. km meridionally, driven by seasonal winds. They con- The actual ACC transport produced by the forced ¯ow cluded that time dependence of E due to density ad- is dif®cult to calculate because of the complicated shape vection by the resulting ¯ow produces a negligible per- of the f/H contours, but there is another component that turbation to the assumed ¯ow, showing that it is self- should be considered too. There are contours of f/H that consistent to take E as constant over these timescales. pass all the way around Antarctica (dark shading in Fig. Although the assumed length scales are rather large, the 2). Any ¯ow along these contours needs no curl of ␶/H effect of density advection is particularly small at high to drive it. In the linear, unstrati®ed case, the ¯ow along latitudes so that, at around 60ЊS, this scaling would still such contours cannot come into a Sverdrup balance and apply over length scales reduced by a factor of 10 [see will (as shown below) continue to accelerate until either Eq. (8.5) and following comments in Gill and Niiler the forcing reverses or a frictional balance is attained.

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Being unconstrained by the topographic Sverdrup bal- Sverdrup response are capable of producing circulation ance, this is often called a (linear) ``free'' mode (Read around Antarctica, and the two are quite closely related. et al. 1986; Branstator and Opsteegh 1989), analogous The topographic Sverdrup balance gives the component to a purely zonal ¯ow in the ¯at bottom case (the ¯ow of ¯ow across f/H contours, and the component along is free in the sense that, in the absence of strati®cation f/H contours is then inferred by mass continuity (except and viscosity, it could persist inde®nitely without forc- that this is insuf®cient for f/H contours that are closed). ing, unlike the mode forced by curl of ␶/H). For forcing Thus, close to the closed f/H contours around Antarctica with a period longer than the Sverdrup spinup time, this there are contours of f/H, that almost close around the is therefore the mode that comes to dominate the so- continent, and the ¯ow along these contours will be very lution, unless strati®cation comes to balance the forcing. sensitive to the Sverdrup transport across f/H contours. Integrating (1) around a closed contour of f/H, drop- A simple example would be a wind ®eld that produces ping the effect of strati®cation, gives Sverdrup transport to larger (negative) values of f/H (i.e., toward the unblocked f/H contours in shallower ␶ regions near Antarctica) to the west of Drake Passage, ␳ u ´ ds ϭ ´ ds, (6) 0 Ͷ t Ͷ H and the opposite way east of Drake Passage. The water f/Hf/H could then ¯ow through Drake Passage along unblocked ١⌿/H. Here, the line integral of wind f/H contours and continue eastward around Antarctica where u ϭ k ϫ stress produces an accelerating ¯ow [not necessarily fol- in the deeper region of f/H contours, which are blocked lowing the f/H contour, it is only the integral acceler- only in Drake Passage. Alternatively, the ¯ow on un- ation that is speci®ed by (6), although for periods much blocked contours might not pass through Drake Passage longer than the topographic Rossby wave period all but could return the ``long way around'' in a westward ¯ows across f/H contours must be proportional to the current. The difference between these two cases is the wind stress rather than its time integral, leaving the behavior of the free mode. Thus, the free mode also accelerating ¯ow to follow the f/H contour in this limit], makes possible an ``almost free mode,'' in which trans- in contrast to the Sverdrup balance case where the curl port is along f/H contours almost everywhere, but skips produces a steady ¯ow. In reality, of course, the accel- across contours at certain places. eration will be halted, either by some kind of (eddy) The dynamics involved is illuminated by considering friction or by a feedback from density advection on the the role of the Ekman transport. Assuming a timescale value of E in (3); so for times longer than the frictional longer than that of topographic Rossby wave, so that (or advection) time constant the ¯ow will follow the the time-dependent term may be dropped from (1), and wind stress, with a time lag. The free ¯ow thus obeys taking the strati®cation to be constant in time, divide dynamics rather like the frictional zonal jet assumed by (1) by f and take the curl, then subtract the time average Clarke (1982) and Wearn and Baker (1980), but topog- to give raphy has been taken into account; and a higher effective friction is no longer due to larger-scale topographic ef- ␶Ј (ϫ , (8 ١ ´ J(pЈ, H/ f ) ϭϪk fects, which need not act as a drag at all, but to the b f narrow, convoluted path of the current and to small- scale topographic drag or effects of strati®cation. where the prime denotes deviations from the time av- The distinction between Sverdrup and free ¯ow can erage. The right-hand side of (8) is the convergence of be made more formally (Hughes 1995), especially where the Ekman transport, and the left-hand side is the di- the boundary follows contours of f/H, which could rea- vergence of the depth-integrated geostrophic ¯ow. Thus sonably be considered to be the case here. The inviscid we see that a geostrophic ¯ow follows H/f contours formula for the free ¯ow component is except where the depth-integrated geostrophic ¯ow be- f comes convergent in order to feed a divergent Ekman transport (or vice versa). The importance of the free ١ ⌿ ΗΗH ␶ mode becomes apparent if (8) is integrated over an areaץץ ␳ 0 ds ϭ ´ ds, (7) tfͶͶ H H bounded by a closed contour of H/f. The left-hand sideץ 0 -then vanishes, leaving the Ekman transport into the re ץ H gion unbalanced. In order to balance this transport, one where ⌿ 0 ϭ⌿0( f/H, t) is the free mode component of of the terms that was ignored in (1) must be reinstated. the streamfunction. Even without friction it is dif®cult Initially, the most important will be the acceleration, to work out the size of the response, because of the producing an accelerating circulation around closed f/H complicated form of the integrals involved and their contours until either friction or strati®cation become sensitive dependence on the shape of depth contours. important. However, a pure free mode will not generally One thing is clear though: the free mode response is occur. Since the divergence of the Ekman transport will driven by wind stress (not curl), averaged along lines not generally be constant along the closed H/f contours, that fall mostly on the southern side of Drake Passage. it will vary, producing a ¯ow across contours. The av- It should be stressed that both the free mode and the erage divergence of Ekman transport along an H/f con-

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC AUGUST 1999 HUGHES ET AL. 1977 tour is balanced by the time-dependent term, but the yr and amplitude 2 cm sϪ1, produces a peak displace- difference from that average will produce ¯ows across ment of about 100 km, small on the scale of the ACC. H/f contours of both signs, integrating to zero and link- ing the free mode ¯ow to ¯ow along nearby H/f con- 3. Theory of measurement tours. Thus, an almost free mode is produced. Whether the free or the almost free mode is the more important From 1976 to 1981, as part of the ISOS program, depends on the geometry, the form of the wind stress BPRs were deployed across Drake Passage at about forcing, and the time it takes for the free mode to reach 500-m depth in an attempt to monitor the transport of a steady state, and is dif®cult to assess analytically. the ACC (Wearn and Baker 1980; Whitworth 1983; The third possibility is that transport can occur due Whitworth and Peterson 1985; Peterson 1988a). In to a forced mode that is not closely related to the free 1979, a year-long deployment of moored current meters mode. If such a mode is to pass right around Antarctica and temperature sensors was undertaken along a transect without making use of those f/H contours that pass most crossing the BPRs, and data from this year were used of the way around the continent, it would require a to show that the majority of the transport variability for complex series of transports across f/H contours, alter- periods shorter than a year is barotropic, and to give a nating between passing to higher and then lower values calibration relating pressure differences across Drake several times along the circuit. Again, the likely size of Passage to the net transport above 2500 m (Whitworth this component is dif®cult to assess analytically, but it and Peterson 1985). seems reasonable to predict that it would be smaller For barotropic variations, the transport variation be- than the free or nearly free modes, which rely on a wind tween two points depends not only on the pressure dif- stress aligned with the mostly zonal closed H/f contours. ference variations, but also on the value of f/H where The essentials of the argument can be summarized as the current ¯ows. The total transport is follows: it is much easier to produce a barotropic ¯ow b 0 b along f/H contours than across contours. The compo- T ϭ udzdsϭ Hug ds ϩ TEk, (9) nent of the ¯ow that encircles Antarctica is therefore ͵͵ ͵ a ϪHa likely to follow those f/H contours that encircle, or almost encircle, the continent. where ug is the geostrophic velocity perpendicular to The shaded region in Fig. 2 is an attempt to show the section between horizontal positions a and b, and the zone that might be expected to play a part in the TEk is the transport across this section in the Ekman free and almost free modes. Dark shading represents layer (plus any other ageostrophic ¯ow that may occur). s, soץ/pץvalues of f/H that, at the south side, go all the way Geostrophy gives ␳0 fug ϭ pץ around Antarctica, although almost all of this area is at b H depths less than 1000 m. The lighter shading is for Tg ϭ ds, (10) sץ f ␳0 ͵ contours that are only interrupted by small-scale features a at Drake Passage. The smallest scales will certainly be where Tg is the geostrophic contribution to the transport. irrelevant here, since nonlinear effects can effectively If points a and b both lie on the same contour of f/H, smooth out the f/H contours. The scale over which this then the path of integration can be taken along this smoothing is effective depends on the strength of the contour, so H/f can be taken out of the integral giving current, and the mean ¯ow in Drake Passage is very H strong. An estimate of the smoothing effect can be made Tgbaϭ (p Ϫ p ). (11) f ␳ by comparing vorticities u/L and f␦H/H, where L is the 0 length scale to be smoothed out. Assuming a ␦H/H of When the points are not connected by a contour of 0.1,a1msϪ1 mean current could smooth such a feature f/H, this simpli®cation is not possible and the relation- over a distance of about 100 km. ship between transport and pressure depends on the path This picture of the barotropic response to winds dem- of the current, which might ¯uctuate over time. For a onstrates that it makes little sense to think of wind- region as constricted as Drake Passage, the possible driven ¯uctuations as changes in the strength of the variation in f is quite small [1.22 to 1.27 (ϫ10Ϫ4 sϪ1) mean ¯ow, for timescales shorter than a year. Any bar- for the ISOS BPRs], but with the BPRs at only 500-m otropic ¯uctuations in transport must be strongly to- depth, there is no section joining these two points that pographically controlled (much more so than the path does not undergo a depth change of at least a factor of of the mean ¯ow) and consist of a free mode and a 2. The importance of this effect is demonstrated by the Sverdrup response that bear little relation to the mean large difference found by Whitworth and Peterson ¯ow (and probably also some response in the narrow (1985) when they attempted to correct their transport jets of the ACC, neglected here). Thus the transient estimates for the effect of ¯uctuations in the currents current ¯ows across streamlines of the mean ¯ow. This on the shelf slope between the 500 m and 2500 m con- need not produce strong interactions with the mean ¯ow tours. Thus ¯uctuations in pressure difference between if the ¯uctuating current does not signi®cantly displace two points at the same depth, despite being a good mea- the mean current. A ¯uctuating current, with period 1 sure of the ¯uctuations in the horizontally integrated

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC 1978 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 current (if the two points are at similar latitudes), need on that side of the closed contours. The area south of not be a good measure of the net transport ¯uctuations, the closed contours around Antarctica is so much small- integrated over depth as well as horizontally. They may er than the area to the north that we would expect almost instead represent movements of the current so that it all of the bottom pressure signal to be seen at the south. ¯ows with varying distributions of f/H values, even in For the Sverdrup mode things are more complicated the purely barotropic geostrophic case. For the Sverdrup since it is not so easy to see what bottom pressure dis- component of the response to wind forcing, this can tribution would arise; but it seems reasonable to assume make observations dif®cult to interpret since this com- that it would still be a change in bottom pressure across ponent is due to ¯ow across f/H contours varying over the current that has the same sign at all longitudes (at time, so the current must be at different values of f/H least for that part of the current that passes south of at different times. Africa, Australia, and South America), permitting a sim- If the current is assumed to have a ®xed path, or one ilar argument to be made. Certainly, the almost free for which the distribution over values of f/H does not mode must produce a bottom pressure ®eld close to that vary signi®cantly in time (implying that the current is of the free mode, so we would expect both free and either a free mode or a part of the Sverdrup response almost free modes to be re¯ected much more strongly that is not forced locallyÐa description that applies well in bottom pressure at the southern side of Drake Passage to the almost-free mode), then the relationship between than at the northern side. transport and pressure difference can be used to infer an effective value of H/f: 4. Model results pץ b H ds A complete justi®cation of the approximations made sץ f ͵ HT␳ a in the discussion above would require some very so- ϭϭ0 . (12) f e (p Ϫ p )(p Ϫ p ) phisticated scaling arguments. Some arguments have ΂΃ ba ba been given for large scales, on the assumption that in- For a very narrow geostrophic current, this reduces to teractions with smaller-scale processes are not domi- the value of H/f at which the current ¯ows. For broader nant, but that assumption is hard to justify analytically. currents it is a weighted average of the values of H/f Instead, we will use a rather more sophisticated nu- at which signi®cant pressure gradient exists. merical model to test these scalings. The Fine Resolu- Thus, implicit in the notion that bottom pressure dif- tion Antarctic Model, which is used, has its limitations, ferences are a monitor of transport ¯uctuations is the but it is probably safe to say that the real ocean is at assumption that the current that produces those transport least as complicated as the model ocean. Any simpli- ¯uctuations ¯ows with an effective f/H that does not fying assumptions that do not hold in the model ocean vary in time. That assumption is related to the role of are unlikely to hold in the real ocean. In this way we the Ekman layer transport, mentioned above. If the in- can at least make sure that our assumptions are consis- tegral from a to b in (10) is taken along two different tent with a more complete dynamical system, closer to paths, with different Ekman ¯uxes across those paths, the real ocean. it becomes clear that Tg is a path-dependent quantity; FRAM (FRAM Group 1991) is a model of the South- it is only the total transport that is independent of path ern Ocean, south of 24ЊS, with a resolution of 0.25Њ in (ignoring changes in free surface height). This is a se- latitude by 0.5Њ in longitude and 32 vertical levels. The vere problem unless the geostrophic transport is much model was spun up by relaxation to Levitus (1982) tem- greater than the Ekman transport, and is therefore not perature and salinity values. The data considered here determined by the local wind stress. are from six years of ``free running,'' in which relaxation The above discussion concerns the relationship be- to the Levitus climatology is only applied in the surface tween volume transports and pressure differences but layer, as a crude approximation to climatological heat does not address how the ¯uctuations in pressure dif- and freshwater ¯uxes. The wind stresses are monthly, ference are apportioned between the two pressure mea- linearly interpolated from the Hellerman and Rosenstein surements. The additional information that is needed is (1983) climatology. The topography is smoothed to mass continuity. For the situation considered here the about 1Њ resolution to avoid instabilities. Grose et al. mass of water in the ocean is conserved so that, ignoring (1995) give a good description of the strengths and the variation of gravity with latitude, the global integral weaknesses of the model in its representation of the of bottom pressure must remain constant. The unforced mean ¯ow in the Drake Passage region. free mode is the simplest to analyze in this respect since The dataset used comprises 72 monthly snapshots setting ⌿ to a function of f/H tells us [from (1)] that over the 6-yr free running period. Total volume transport pb is a function of f/H. Thus, in going from no ¯ow to is also available as a daily time series over almost seven a free mode ¯ow, the bottom pressure on one side of years (Fig. 3). The transport variability can be decom- the f/H contours must rise, and that on the other side posed into three parts: a long-term climate drift; an an- must fall. Conservation of mass tells us that the size of nually repeating signal, and a shorter period variability the rise or fall must be in inverse proportion to the area that does not tend to repeat from year to year. The long-

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Bottom Water formation (Killworth and Nanneh 1994) or other transient thermohaline effects, demonstrating how the thermohaline circulation can affect transport on interannual timescales. The other nonrepeating com- ponent must be intrinsic (i.e., unforced) ¯uctuations due to nonlinear activity within the current since there is no forcing on timescales shorter than a month. It is note- worthy that, although smaller in magnitude than the annually repeating component, these ¯uctuations are not negligible, even in FRAM, which has a less energetic FIG. 3. Time series of Drake Passage transport from FRAM. The eddy ®eld than the real ocean (Stevens and Killworth top curve shows the complete time series, with a polynomial ®t su- 1992). perimposed. The middle curve is the annually repeating component (with arbitrary mean), and the lower curve is the remainder after Woodworth et al. (1996) presented correlations of subtracting the polynomial and annually repeating components from subsurface and bottom pressure (with a linear climate the complete time series (again, with arbitrary mean). drift removed) with transport, from FRAM. The re- sulting plots (particularly for bottom pressure, for which the eddy ®eld is less intrusive) clearly show the in¯u- term drift and annually repeating part are extracted by ence of the f/H contours shown in Fig. 2 and demon- simultaneous least squares ®tting of a ®fth-order poly- strate that it is pressure to the south of the ACC that is nomial and 12 monthly values with linear interpolation (negatively) correlated with transport. Some statistically between them (this form is chosen to match that of the signi®cant positive correlations are seen to the north, wind forcing). Since FRAM is a rigid-lid model, and but these are unlikely to be realistic since all occur on the streamfunction is set to the same constant on South f/H contours directly connected to the northern open America, Africa, and Australia, the transports south of boundary, where a ¯at-bottom Sverdrup balance is ap- these three continents are equal at all times. plied (Stevens 1991). The signi®cant positive correla- The rigid-lid formulation also avoids the use of pres- tions on the Patagonian shelf, north of Drake Passage, sure in the model calculations, although pressure gra- are worth noting though, especially as similar correla- dients can be inferred (at model velocity points) from tions are not seen at the northern ends of the other choke the model dynamics. Pressures are then calculated at points south of Africa and Australia. These plots are tracer grid points by integration of the gradients. (The not reproduced here, but see the later section using ®nite difference procedure permits the pressure differ- POCM data for similar plots. The FRAM domain only ence between diagonally opposed corners of the velocity extends to 24ЊS, so the ``rest of the World Ocean'' is grid box to be calculated from the gradient at the ve- rather smaller in FRAM than in reality; but it is still locity point. The pressure gradient was integrated in an pressure to the south that re¯ects transport. ad hoc manner until the whole model domain had been In an attempt to de®ne the patch of the current that covered.) This procedure is necessarily approximate is responsible for transport ¯uctuations, while minimiz- since the pressure gradients do not have exactly zero ing the effect of eddies, a set of streamfunction ®elds curl due to imperfect convergence of the streamfunction was spatially smoothed using a 21 ϫ 21 gridpoint run- calculation, so there is no unambiguous pressure ®eld. ning mean ®lter. For each grid point of the resulting 95 Even so, the pressures calculated are consistent to within smoothed streamfunction ®elds (streamfunction at 10- 10 Pa (0.1 mb, or approximately 1 mm of water), as day intervals), a simultaneous ®t was performed to the was shown by comparing pressures on either side of the polynomial and annually repeating transport time series periodic boundary. Two constants have to be chosen in of Fig. 3. The resulting annually repeating ®t is shown this procedure: the spatial average pressures on the two in Fig. 4. The streamfunction on northern land masses grids produced by integration in diagonal steps. The is zero in FRAM, so the ®t is close to zero here and difference in constants was chosen to minimize ``check- close to 1 around Antarctica. If the transport current erboarding,'' and then the sum was chosen to give zero follows a preferred path, it will show up as the region area average. Since this procedure was followed using of highest gradient. Except in the eastern Indian Ocean surface pressures, mass is not precisely conserved when sector, where the ®t is large but correlations are poor, density changes occur. However, the density forcing is the current tends to follow the f/H contours highlighted by relaxation to annual mean Levitus values in the sur- in Fig. 2 (although the response in the Weddell Sea is face layer and has no signi®cant seasonal cycle. odd, but still related to f/H contours). Figure 3 immediately tells us several things about the A second way to look at the path of the current in transport ¯uctuations in FRAM. Since the winds are FRAM is in terms of the ®t between bottom pressure annually repeating, neither the long-term trend nor the and transport. Since the correlation is very good close shorter period ¯uctuations can be attributed to the wind to Antarctica, the ®t can be used to de®ne an effective forcing. The long-term trend is a climate drift of the f/H or H/f, as de®ned in (12). This was calculated by model and may be attributable to the lack of Antarctic choosing the ®rst minimum (i.e., most negative value)

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FIG. 4. The ®t of spatially smoothed streamfunction (from 95 ®elds at 10-day intervals) on the annually repeating transport time series. Contours are at intervals of 0.2, from Ϫ0.4 to ϩ1.4; positive contours are black. of the ®t of bottom pressure on transport as one travels there are places where the current jumps from one northward from Antarctica (the ®rst minimum was cho- branch of the contour to another. The clearest example sen to avoid strong in¯uence from boundary friction). is in Drake Passage, where no contour exists for some The result is plotted in Fig. 5. Again, the path of the longitudes. This means that there is no value of H/f current in Fig. 4 closely matches the contour, although large enough in Drake Passage for the transport to be

FIG. 5. The effective value of H/f, de®ned by (11), and calculated at each longitude from the linear ®t of bottom pressure near Antarctica on volume transport. (top) Also shows the largest (negative) value of H/f at each longitude (diamonds); (bottom) the position of this H/f contour, superimposed on the model topography.

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC AUGUST 1999 HUGHES ET AL. 1981 produced entirely by geostrophic barotropic ¯uctuations variability, making a deeper reference level appropriate at the south: the pressure change is too small to account for estimates of variability in the total transport. How- for the transport change for a current with any distri- ever, it would probably be pushing the FRAM data too bution of latitudes, at these longitudes. The upper panel far to recommend a reference depth in a place like Drake of Fig. 5 has diamonds marked on it, representing the Passage where the approximate topography produces most negative value of f/H found at each longitude in large distortions in the modeled mean ¯ow (Grose et al. FRAM. Where these lie above the line, the relationship 1995). between bottom pressure and transport cannot be ex- The vertical distribution and behavior in time of the plained by barotropic geostrophic currents. This only baroclinic transport ¯uctuations differ quite markedly, happens in Drake Passage, and there only by a small even between the three Australian sections, demonstrat- margin, or over very short length scales, which can ing that there is no zonally coherent mode in the bar- easily be accounted for by nonlinear processes, meso- oclinic transport. It seems that the total transport across scale baroclinic ¯uctuations, and statistical uncertainties a section is made up of both barotropic and baroclinic in the linear ®t of pressure on transport. Nonetheless, components but, whereas the total ¯ow must exhibit it seems likely that this is related to the positive cor- zonal coherence, the form of the baroclinic ¯ow is co- relations seen to the north of Drake Passage, perhaps herent only over short distances. At any one place then, re¯ecting a part of the transport through the passage that it is impossible to separate the large-scale barotropic occurs in the Sverdrup mode. The value of H/f shown mode that is guided by f/H contours from the smaller- in the upper panel lies in the lightly shaded region of scale baroclinic ¯uctuations. The exception to this is to Fig. 2, except east of Drake Passage to 60ЊE where it the south of the ACC, where strati®cation becomes weak moves to the deeper (unshaded) region. Thus, this re- enough for the baroclinic ¯uctuations to be small. In sponse seems more closely related to the almost free addition, the waveguiding effect of f/H contours ensures mode than to the free mode. that this barotropic signal is representative of a broad The model can also be used to test the assumptions range of longitudes. Here, it seems, is a second reason of depth independence and geostrophy. While the above for bottom pressure to the south of the ACC to be a results on the importance of f/H contours are strongly much more reliable indicator of transport ¯uctuations indicative of a large-scale barotropic mode, it is not clear than pressures farther north. that the barotropic signal will be the dominant signal at This problem of local baroclinic activity masking the any one place. To test this, transports were calculated large-scale signal has been noted several times before. from the FRAM data at ®ve sections: south of South Peterson (1988a) notes a peak at about the 1.5-month Africa, western Australia, central Australia, east Aus- period in the bottom pressure spectrum from the north- tralia, and in Drake Passage. The results from south of ern ISOS records, which he attributes to mesoscale eddy South Africa are not shown, as the baroclinic transports activity. Johnson (1990) attempts to explain the lack of here are enormous due to the proximity of the high- a clear relationship between these northern Drake Pas- variability Agulhas retro¯ection to the coast. Transports sage measurements and zonal wind stress in terms of from the other sections are shown in Fig. 6. coastally trapped waves propagating southward along It is clear from this ®gure that the transport ¯uctua- the western coast of South America. Meredith et al. tions are mostly geostrophic, although some signi®cant (1996) conclude that the ND1 record is unsuitable for ageostrophic ¯uctuations occur. What is more striking monitoring transport variability because it is dominated is that the variability at each section is not barotropic. by movements of the Sub-Antarctic Front, and also note (Recall that the argument in favor of a barotropic re- that the Myrtle record (another BPR system situated sponse depends on an assumption of a suitably large about 100 km north of the SD2 position) is dominated length scale. We might expect baroclinic effects to be by local processes for periods longer than about 4 days. important at a single meridional section with an effec- This conclusion is consistent with the relatively poor tive zonal length scale of one grid point.) Depending agreement between altimeter-derived subsurface pres- on the reference depth, the baroclinic transport ¯uctu- sures and bottom pressure at the Myrtle site (Woodworth ations can be comparable to, and sometimes larger than, et al. 1996). the total. For the Drake Passage and western Australia Finally, the FRAM data can be used to look at the sections, the baroclinic transport ¯uctuations relative to relationship between transport ¯uctuations and winds. 2391.5 m are quite small, so this depth may serve as a Since the winds repeat exactly from year to year, we good reference depth for the barotropic ¯ow. This seems have the advantage that we can ®lter out many of the to contradict the ®nding of Whitworth and Peterson nonwind effects by considering the annually repeating (1985) that 500 m provides a good reference level, but transport time series from Fig. 3. No useful spectral they were only concerned with transport above 2500 m. information can be extracted since we are now com- A shallower reference level must be expected for this paring 12 monthly values of transport with 12 numbers component of the transport variability, but the FRAM derived from the monthly wind ®elds, so a correlation results suggest that ¯ow ¯uctuations deeper than 2500 coef®cient is the best that can be done. m form an important component of the total transport Five time series were calculated from the wind ®elds:

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FIG. 6. Time series of (solid lines) total transport and (dashed lines) geostrophic transport through meridional sections of FRAM at Drake Passage (289ЊE), western Australia (119ЊE), central Australia (131.5ЊE), and east Australia (144ЊE). In each panel, the top line shows the complete transport, and lower lines show baroclinic transport relative to reference depths of 32.35, 532, 2391.5, 3529 m, and the bottom. Mean values are arbitrary. Where the reference depth is deeper than the ocean, the bottom is taken as reference depth.

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FIG. 7. Annual time series of transport and ®ve integrated measures FIG. 8. Correlation coef®cients between annually repeating trans- of wind stress (de®ned in the text), from FRAM. Correlation coef- port from FRAM and (line) zonal average eastward wind stress ␶; ®cients between each wind stress time series and the transport are (diamonds) zonal integral of curl (␶/ f). The value of correlation shown to the right. A coef®cient of 0.576 is signi®cant at the 95% signi®cant at the 95% level is also marked. level. mode). The zonal averages were only calculated for zonal average of eastward wind stress through the Drake wind stresses over the sea. South of about 67ЊS, a sig- Passage latitudes (DP z-a); zonal average of eastward ni®cant fraction of a latitude circle is occupied by land, wind stress over the ACC, de®ned as the area between so values this far south are only representative of a the 0 and 180 Sv streamlines that pass through Drake limited longitude range. The maximum correlation at Passage (ACC z-a); zonal integral of the wind stress 65ЊS for zonal average winds is then what might be curl at the northernmost latitude of Drake Passage (N expected, although the high correlations for curl farther curl); zonal integral of the wind stress curl at the south- south are curious. ernmost latitude of Drake Passage (S Curl); and integral of tangential wind stress along the northernmost f/H contour ( f/H ϭϪ4 ϫ 10Ϫ8 sϪ1 mϪ1, H/f ϭϪ2.5 ϫ 5. Bottom pressure measurements 107 s m) to pass right around Antarctica ( f/H Circn). As described in the introduction, instruments have Figure 7 shows these time series, together with the trans- been deployed to the north and south of Drake Passage, port time series, with correlation coef®cients between at various positions, since 1989. Figure 9 summarizes the winds and transport. The 95% signi®cance level the duration and depth of each deployment at the po- requires a correlation coef®cient of 0.576. Neither of sitions marked on Fig. 1. The end of one time series the wind curl time series is signi®cant at this level, and the start of the next are typically separated by a gap although the difference (N Curl Ϫ S Curl) gives a cor- (or sometimes an overlap) of one or two days. In ad- relation coef®cient of 0.596. The difference time series dition, each BPR record suffers from a long period drift. is, of necessity, strongly correlated with the DP z-a time An attempt has been made to remove this drift by ®tting series. The strongest correlation is clearly with winds a low-order polynomial to the records and examining averaged along the f/H contour, although other mea- sures of the wind ®eld to the south of Drake Passage give similar correlations, as illustrated in Fig. 8. This ®gure shows the correlation between transport and zon- ally averaged eastward wind stress (line), and zonally integrated wind stress curl (diamonds), at each latitude in FRAM (with the 95% signi®cance value superim- posed). The highest correlation for wind is at about 65ЊS, approximately the southernmost latitude of Drake Passage, and even higher correlations are found for wind stress curl south of this latitude. Once again, the FRAM data favor a southern mode for the transport variability, consistent with the idea of a barotropic current following FIG. 9. Schematic showing the duration and depth of deployment f/H contours (either a free mode or an almost free (m) of the BPRs at positions shown in Fig. 1.

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC 1984 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 the residuals. There were three pressure sensors on each BPR, and the order of the polynomial ®t was the min- imum that allowed the long period behavior of the re- siduals to match. This was usually a linear ®t, but in some cases a quadratic ®t was necessary. It is hard to tell how successful this has been, so the BPR records must be regarded as suspect for annual and longer pe- riods. A one cycle per day tide-killing ®lter has been applied, and the BPR datasets resampled at daily inter- vals. For comparison with the BPR records, wind stresses calculated from the European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological analyses were used. Of the time series of Southern Ocean winds available over the whole time considered here, the ECMWF analyses were described by Trenberth (1992) as being the most reliable. The particular dataset used is the ECMWF Tropical Ocean±Global Atmosphere analysis, which runs from 1985 to the end of 1994. Full details of the assimilation schemes and physical param- eterizations used in this analysis can be found in ECMWF (1991, 1992). Wind stresses were computed from the 10-m winds in this analysis, and supplied for 12-h intervals on a 2.5Њ grid by the U.S. National Center for Atmospheric Research. A standard quadratic bulk formula was used, with a neutral drag coef®cient following those of Large and Pond (1982), Dittmer (1977), and Schacher et al. (1981). For comparison with the BPR data, daily values were computed from the 12-h values as 0.25 ϫ (␶ FIG. 10. Time series of bottom pressure and zonally averaged Ϫ12 ECMWF-derived wind stresses. Dashed lines mark where the pressure ϩ 2␶ 0 ϩ ␶ ϩ12), where ␶ 0 is the wind stress at midday, time series have been joined by end point matching. Here P north and the other values are at the previous and following consists of the records from FS1 and ND2, P south is shown inverted midnight. and consists of records from FS3 and SD2. The wind time series are Six time series were calculated from the wind stress- de®ned in the text. Each time series has been smoothed with a 29- es: three zonal averages and three zonally integrated day running mean. wind-stress curls. The three zonal averages are inte- grated over the ranges 40Њ±65ЊS [similar to the range edith et al. 1996), the ®ve FS3 and SD2 time series were used by Peterson (1988a) and referred to here as the concatenated into a single time series. ACC region], 55Њ±62.5ЊS (approximately the Drake Pas- The concatenated BPR time series (southern pressure sage latitudes, referred to here as DP), and 60Њ±65ЊS is shown inverted), and the three zonally averaged wind (south of Drake passage, referred to here as South). The stress time series, are shown in Fig. 10, after application curls are integrated over ranges 40Њ±45ЊS [similar to the of a 29-day running average smoother for display pur- northern curl region of Peterson (1988a) and referred poses only (this effectively removes the fortnightly and to here as Curl far N], 52.5Њ±57.5ЊS (at the northern end monthly tides). Dashed lines show where end point of Drake Passage; Curl N), and 60Њ±65ЊS [the southern matching has been used to join up the time series. Visual end of Drake Passage, similar to the southern curl region inspection is enough to see that the three wind stress of Peterson (1988a); Curl S]. time series are strongly correlated, highlighting the dif- In order to see if any useful long-period information ®culty in establishing a forcing mechanism for any cor- is contained in the BPR records, concatenated time se- relations with bottom pressure. Correlations with bottom ries were constructed by end point matching. For this pressures are much less obvious, unless the time series procedure, a 60-day low-pass ®lter was applied to the are broken at the dashed lines, when a correlation can individual records, and a linear extrapolation made to be discerned between southern pressures and winds. No the central times between BPR records. A datum shift consistent correlation is apparent between winds and was then applied to each record to match up the ex- northern pressures. In order to quantify the agreements trapolated values. The four FS1 time series were con- and examine their frequency dependence, cross-spectra catenated in this way, as were the two ND2 time series. were calculated using both concatenated time series, and In view of the similarity observed between records at all of the individual (1 yr) time series (including ND1 different southern sites (Woodworth et al. 1996; Mer- and SD1). For the northern pressures, the only squared

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FIG. 11. Squared coherences from cross-spectra between southern bottom pressure and six integrated wind time series. The 95% signi®cance value is marked in each panel, as are the fortnightly and monthly tidal periods in the left-hand panels, and semiannual and annual periods on the right. Values on the left are calculated treating each BPR deployment separately, using a 90-day window half-width; those on the right are calculated from the concatenated pressure time series using a 360-day window half-width. coherences that were signi®cant at the 95% level were days. The 95% signi®cance value is calculated assuming for wind stress±pressure correlations at periods of about an effective time series length corresponding to the 10 and 20 days (in light of the theory discussed above, smallest number of pairs used to calculate a covariance. the frequency range of interest is periods longer than This value, and the monthly and fortnightly tidal peri- 10 days; some squared coherences are signi®cant at ods, are marked on the ®gure. The right-hand panel shorter periods). Pressure to the north is not signi®cantly shows values calculated using the concatenated time coherent with pressure to the south for periods longer series, with a window half-width of 360 days. The 95% than 10 days. In view of the poor coherences and the signi®cance value is again marked, together with the theoretical arguments favoring bottom pressure to the semiannual and annual periods. Signi®cant coherences south as a measure of transport, the northern pressures are found at all periods between about 15 and 220 days, will not be discussed further. with the exception of a window around 50 days (this Figure 11 shows squared coherences for cross-spectra may be related to the Indonesian Through¯ow; see between southern pressure and each of the six wind later). At almost all of these periods, the highest co- ®elds. The cross-spectra were calculated by computing herence is with zonally averaged wind stress south of auto- and cross-covariances, multiplying the covarianc- Drake Passage, although all the zonal averages give high es by a Tukey [0.5 ϫ (1 ϩ cos)] window and Fourier coherences. Coherences with wind stress curl are gen- transforming. For the left-hand plot, the covariances erally much lower. The curious exception to this pattern were calculated only using pairs of values from the same is at periods close to 20 days, where the zonal averages BPR deployment, and the window half-width was 90 including winds from farther north do better. As a visual

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(coherence was barely signi®cant at the 95% level for this period, so the phase shift will have a large standard error). A similarly calculated time series is shown in Fig. 12, using daily atmospheric pressures from the BAS meteorological database, and with a 29-day running mean ®lter applied. Figure 13 shows cross-spectra between pairs of the three time series, concatenated bottom pressure record from southern BPRs, Faraday sea surface pressure (SSP), and zonally averaged winds (south), calculated with a window half-width of 360 days. A broad range of high coherence is clear between bottom pressure and Faraday SSP, although this does not extend to the annual FIG. 12. The negative of the subsurface pressure record from Fara- period as Peterson (1988b) found. Phase is close to zero day, smoothed with a 29-day running mean. over all of this coherent range. Faraday SSP shows a now-familiar pattern of coherence with the winds, with a dip around a 50-day period, and a high semiannual inspection of the time series showed, coherences at an- nual and longer periods are poor, suggesting either that coherence. Compared with the BPRs, the Faraday record the dynamics on these timescales are dominated by fac- shows higher coherence with the winds at an annual tors other than wind stress or that end point matching period and close to 20 days. Phase lags are near zero of the time series fails to capture the long-period pres- for periods between about 15 and 200 days with a phase sure variability. Both of these scenarios are plausible. lag of about 65Њ at the annual period (winds lead trans- If the end-point matching is doing a poor job of cap- port). The long-period coherences with winds are higher turing the long-period variability, then a long, contin- for Faraday than for the BPRs, indicating that the Far- uous pressure record is needed for annual periods and aday record may be the better monitor of circumpolar longer. Such a record is available from the tide gauge transport at annual periods and longer, but the Faraday maintained by POL at the British Antarctic Survey record is complicated by its coastal situation. Higher (BAS) base, Faraday (now owned by the Ukraine and coherence with winds may be at least partly attributable renamed Vernadsky). Peterson (1988b) noted that the to local coastal processes, so it is still not clear that subsurface pressure at Faraday, calculated by converting transport ¯uctuations are strongly in¯uenced by the sea level to pressure units and adding the atmospheric wind at the annual period, although the signi®cant co- pressure, was strongly coherent with the ISOS southern herence is suggestive of this. Formation and melting of BPR record for periods of about 6 to 600 days, although ice will certainly produce a steric signal at the annual a phase shift of about 60Њ occurred at the annual period period, which may predominate over the wind forcing.

FIG. 13. Squared coherences and phase for cross-spectra between (top) the concatenated southern BPR record and Faraday subsurface pressure; (center) Faraday subsurface pressure (inverted) and zonally averaged southern wind stress; and (bottom) the concatenated southern BPR record (inverted) and zonally averaged southern wind stress. Spectra are calculated using a 360-day window half-width, and the 95% signi®cance values are shown, together with semiannual and annual periods and monthly and fortnightly tidal periods. Periods are marked in days, and positive phase means that the second named time series lags the ®rst.

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6. Model results with realistic forcing onstrating the importance of the Indonesian Through- ¯ow here. The time series chosen for comparison with So far, a model (FRAM) with simpli®ed forcing has winds and measurements is the transport through Drake been used, along with theoretical arguments, to deter- Passage, sampled every 3 days. Practically identical re- mine the nature of the Southern Ocean's response to sults are found using the African section. winds on the barotropic timescale. The simpli®ed forc- With realistic forcing, it must be hoped that the model ing (climatological monthly winds) is in some ways an will produce realistic transports. If this is the case and advantage for identifying the mechanism behind the re- Faraday subsurface pressure is a good monitor of trans- sponse, but precludes direct comparison between model port, then the two time series should be highly corre- and data as well as severely limiting the investigation lated. Figure 14a shows the cross-spectrum of these time of the frequency dependence of the dynamics. For this, series for the period 1988 to 1995. Coherence is sig- we need a model, preferably eddy permitting, that is ni®cant at many frequencies between about 10 days and forced with winds as close to the real winds as possible. the semiannual period, with particularly high values be- Such a model is the ¼Њ (average) Parallel Ocean Cli- tween about 80 days and the semiannual period (the mate Model (POCM) described by Stammer et al. (1996) range that FRAM is most sensitive to is about 60 days and Semtner and Chervin (1992). This model is basi- to annual). Phases are also close to zero over the regions cally similar to a global (apart from the Arctic) version of high coherence. The low coherence for periods longer of FRAM except that it uses a free surface formulation than semiannual suggest that either processes other than that removes the need to smooth the topography beyond transport ¯uctuations dominate the Faraday pressure the grid resolution, although the vertical resolution is signal at the annual period or the model transports at less than FRAM with only 20 levels. The resolution of annual period are particularly poor. this model increases toward the poles on a Mercator Figure 14b shows cross-spectra between zonal av- grid, giving square grid cells 0.4Њ of longitude wide, erages of model eastward wind stress at six latitudes between the equator and latitude 75Њ (equivalent to and model transport. For the 10-day to semiannual pe- about 28.5 km at 50ЊS, 15.2 km at 70ЊS). riod band, coherences increase southward from 45ЊS, The version of the model used here is POCM࿞4B for peaking at around 60Њ±65ЊS. For periods longer than the period 1988 to 1996. This version was forced by semiannual, the winds as far north as 50ЊS seem to be 3-day averages of wind stresses derived from ECMWF most important, suggesting that a different mode dom- 10-m winds (Stammer et al. 1996) starting from 1987. inates at the annual period. The dip in coherence seen Results from 1987 are not considered here as the trans- in the measurements at 50 days is also present in the port dropped throughout this year from an initial value model results. It is interesting to note that the coherence near 192 Sv to a mean value of 166 Sv, as a response between transports south of Africa and Australia is to the change from an overestimated climatalogical wind smallest (and not quite signi®cant at the 95% level) at stress applied in a previous version of the model. about 47 days, suggesting that this feature might be The 3-day sampling of the model ®eld produces an related to the Indonesian through¯ow and thus to the aliasing of inertial oscillations to different periods be- dynamics of tropical 40±60 day oscillations. tween 6 days and in®nity at different latitudes (Jayne For a pure free mode response to winds, transport and Tokmakian 1997). These are clearly visible in time should respond with a phase lag of ␲/2. For a forced series of velocity and are unlikely to be realistic when (topographic Sverdrup) response the phase lag would forced by 3-day winds; however, the variation of an be ␲/2 for periods much shorter than the relevant to- aliased period with latitude has a mitigating effect when pographic Rossby wave mode and would represent a calculating transports, and inertial oscillations do not small lag for longer periods. Friction would give a sim- appear to be a large problem here. ilar picture to the forced response, with the relevant time Transports were calculated as integrals of the zonal being the frictional spindown time. The phases in Figs. velocities across the ®ve meridional sections used in 13 and 14 show that a lag of ␲/2 is not attained for any FRAM. These now differ from section to section be- period longer than about 10 days, so the pure free mode cause the model allows an Indonesian Through¯ow response can only be relevant for very short periods. from the Paci®c to the Indian Ocean, and the free surface As suggested at the end of the ``dynamics'' section, an allows a small divergence of the depth-integrated ¯ow. almost-free mode, for which f/H contours are not quite The sections south of Africa and South America show closed, is probably important. This mode will be par- standard deviations of 6.25 and 6.15 Sv, respectively, ticularly sensitive to winds in the regions where it is and the difference time series has a standard deviation necessary for the current to cross f/H contours and will of 1.66 Sv, part of which may be aliased inertial oscil- react to these winds with a ``forced'' rather than free lations (the discrepancy is greatest at periods shorter response. than 15 days, consistent with aliassed inertial oscilla- The POCM model transport ¯uctuations, like those tions south of about 60ЊS). In contrast, the difference in FRAM, are most strongly related to sea level ¯uc- between transport through Drake Passage and south of tuations south of Drake Passage, as shown by the cor- Australia has a standard deviation of about 5.2 Sv, dem- relation coef®cient between transports through Drake

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FIG. 14. Cross-spectra as in Fig. 13 for (a) minus Faraday subsurface pressure and POCM-4B model transport through Drake Passage and (b) model transport and zonally averaged model wind stresses at six latitudes.

Passage or south of Australia and 9.9-day averaged sea 0.4 to 0.6 (with a peak value of 0.621), but only very surface heights (Fig. 15). Since the transports through small correlations occur to the north of Drake Passage. Drake Passage and south of Australia differ signi®cantly Conversely for Drake Passage transport, the correlation in this model, the correlation with each of these time with sea surface height close to Australia is very small, series is given. In both cases the southern mode is dom- but correlations of 0.4 to 0.45 occur near the southern inant with (negative) correlations greater than 0.6 oc- tip of South America, peaking at 0.464 to the northeast curing at almost all longitudes, peaking at more than of Drake Passage. Interestingly, similarly high corre- 0.75. The northern correlations differ dramatically be- lations occur off the coast of Alaska peaking at 0.461, tween the two cases. For the transport south of Australia, and in regions of the northeast and southeast Paci®c. positive correlations on the Australian shelf are typically Lagged correlations trace the origin of this signal to the

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FIG. 15. Correlation coef®cients between 9.9-day averaged sea surface heights and transport through (top) the region south of Australia and (bottom) Drake Passage, from the POCM.

Unauthenticated | Downloaded 09/27/21 07:29 PM UTC 1990 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 eastern equatorial Paci®c and produce patterns consis- past observations of correlations between wind stress tent with the propagation of coastal Kelvin waves to and southern pressure, from the ISOS experiment both north and south, radiating Rossby waves into the (Wearn and Baker 1980; Peterson 1988a). Paci®c before arriving at Drake Passage and Alaska. Given the strong correlations between different mea- The patch of moderately high correlations centered on sures of the wind forcing in the Southern Ocean, a con- 50ЊS, 250ЊE, is negative, consistent with Fig. 4 which vincing demonstration that this model applies to the real shows the current passing to the north of this region. ocean is dif®cult to achieve using only observational Another interesting point is the very low correlations data. However, cross-spectra between bottom pressure near the South African coast. This is not due to the and winds show slightly better coherences with winds small difference between transports through Drake Pas- to the south of Drake Passage than with other measures sage and south of Africa since the equivalent correlation of wind stress, and the POCM model results show that plot calculated using transport south of Africa (not the measured bottom pressure ¯uctuations south of shown) is practically indistinguishable from that using Drake Passage are highly correlated with model trans- Drake Passage transport. port. A number of features suggest that it is not the Quantitative interpretation of the signi®cance of these inviscid free mode response that dominates, but either correlations should be treated with extreme caution, as a viscously damped free mode or the almost free mode the time series involved may have signi®cant annual that requires wind forcing for the current to cross f/H and semiannual components. To give some quantitative contours in certain locations. The small phase lag be- guidance however, assuming each of the 148 9.9-day tween winds and both pressure and POCM transport is averages to be independent, a correlation coef®cient of consistent with either of these interpretations. 0.16 would be signi®cant at the 95% level. Assuming There is some evidence for the importance of the every third value to be independent (probably more re- almost free mode in FRAM: although the current seen alistic), this increases to 0.27. Correlations of transports in FRAM follows f/H contours most of the time, there with pure semiannual and annual signals have the fol- are places where it has to skip across a few contours. lowing maximum possible values: Drake Passage trans- If correlation coef®cients are calculated between FRAM port with semiannual, 0.224; with annual, 0.356. Trans- transport and eastward wind stress at each grid point, port south of Australia with semiannual, 0.176; with several ``hot spots'' of high correlation appear (D. Stev- annual, 0.683. Thus, the relatively high correlations be- ens 1996, personal communication). Two of these hot tween transport south of Australia and sea levels in the spots are between the southern tip of South America North Paci®c and Indian Oceans are probably simply and the Falkland Islands and over the Scotia island arc, due to a favorable phase of the annual signal. regions where the current appears to skip over f/H con- Thus, the POCM data seem to con®rm that the pos- tours. The third is at about 40ЊS, 230ЊE, at a sensitive itive correlations north of Drake Passage are real, but point where f/H contours can either return along the they are not representative of the ¯ow over a broad range Paci®c Antarctic Rise or can cut across the top of the of longitudes in the way that southern pressure is. In South Paci®c basin. It therefore seems reasonable that particular, northern pressure in Drake Passage is very the almost-free mode should be particularly sensitive to weakly related to ¯ow south of Australia, and vice versa. winds in these regions. The fact that these hot spots The relationship with the dynamics of the equatorial occur east and west of South America may also offer Paci®c suggests that baroclinic effects are likely to be an explanation for the positive transport±pressure cor- important in interpreting the northern pressure signal, relation seen in FRAM over the Patagonian shelf, sug- and is consistent with the failure to ®nd a clear rela- gesting that the Sverdrup mode also plays a role in the tionship between northern pressure and winds over the region of Drake Passage where the range of f/H con- Southern Ocean. tours is narrowest. In the POCM, the northern corre- lations still occur but are further complicated by the fact that the associated sea surface height anomalies seem 7. Discussion to have their origin in the equatorial Paci®c, propagating Theoretical arguments have suggested that transport to the south (and north) as coastal Kelvin waves. ¯uctuations through Drake Passage may be dominated An interesting feature in both the pressure measure- by a barotropic mode that follows f/H contours around ments and the POCM transports is a relatively poor much of Antarctica. It has been shown using FRAM coherence with southern winds at a period of about 50 that, while the barotropic mode might be locally days. Suggestively, this is the same period at which the swamped by baroclinic variability, it forms a good de- POCM results show that the Indonesian Through¯ow is scription of the larger-scale variations in the model. most in¯uential in decoupling transports south of Aus- Both theoretical arguments and model results support tralia from the other choke point transports, which may the idea that it is pressure to the south of Drake Passage imply a link with the 40±60 day tropical oscillations, that is the best monitor of transport ¯uctuations, al- although further investigations are needed to con®rm though northern pressures may be related to local trans- this link. port in a more complicated way. This is in line with The idea of a more southerly mode for the transport

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¯uctuations should be useful in interpreting other ob- arctic Circumpolar Current and their relation to the wind.'' Deep- servations; in particular, BPR and tide gauge measure- Sea Res., 29A, 1381±1388. , A. M. Mestas-Nunez, and M. H. Freilich, 1990: Global wind ments at other choke points where zonal coherence stress and Sverdrup circulation from the Seasat scatterometer. J. seems much higher to the south than to the north (P. L. Phys. Oceanogr., 20, 1175±1205. Woodworth and T. Whitworth 1996, personal commu- Clarke, A. J., 1982: The dynamics of large-scale, wind-driven vari- nication). This is to be investigated further as part of a ations in the Antarctic Circumpolar Current. J. Phys. Oceanogr., joint analysis of all the WOCE choke point datasets. It 12, 1092±1105. Dittmer, K., 1977: The hydrodynamic roughness of the sea surface would also be enlightening to further investigate these at low wind speeds. Meteor. Forschungsergeb., 12(B), 10±15. ideas using other wind stresses, for example, those from ECMWF, 1991: European Centre for Medium-Range Weather Fore- the ERS scatterometers. A potential problem with such casts model physical parameterisation. ECMWF Research Man- a study is that the variability in the southern mode may ual 3, 97 pp. , 1992: European Centre for Medium-Range Weather Forecasts be dif®cult to examine in satellite data due to the pres- data assimilation. ECMWF Research Manual 1, 82 pp. ence of sea ice. It is possible that the effect of sea ice FRAM Group, 1991: An eddy-resolving model of the Southern on wind stress might account for some of the anomalous Ocean. Eos, Trans. Amer. Geophys. Union, 72(17), 169±175. behavior seen at the annual period, although there are Gill, A. E., 1968: A linear model of the Antarctic circumpolar current. undoubtedly steric effects at the annual period due to J. Fluid Mech., 32, 465±488. , and P. P. Niiler, 1973: The theory of the seasonal variability in the seasonal cycle of ice formation and melting. The the ocean. Deep-Sea Res., 20, 141±177. high correlation between the POCM transports and mea- Grose, T. J., J. A. Johnson, and G. R. Bigg, 1995: A comparison sured pressures suggests that it will be worthwhile to between the FRAM (Fine Resolution Antarctic Model) results use this and similar models to investigate the dynamics and observations in Drake Passage. Deep-Sea Res., 42, 365±388. of these transport ¯uctuations in more detail. Han, Y. -J., and S. -W. Lee, 1981: A new analysis of monthly mean wind stress over the global ocean. Climatic Research Institute Finally it is worth noting that, for the southern mode, Rep. 26, 148 pp. [Available from Oregon State University, Cor- it is misleading to speak of transport ¯uctuations in the vallis, OR 97331-4501.] ACC, for semiannual and shorter periods at least. The Hellerman, S., and M. Rosenstein, 1983: Normal monthly wind stress controlling dynamics, and therefore the path followed over the world ocean with error estimates. J. Phys. Oceanogr., by the mean ACC, are different from those of the ¯uc- 13, 1093±1104. Hughes, C. W., 1996: The use of topographic wave modes to solve tuating current. If coherence around Antarctica can be for the barotropic mode of a rigid-lid ocean model. J. Atmos. established, the ¯uctuations should properly be termed Oceanic Technol., 13, 751±761. ¯uctuations in Antarctic circumpolar transport. , 1997: Comments on ``On the obscurantist physics of `form drag' in theorizing about the Circumpolar Current.'' J. Phys. Oceanogr., 27, 209±210. Acknowledgments. The authors are grateful to Bob , and P. D. Killworth, 1995: Effects of bottom topography in the Spencer and the POL Technology Group for deploying large-scale circulation of the Southern Ocean. J. Phys. Ocean- and recovering the BPRs and calibrating the data. We ogr., 25, 2485±2497. are also indebted to Robin Tokmakian (Naval Post- , M. S. Jones, and S. Carnochan, 1998: The use of transient features to identify eastward currents in the Southern Ocean. J. graduate School, Monterey) for her time spent extract- Geophys. Res., 103, 2929±2944. ing and sending the relevant POCM data, to Tony Craig Jayne, S. R., and R. Tokmakian, 1997: Forcing and sampling of ocean (NCAR) for supplying the gridded wind stress data, to general circulation models: Impact of high-frequency motions. the Permanent Service for Mean Sea Level at POL for J. Phys. Oceanogr., 27, 1173±1179. Johnson, G. C., and H. L. Bryden, 1989: On the size of the Antarctic Faraday sea levels, to William Connolley (BAS) for the Circumpolar Current. Deep-Sea Res., 36, 39±53. Faraday atmospheric pressures, and to Phil Woodworth Johnson, M. A., 1990: A source of variability in Drake Passage. and Dave Stevens for useful discussions. This work was Contin. Shelf Res., 10, 629±638. funded partly by the U.K. Defence Research Agency Killworth, P. D., and M. M. Nanneh, 1994: Isopycnal momentum and the U.K. Natural Environment Research Council. budget of the Antarctic Circumpolar Current in the Fine Reso- lution Antarctic Model. J. Phys. Oceanogr., 24, 1201±1223. Klinck, J. M., 1991: Vorticity dynamics of seasonal variations of the Antarctic Circumpolar Current from a modeling study. J. Phys. REFERENCES Oceanogr., 21, 1515±1533. Large, W. G., and S. Pond, 1982: Sensible and latent heat ¯ux mea- Anderson, D. L. T., and A. E. Gill, 1975: Spin-up of a strati®ed ocean, surements over the oceans. J. Phys. Oceanogr., 12, 464±482. with applications to upwelling. Deep-Sea Res., 22, 583±596. Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA , and P. D. Killworth, 1977: Spin-up of a strati®ed ocean, with Prof. Paper No. 13, U. S. Govt. Printing Of®ce, 173 pp. topography. Deep-Sea Res., 24, 709±732. Meredith, M. P., 1995: On the temporal variability of the transport Baker, D. J., Jr., 1982: A note on Sverdrup balance in the southern through Drake Passage. Ph.D. thesis, University of East Anglia, ocean. J. Mar. Res., 40(Suppl.), 20±26. Norwich, United Kingdom, 227 pp. [Available from University Branstator, G., and J. D. Opsteegh, 1989: Free solutions of the bar- of East Anglia, Norwich NR4 7TJ, United Kingdom.] otropic vorticity equation. J. Atmos. Sci., 46, 1799±1814. , J. M. Vassie, K. J. Heywood, and R. Spencer, 1996: On the Bryden, H. L., and R. A. Heath, 1985: Energetic eddies at the northern temporal variability of the transport through Drake Passage. J. edge of the Antarctic Circumpolar Current in the southwest Pa- Geophys. Res., 101, 22 485±22 494. ci®c. Progress in Oceanography, Vol. 14, Pergamon, 65±87. , , R. Spencer, and K. J. Heywood, 1997: On the processing Chelton, D. 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