LETTERdoi:10.1038/nature12432

Rapid cross-density ocean mixing at mid-depths inthe Drake Passage measured by tracer releaseAndrew J. Watson1{, James R. Ledwell2, Marie-Jose Messias1{, Brian A. King3, Neill Mackay1, Michael P. Meredith4,5,Benjamin Mills1{ & Alberto C. Naveira Garabato3,6

Diapycnal mixing (across density surfaces) is an important processin the global ocean overturning circulation1–3. Mixing in the interiorof most of the ocean, however, is thought to have a magnitude justone-tenth of that required to close the global circulation by thedownward mixing of less dense waters4. Some of this deficit is madeup by intense near-bottom mixing occurring in restricted ‘hot-spots’associated with rough ocean-floor topography5,6, but it is not clearwhether the waters at mid-depth, 1,000 to 3,000 metres, are returnedto the surface by cross-density mixing or by along-density flows7. Herewe show that diapycnal mixing of mid-depth ( 1,500 metres) watersundergoes a sustained 20-fold increase as the Antarctic CircumpolarCurrent flows through the Drake Passage, between the southern tipof South America and Antarctica. Our results are based on an open-ocean tracer release of trifluoromethyl sulphur pentafluoride. Weascribe the increased mixing to turbulence generated by the deep-reaching Antarctic Circumpolar Current as it flows over rough bottomtopography in the Drake Passage. Scaled to the entire circumpolarcurrent, the mixing we observe is compatible with there being a south-ern component to the global overturning in which about 20 sverdrups(1 Sv 5 106 m3 s21) upwell in the Southern Ocean, with cross-densitymixing contributing a significant fraction (20 to 30 per cent) of thistotal, and the remainder upwelling along constant-density surfaces.The great majority of the diapycnal flux is the result of interactionwith restricted regions of rough ocean-floor topography.

Our present understanding of diapycnal mixing in the SouthernOcean is based largely on indirect inference. Observations of velocityand density ‘fine structure’, at vertical scales of order 10–100 m, havebeen used to infer the turbulence responsible for vertical mixing8–11,which occurs at centimetre scales and is more difficult to measure.These studies use empirical parameterizations12,13 to represent the cas-cade of energy from larger to smaller spatial scales, induced by non-linear interactions in the internal wave field. The observations suggestthat diapycnal mixing is enhanced over rough bottom topography. Amechanism thought likely to be responsible for this is the breaking ofinternal lee waves, generated as the deep-reaching Antarctic Circum-polar Current (ACC) encounters sea-floor features having lateral scalesof a few kilometres. Accordingly, wave radiation theory has been used toestimate the energy flux into lee waves, using observation- and model-based estimates of the deep flow, and the spectral properties of suchsmall-scale topography14,15. These studies indicate that the radiation oflee waves is sufficiently energetic to support the fine-structure estimatesof diapycnal mixing. However, the fine-scale estimates are highly infer-ential, and the observations underpinning them are sparse. Their rele-vance to the integrated diapycnal mixing that affects the large-scale oceancirculation has therefore remained unclear. Furthermore, given that mostof the turbulence generated by interaction with topography occurs withinabout 1,000 m of the bottom8,16, the question of how the water at mid-depths is returned to the surface remains unanswered. A long-standing

view is that this is accomplished by diapycnal down-mixing of buoyancy2,but the rates of mixing typically measured in the ocean’s interior are low.An alternative suggestion is that this overturning is mostly forced mech-anically, by the wind acting on the surface of the Southern Ocean7,18. In thelimit of no internal diapycnal mixing, modification of water densitieswould occur only in the surface layer, by interaction with the atmosphere.

Recently, a series of microstructure measurements of the centimetre-scale turbulence responsible for vertical mixing has been conductedwithin, or in association with, the DIMES project (‘Diapycnal andIsopycnal Mixing Experiment in the Southern Ocean’; http://dimes.ucsd.edu)16,17,19. These observations are much less reliant on assump-tions concerning the generation of turbulence than are the fine-structuremeasurements discussed above, but they are snapshots of a highly epis-odic and heterogeneous process, so it is difficult to scale up from these toan estimate of the mixing important on the regional or global scale. Theresults lend support to the idea that most mixing in the deep SouthernOcean stems from the breaking of internal lee waves, but there is asuggestion that the extent of intense turbulent mixing may have beenconsiderably overestimated by the indirect methods. The motivation forour tracer experiment was therefore to provide an independent andunequivocal measurement of diapycnal mixing, directly relevant to lar-ger scales and thus applicable to models of the ocean general circulation.

The tracer, 76 kg of trifluoromethyl sulphur pentafluoride (CF3SF5;ref. 20), was released within 3 m depth of an isopycnal surface (withpotential density, referenced to 1,500 dbar, of 34.614 kg m23) in Febru-ary 2009, as part of the DIMES project. The release location (red star inFig. 1A) was near 58u S, 107uW, about 2,000 km upstream of the DrakePassage, in the ACC between the Subantarctic and Polar Fronts, and ata depth of about 1,500 m (ref. 19), in the upper circumpolar deep water(UCDW) mass. The vertical and horizontal dispersion of the tracerwas measured one year later, in the region between 57u–62u S and105u–85uW, between the release site and the Drake Passage19. Thevertical turbulent diffusivity integrated over that period was found tobe (1.3 6 0.2) 3 1025 m2 s21, which is typical for the interior of the oceanfar from boundaries. It is smaller by a factor of ten than the diffusivitiesof around 1024 m2 s21 that (on average) would be required to close theabyssal overturning circulation by down-mixing of buoyancy alone1,2.

In December 2010 and April 2011 two further surveys of the easternpart of the tracer patch were carried out as it flowed through the DrakePassage, yielding five meridional sections through the patch (Fig. 1).Mean vertical profiles of the sections are shown in Fig. 1B. The profilesare plotted against potential density, and also mapped into depth usinga representative density–depth profile for the Drake Passage (the aver-age of the potential density–depth profiles for the stations occupied inApril 2011). The dashed horizontal line shows the ‘target’ density atwhich the release was made.

The surveys can be used to constrain diapycnal diffusivities both inthe eastern Pacific and the Drake Passage sectors of the ACC. The

1School of Environmental Sciences, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, UK. 2Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA. 3NationalOceanography Centre, Empress Dock, Southampton SO14 3ZH, UK. 4British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK. 5Scottish Association for Marine Science, Oban, PA371QA, UK. 6University of Southampton, National Oceanography Centre, Empress Dock, Southampton SO14 3ZH, UK. {Present address: College of Life and Environmental Sciences,University of Exeter, LaverBuilding, Exeter EX4 4QE, UK.

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growth in the second moments of the profiles in Fig. 1 can be used toestimate diffusivity averaged over the period since release4. These areshown in Fig. 2. The estimates obtained by averaging over the pathfrom the release point to sections (e) and (f) east of the Drake Passageare two to four times larger than those confined to the Pacific sector,indicating a large increase in the rate of cross-density mixing as thetracer is advected through the Drake Passage. This is consistent withthe idea that the rough bottom topography, which dominates eastwardof about 70uW, greatly influences mixing rates. The tracer has residedin the high diffusivity region for only a comparatively short time (aconservative estimate would be one quarter of the total time since release,assuming no increase in eastward velocity in the Drake Passage) so theobserved broadening of profiles implies that the tracer experiences a rateof diapycnal mixing that is about an order of magnitude greater in theDrake Passage than in the eastern Pacific.

To obtain a more quantitative estimate of the mixing rate in the DrakePassage, we solved the advection–diffusion equation for the tracer on atwo-dimensional (longitude and depth) domain divided into two sub-regions, east and west of 67uW, this being approximately the longitudeof the Phoenix ridge, which marks the western extent of the sea-floormountains in the Drake Passage. Vertical and horizontal diffusion andhorizontal advection velocities in the two subregions were adjusted togive the best fits to the mean profiles (b) to (f) of Fig. 2 (see Methodssection for full details). Uncertainties in the fitted parameters were esti-mated from the variation of the chi-squared statistic in parameter space

around its minimum value21. The best values estimated for the diapycnaldiffusivity in the Drake Passage and in the eastern Pacific were respect-ively (3.6 6 0.6) 3 1024 m22 s21 and (0.178 6 0.006) 3 1024 m22 s21,where uncertainties are 2s.

Our conclusion is that diapycnal diffusivity in the UCDW throughthe Drake Passage, about 2 km above the bottom, averages about 20times the values immediately to the west in the eastern Pacific sector ofthe ACC. The measurements at the eastern exit of the Drake Passagewere made towards the leading edge of the tracer patch. This mightintroduce systematic errors, biasing the mixing rate low because ver-tical shear has narrowed the extent of the tracer distribution, or high ifmore rapidly advected tracer also experiences higher vertical diffusi-vity than average. We estimate that such systematic errors should becontained within confidence intervals broadened by a further factor ofaround 1.5.

Elevated cross-density mixing has previously been observed in thevicinity of mid-ocean ridges5,6, caused by breaking of internal wavesgenerated by bottom currents interacting with the rough topography,and the view that substantial diapycnal mixing occurs in restrictedareas by such interaction is now widely accepted. Although the driverfor near-bottom currents at the mid-ocean ridges is the internal tides,in the Southern Ocean the driver is mostly the deep-reaching ACC andthe eddies associated with it. Globally, it has been estimated that0.2 TW (about 20% of the wind energy put into the circulation ofthe ocean) may be dissipated by such interaction22, much of it in theSouthern Ocean15. The great majority of the energy goes into the layerwithin about a kilometre of the bottom15, and the diapycnal mixinginduced there is likely to be of considerable importance in the modi-fication of the deepest water masses. This forms the return path for thelower limb of the meridional overturning circulation, supporting a fluxof Antarctic bottom water of order 10 Sv (ref. 15). In contrast, the layerstudied by the tracer release is 2–3 km from the bottom over most ofthe area, except in the restricted zones where it contacts the continentalslope at the northern limit of the Drake Passage, or approaches thepeaks of the highest submarine mountains. Our measurements suggestthat even these limited sources of high dissipation are sufficient toproduce substantially increased average mixing rates.

Profiles of turbulent dissipation made at the same time as tracermeasurements during DIMES also show a substantial intensificationof turbulence between the eastern Pacific and the Drake Passage abovethe rough topography16. The rates of mixing we measured in theUCDW seem to scale, very approximately, with the input of powerinto lee-wave radiation. Using the calculations of ref. 22, we find thatthe energy density of lee-wave generation in the ACC between thetracer release and our section (d) (see Fig. 1) averages 0.6 mW m22,whereas in the Drake Passage between sections (d) and (e)/(f) it isaround 20 mW m22, and so a factor of approximately 30 greater.This is comparable to the 20-fold enhancement in diapycnal mixingrates we observe.

Using this approximate proportionality between lee-wave energiesand mixing in the UCDW, we can make a rough estimate of the rates ofmixing averaged around the ACC, as follows. Using the calculations ofref. 22 again, we find the average lee-wave energy dissipation under theACC to be about 3 mW m22 (the ACC being here defined as the areabetween the Subantarctic front in the north and the southern ACCfront in the south23). Multiplying this by the relatively constant ratiobetween our measurements and lee-wave energies in the regions we havestudied, we predict diapycnal mixing averaging (0.6–1) 3 1024 m2 s21

for the UCDW as a whole. The mixing is concentrated over regions ofrough topography such as the Drake Passage, the Scotia Sea, Crozet–Kerguelen and the southeast Indian ridge. This figure is in the range ofvalues found by ref. 24 to be compatible with a southern component ofmeridional overturning of order 20 Sv, given observed temperature andsalinity distributions. The mixing rate can be used in combination withdata for the density structure of the Southern Ocean to estimate thecontribution to this overturning due to diapycnal processes: we find

110º W

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December 2010

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Figure 1 | Location of the tracer experiment and the vertical spread of thetracer during the first two years after release. A, Release in February 2009(red star) and subsequent measurements and surveys: (a), East Pacific survey,one year after release19; (b) and (c), sections near 78uW, at 1.9 years and 2.2years after release; (d), section at the western entrance to the Drake Passage, 1.9years after release; (e) and (f), sections at the eastern exit of the Drake Passage,1.9 and 2.2 years after release. B, Mean profiles obtained from each of theselocations. These are plotted in potential density space (right-hand axis, s1.5,referenced to 1,500 dbar). Potential density is also translated into a depth scale(left-hand axis) using a mean density–depth profile appropriate to the DrakePassage (the mean of sections (c) and (f)).

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(see Supplementary Information) that this is 3–6 Sv at the density levelof deepest UCDW, where the tracer was released. Our measurementssupport the view, therefore, that about 20%–30% of the southern com-ponent of the overturning circulation at mid-depths is sustained bydiapycnal processes, with the remainder being accomplished by iso-pycnal transport25. Our analysis implies that almost the entire diapyc-nal component is generated over the restricted regions of rough bottomtopography below the ACC, by the interaction of the deep-reachingcurrent with the sea floor.

METHODS SUMMARYInjection. At the pressure and temperature of release, CF3SF5 is a liquid immis-cible with water. It was released by being forced at high pressure through fineorifices, causing it to emulsify into fine droplets that dissolved without settlingappreciably in the water column. The injection package was towed slowly throughthe water at about 1,500 m depth, and included a conductivity–temperature–depth(CTD) instrument to allow monitoring of the density of the water, with the towingwinch constantly adjusted to keep the package at the target density.Sampling and analysis. Water samples were collected using conventional 10-litreNiskin bottles. Two-litre subsamples were drawn from these into ground-glass-stoppered bottles, filled from the bottom using Tygon tubing and with the sampleoverflowed by at least two litres to expel all water that had contacted the atmo-sphere. Samples were kept cold and analysed within 24 h of collection. For analysis,subsamples of about one litre were stripped of volatiles using a vacuum purge-and-trap, gas chromatography and electron capture detection. Calibration for CF3SF5

used a gravimetrically prepared gas standard.Diapycnal diffusivities. These were examined by plotting individual tracer pro-files and section averages (see Fig. 1) as a function of potential density, and trans-forming these into depth space using a depth–density profile representative of theDrake Passage. Gaussian curves were fitted to these profiles, and average mixingrates were calculated from the width of these fitted curves. More detailed estimatesused the numerical solution of the advection–diffusion equation in two dimen-sions, optimizing the fit to the observed average profiles ((b) to (f) in Fig. 1) asfunctions of diapycnal diffusivity and along-stream velocity in two subregions: eastof 67uW (the Drake Passage) and west of this longitude (east Pacific).

Online Content Any additional Methods, Extended Data display items and SourceData are available in the online version of the paper; references unique to thesesections appear only in the online paper.

Received 14 March; accepted 3 July 2013.

1. Munk, W. & Wunsch, C. Abyssal recipes II: energetics of tidal and wind mixing.Deep-Sea Res. I 45, 1977–2010 (1998).

2. Munk, W. H. Abyssal recipes. Deep-Sea Res. 13, 707–730 (1966).3. Lumpkin, R. & Speer, K. Global ocean meridional overturning. J. Phys. Oceanogr.

37, 2550–2562 (2007).4. Ledwell, J.R.,Watson,A. J.&Law,C.S.Evidence forslowmixingacross thepycnocline

from an open-ocean tracer-release experiment. Nature 364, 701–703 (1993).5. Ledwell, J. R. et al. Evidence for enhanced mixing over rough topography in the

abyssal ocean. Nature 403, 179–182 (2000).6. Polzin, K. L., Toole, J.M., Ledwell, J. R.&Schmitt, R.W.Spatial variabilityof turbulent

mixing in the abyssal ocean. Science 276, 93–96 (1997).7. Toggweiler, J. R. & Samuels, B. On the ocean’s large scale circulation near the limit

of no vertical mixing. J. Phys. Oceanogr. 28, 1832–1852 (1998).8. Garabato, A. C. N. et al. Widespread intense turbulent mixing in the Southern

Ocean. Science 303, 210–213 (2004).9. Kunze, E. et al. Global abyssal mixing inferred from lowered ADCP shear and CTD

strain profiles. J. Phys. Oceanogr. 36, 1553–1576 (2006).10. Sloyan,B. M.Spatial variability of mixing in the Southern Ocean. Geophys. Res. Lett.

32, L18603 (2005).11. Wu, L., Jing, Z., Riser, S. & Visbeck, M. Seasonal and spatial variations of Southern

Oceandiapycnalmixing fromArgoprofiling floats.NatureGeosci.4,363–366(2011).12. Gregg, M. C. Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94,

9686–9698 (1989).13. Polzin, K. L., Toole, J. M. & Schmitt, R. W. Finescale parameterizations of turbulent

dissipation. J. Phys. Oceanogr. 25, 306–328 (1995).14. Nikurashin, M. & Ferrari, R. Radiation and dissipation of internal waves generated

by geostrophic motions impinging on small-scale topography: application to theSouthern Ocean. J. Phys. Oceanogr. 40, 2025–2042 (2010).

15. Nikurashin, M. & Ferrari, R. Radiation and dissipation of internal waves generatedby geostrophic motions impinging on small-scale topography: theory. J. Phys.Oceanogr. 40, 1055–1074 (2010).

16. St Laurent, L. et al. Turbulence and diapycnal mixing in Drake Passage. J. Phys.Oceanogr. 42, 2143–2152 (2012).

17. Waterman, S., Naveira Garabato, A. C. & Polzin, K. L. Internal waves and turbulencein the Antarctic Circumpolar Current. J. Phys. Oceanogr. 43, 259–282 (2013).

110º W

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Vertical mixing rate (×10–5 m2 s–1)

2.2 years

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1 year

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Figure 2 | Mean diapycnal diffusivities from the point of release. These arecalculated from the second moments of the mean profiles in Fig. 1. They areaverages over the times since release, and their spatial extents are indicated bythe grey arrows above the inset. The approximately threefold increase in themean when averaged over a path including the Drake Passage indicates thatdiffusivities increase by at least an order of magnitude east of 70uW comparedto west of 70uW. We note that the water column in the Drake Passage is less

stratified than in the eastern Pacific, and so the tracer distribution on survey (a)in Fig. 1 occupies a wider depth span when mapped in a Drake Passage depth–density profile than when used in the calculations of ref. 19. Correspondingly,the diffusivity shown here for the Pacific sector after one year is about 25%larger than that quoted in ref. 19. Error bars show 95% confidence limits,calculated from the statistics of individual profiles (see SupplementaryInformation for details).

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18. Marshall, J. & Speer, K. Closure of the meridional overturning circulation throughSouthern Ocean upwelling. Nature Geosci. 5, 171–180 (2012).

19. Ledwell, J. R., St Laurent, L. C., Girton, J. B. & Toole, J. M. Diapycnal mixing in theAntarctic Circumpolar Current. J. Phys. Oceanogr. 41, 241–246 (2011).

20. Ho, D. T., Ledwell, J. R. & Smethie, W. M. Use of SF5CF3 for ocean tracer releaseexperiments. Geophys. Res. Lett. 35, L04602 (2008).

21. Bevington, P. R. & Robinson, D. K. Data Reduction and Error Analysis in the PhysicalSciences (McGraw-Hill, 1992).

22. Nikurashin, M. & Ferrari, R. Global energy conversion rate from geostrophic flowsinto internal lee waves in the deep ocean. Geophys. Res. Lett. 38, L08610 (2011).

23. Orsi, A. H., Whitworth, T. & Nowlin, W. D. On the meridional extent and fronts of theAntarctic Circumpolar Current. Deep-Sea Res. I 42, 641–673 (1995).

24. Zika, J. D., Sloyan, B. M. & McDougall, T. J. Diagnosing the Southern Oceanoverturning from tracer fields. J. Phys. Oceanogr. 39, 2926–2940 (2009).

25. Webb, D. J. & Suginohara, N. Oceanography—vertical mixing in the ocean. Nature409, 37 (2001).

Supplementary Information is available in the online version of the paper.

Acknowledgements We thank the officers and staff of the RV Thomas Thompson, RRSJames Cook andRRS James Clark Ross for their assistance inmaking theobservations atsea. We thank the UK Natural Environment Research Council and the US NationalScience Foundation for funding the DIMES experiment. A.J.W. thanks the Royal Societyfor support.

Author Contributions A.J.W., J.R.L., M.-J.M., M.P.M. and A.C.N.G. planned and directedthe tracer experiment. M.J.M. led the chemical analysis at sea, and, together with A.J.W.,J.R.L., N.M. and B.M., obtained the tracer data. A.J.W., J.R.L., M.P.M., N.M., B.A.K. andA.C.N.G. analysed the physical oceanographic data. N.M. carried out thetwo-dimensional model computations. M.P.M., A.J.W. and A.C.N.G. planned anddirected the research cruises. A.J.W. wrote the initial draft of the paper and all authorscontributed to its revision.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of the paper. Correspondenceand requests for materials should be addressed to A.J.W.(andrew.watson@exeter.ac.uk).

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METHODSTracer injection. The 75 kg of trifluoromethyl sulphur pentafluoride (CF3SF5)was deployed with a towed system similar to that described by ref. 26 for aninjection of SF6 in the North Atlantic. The underwater components of the injectionsystem included a CTD unit that measured temperature, conductivity and pres-sure, from which density was calculated; a set of water samplers for calibration;control units; two tracer reservoirs; a primer reservoir; lead-acid batteries; and twohigh-pressure pumps feeding eight 25-mm-diameter ceramic orifices. In operation,the tracer was forced by the pumps through the orifices at pressures of approxi-mately 10 MPa. These components were mounted on an aluminium frame thatwas made neutrally buoyant with a set of glass floats mounted on the top of theframe. The frame was attached to the termination of the CTD cable with a 2.5-mtether to remove much of the ship’s motion. The CTD cable was held down witha hydroweight suspended below the termination. The system was kept within ametre (root mean squared (r.m.s.) distance) of the target density surface with afeedback system whereby the departure from the target density measured at theCTD was used to adjust the winch. A primer fluid, 2,3-dihydroperfluoropentane,was used to test the system on deck (because the tracer is a gas at normal temper-ature and pressure), and was also used to keep the orifices clear as the injectionsystem was lowered to the target surface.

The tracer was injected in a crude ‘x’ pattern centred near 58.1u S, 106.7uW at anaverage rate of 0.9 g per second. The target density was originally defined as apotential density, referenced to 1,500 dbar, of 34.6077 kg m23. This density corre-sponded closely with the 27.90 kg m23 neutral density surface in the region of theinjection. The average tow speed during injection was 0.50 m s21, and the overallinjection track length was 40 km. The initial distribution of the tracer was sampledwithin two weeks of release with both a towed array of samplers similar to that usedin previous experiments26 and with a conventional CTD/rosette system with 22four-litre Niskin bottles. The mean vertical profile of the tracer obtained with thetwo methods agreed, but the measurements were more accurate for the CTD/rosette samples. Samples were transferred into syringes and analysed by the headspace method27. The mean vertical distribution exhibited a single peak, approxi-mately Gaussian, with the centre of mass 2 m below the target density surface andwith r.m.s. spread about this centre of mass of 5.5 m. The slight sinking of thetracer was probably due to a density excess of the tracer plume immediately afterinjection, and the r.m.s. spread was probably due to turbulence behind the towedinjection system.Sample collection and analysis technique. The released tracer and two transienttracers, trifluorochloromethane (CFC-13) and dichlorodifluoromethane (CFC-12),were measured on board ship by a purge-and-trap gas chromatographic method withelectron capture detection. The instrumentation was developed at the University ofEast Anglia following earlier designs20,28,29.Water sampling used an instrument pack-age including a CTD and rosette of 24 ten-litre General Oceanics sampling bottleswith metal springs, the nitrile ‘O’ rings of which had been decontaminated followingstandard chlorofluorocarbon sampling procedures. Water samples were collectedfrom these bottles into two-litre ground-glass-stoppered bottles filled from the bot-tom using Tygon tubing, and overflowed with at least two litres to expel all waterexposed to the air. The glass bottles were stored immersed in sea water at a tem-perature below 5 uC, and analysed within 24 h. The measurement system strippedvolatiles from a 1.1-litre subsample of the water. Calibration for CF3SF5 used agravimetrically prepared gas standard, which agreed within 10% with the calibrationscale of E. Busenberg (personal communication; see also ref. 30). Precision for gasstandards was ,1%, and for duplicate water samples the standard deviation aver-aged 1% or 5 3 10218 mol per litre, whichever was greater.Average profiles, second moments and uncertainty estimates. The depth of theisopycnal on which the tracer was released changes substantially across the studyarea, from approximately 500 m in the south to approximately 2,000 m in thenorth of the Drake Passage (see Supplementary Fig. 1). To examine diapycnaltransport, individual tracer profiles from the surveys were plotted against potentialdensity, and section averages such as those in Fig. 1 were calculated by averagingalong isopycnals rather than at constant depths. However, rates of diapycnaldiffusivity are normally expressed in units of length squared divided by time, byanalogy with molecular diffusivity, so all isopycnal averages were transformed intodepth using a single representative depth–density profile, following the techniquesdescribed in ref. 26. The ‘standard’ density profile used for this is shown inSupplementary Fig. 2, and is the average potential density of sections (c) and (f)(see Fig. 1), intermediate between the eastern and the western Drake Passage.

Estimates of the overall diapycnal diffusivity, averaged over the path since the releasepoint, were calculated by fitting the solution to the one-dimensional diffusion equationwith constant diffusivity to the section-average concentration profiles, assuming aGaussian initial distribution. This solution is c~cm exp ({(z{zm)2=2s2) where zis depth and cm, zm and s are fitted variables. The diffusivity k is then equal to

s2{s20

� �=2t, where t is the time since release and s0 is the second moment of the

initial distribution at time t 5 0.Model to estimate diapycnal diffusivities. More detailed estimates of transportparameters from the tracer distribution require a numerical model treatment. Fullthree-dimensional model realizations are currently in progress, but for this work,approximate estimates were made using a relatively simple two-dimensionalapproach. We solved a two-dimensional realization of the advection–diffusionequation for a conserved tracer c

LcLt

~+: k+cð Þ{u:+c ð1Þ

where k is a tensor of eddy diffusion and u is a velocity. The vertical coordinate wastaken normal to isopycnal surfaces and extended 300 m around the release iso-pycnal, and the horizontal dimension was zonal distance along the path of theACC and in a domain that extended from 120uW to 30uW. Eddy diffusion k wasmodelled with an along-stream isopycnal diffusion kh and a diapycnal, verticaldiffusion kz, whereas velocity had an along-stream component only. Zonal dis-persion was initially set by comparison to the dispersion of clusters of model floatsreleased at 1,500 m in the CCSM model31 (M. E. Maltrud and J. L. McClean,personal communication). These suggest zonal dispersion in the ACC correspond-ing to about 3,000 m2 s21 in the first one to two years following release. Horizontalvelocities were initially set by averaging zonal velocities at the target isopycnalderived from the SATGEM product for Southern Ocean dynamics32. Velocityand the two components of diffusivity were held constant within each of two sectors:west of 67uW (the east Pacific) and east of that point (the Drake Passage). For eachsector the velocities were assumed to decrease with depth according to an exponen-tial profile with a scale height of 1,500 m (ref. 32). Six parameters were then fitted,these being the magnitudes of the along-stream velocity, kh and kz, in each of the twosectors.

To optimize parameters, vertical widths of the distributions predicted by themodel were compared to widths of individual profiles measured on sections (b) to(f) (see Fig. 1). Repeated runs of the model were used to map out and minimize thefollowing cost function as a function of the six variable parameters:

x2~Xn

i~1

wi{Wb-fð Þ2

s2b-f

ð2Þ

Here, wi are the measured widths of the individual profiles and Wb–f are the widthsof the appropriate model profiles with which to compare them (for example, theoutput of the model at the time after release and longitude corresponding to themeasured sections (b) to (f)). s2

b–f are the variances of profile widths as measuredon each of those sections. Within wide limits, we found that the procedure offitting the vertical widths of the profiles ensures that values for diapycnal diffu-sivity are insensitive to the choice of along-stream dispersion, and values quoted inthe text use a constant value for kh set at 3,000 m2 s21, a relatively high value thatincludes the effects of meridional shear dispersion33. The final fit therefore hadfour free parameters, rather than six.

If each profile width is considered to be a measurement of a normally distri-buted variate, and the model gave unbiased estimates of that variate, the expecta-tion value Æx2æ of the cost function would be the number of degrees of freedom ofthe estimation problem, namely N – q, where N is the number of profile widths tobe fitted and q is the number of parameters that are varied to optimize the fit. Forour case N 5 75 and q is 4, so Æx2æ is 71. The increase in the cost function as thefitted parameters are varied about their optimum values can be used to estimatethe uncertainty in the estimations21.

Contours of the cost function x as a function of diapycnal diffusivity in theDrake Passage and the east Pacific are shown in Supplementary Fig. 3. An estimateof the 2s uncertainty in the diffusivity can be made from the change in underlyingparameters required to increase the value of x by two (ref. 21), and these are usedfor our uncertainty estimates in the main text.

Supplementary Fig. 4 shows a histogram of the widths of individual profiles onsection (c) in Fig. 1, the section for which we have the largest number of profiles.The comparison shown there with a normal curve having the same mean andstandard deviation suggests that the statistics are unlikely to be normal, with theupper tail in particular being elevated in comparison to a normal distribution.(However, using the Shapiro–Wilk test34, the hypothesis of normality is notrejected at P 5 0.05 for this data set.) The actual minimum value of the costfunction was 81, higher than the expectation value for normal statistics, whichalso indicates some departure from normality for the data as a whole, and so theuncertainties we quote must be considered guidelines only.

26. Ledwell, J. R., Watson, A. J. & Law, C. S. Mixing of a tracer in the pycnocline.J. Geophys. Res. C 103, 21499–21529 (1998).

27. Wanninkhof, R., Ledwell, J. R. & Watson, A. J. Analysis of sulfur hexafluoride inseawater. J. Geophys. Res. C 96, 8733–8740 (1991).

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28. Smethie, W.M., Schlosser, P., Bonisch,G.&Hopkins, T. S.Renewal andcirculationof intermediate waters in the Canadian Basin observed on the SCICEX 96 cruise.J. Geophys. Res. C 105, 1105–1121 (2000).

29. Law, C. S., Watson, A. J. & Liddicoat, M. I. Automated vacuumanalysis of sulfur-hexafluoride in seawater—derivation of the atmospherictrend (1970-1993) and potential as a transient tracer. Mar. Chem. 48, 57–69(1994).

30. Busenberg, E. & Plummer, L. N. Dating groundwater with trifluoromethylsulfurpentafluoride (SF5CF3), sulfur hexafluoride (SF6), CF3Cl (CFC-13), andCF2Cl2 (CFC-12). Wat. Resour. Res. 44, W02431 (2008).

31. McClean, J. L. et al. A prototype two-decade fully-coupled fine-resolution CCSMsimulation. Ocean Model. 39, 10–30 (2011).

32. Meijers, A. J. S., Bindoff, N. L. & Rintoul, S. R. Estimating the four-dimensionalstructure of the Southern Ocean using satellite altimetry. J. Atmos. Ocean.Technol. 28, 548–568 (2011).

33. Falco, P. & Zambianchi, E. Near surface structure of the Antarctic CircumpolarCurrent derived from World Ocean Circulation Experiment drifter data.J. Geophys. Res. C 116, C05003 (2011).

34. Shapiro, S. S. & Wilk, M. B. Analysis of variance test for normality (completesamples). Biometrika 52, 591–611 (1965).

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