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Is the Indian Ocean MOC driven by breaking internal waves?

Tycho N. Huussen

∗

Scripps Institution of Oceanography, La Jolla, California

Alberto C. Naveira-Garabato

Harry L. Bryden and Elaine L. McDonagh

National Oceanography Centre, Southampton, United Kingdom

∗

Corresponding author address: Tycho Huussen, Scripps Institution of Oceanography, 8851 Shellback

Way, La Jolla, CA 92037. E-mail: [email protected]

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ABSTRACT The Indian Ocean hosts a vigorous basin-scale overturning that constitutes one of the major upwelling branches of the global meridional overturning circulation. The extent to which the Indian Ocean overturning is supported by breaking internal waves, as is commonly presumed, is assessed in this study by quantifying and contrasting the energetics of the overturning and those of the regional internal wavefield. The overturning energy budget is calculated based on a range of inverse estimates of the circulation across 32◦ S. The estimated total power needed to sustain the Indian Ocean overturning circulation varies between 0.17TW and 1.19TW, depending on strength and vertical structure of the overturning solution. The energetics of the internal wavefield are examined in the context of recent estimates of the wind and tidal work on the Indian Ocean and using a fine scale parameterization of turbulent dissipation associated with breaking internal waves. It is found that most of the energy put into internal wave motions is dissipated in the upper few hundred meters of the ocean and that internal wave energy levels in the interior Indian Ocean are too weak to sustain the overturning circulation. This suggests that abyssal mixing mechanisms other than internal wave breaking, such as near-boundary processes in confined passages or canyons, are dominant in supporting the Indian Ocean overturning.

1. Introduction The Indian Ocean meridional overturning circulation (MOC) is an important deep upwelling limb of the global MOC. Global inverse model studies find that almost 40% of the global deep upwelling, across the 28.11 neutral density surface, takes place in the Indian 1

Ocean (Ganachaud and Wunsch 2000; Lumpkin and Speer 2007). This is remarkable because the Indian Ocean is relatively small, covering less than 20% of the world ocean. We assess the energy budget of the Indian Ocean MOC based on a range of recent inverse solutions for the circulation across 32◦ S. Assuming that the advection into (neutral) density layers is balanced by diffusion we solve for the turbulent mixing needed to maintain the density stratification (Section 2). In the same section we compare the energetics of the overturning circulation with published estimates of the energy put into the deep Indian Ocean by winds and tides. The main question addressed in this work is whether the Indian Ocean MOC can be driven by breaking internal waves. Internal waves are capable of carrying energy from ocean boundaries into the interior and generally considered to produce most of the abyssal mixing when they ultimately break and dissipate their energy, e.g. (Wunsch and Ferrari 2004) and references therein. We use a fine scale parameterization, similar to the one used by (Kunze et al. 2006; Naveira-Garabato et al. 2004), to infer the dissipation due to internal wave breaking (Section 3). The comparison of internal wave dissipation with the dissipation needed to sustain the MOC appears statistically robust when considering potential sampling biases in the internal wave observations (Section 4). This study finds that internal wave dissipation rates in the interior Indian Ocean are too weak to support any of the recently published inverse-model solutions for the deep Indian Ocean MOC. The shortfall of internal wave mixing in the interior ocean suggests that boundary mixing processes may be dominant in the abyssal Indian Ocean. The last section of this paper explores the potential role of hydraulic mixing at sill overflows in submarine canyons. This mixing mechanism may be important in the Indian Ocean, because of the 2

abundant Fracture Zones (FZs) with numerous narrow passages and submarine canyons.

2. The energy budget of the deep Indian Ocean MOC We define the energy budget of the deep Indian Ocean MOC as the gain in potential energy due to diapycnal transport of mass. The turbulent mass transport is estimated by assuming a stationary density stratification maintained by a balance between advective mass divergence and diapycnal mass diffusion. Based on inverse estimates of the large scale flow field we calculate the diapycnal mass flux across arbitrary, basin-wide isoneutral surfaces in the Indian Ocean north of 32◦ S, and we infer the gain in potential energy by assuming that the diapycnal diffusion of mass is upward, that is against gravity. The 32◦ S southern limit of the Indian Ocean box considered in this study is chosen because this latitude has been sampled repeatedly and also because it connects south Africa and Australia, which means that the Indian Ocean basin north of this latitude is mostly enclosed by land masses. The only other connection to the world ocean is through the Indonesian Throughflow (ITF). The transport field at 32◦ S and to a lesser extent the ITF account for the advective divergence of mass in our density layer model (Fig. 1).

a. Advection–diffusion balance

We calculate the mixing needed to sustain the Indian Ocean MOC by treating neutral density as a conserved variable. For each of the layers in our Indian Ocean box-model we assume that the advection of density ρ by the velocity field U = (u, v, w) is balanced by

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turbulent diffusion, ∇ · (Uρ) = −∇ · (K∇ρ),

(1)

with K the eddy diffusivity. In the tradition of Munk’s ‘abyssal recipes’ (Munk 1966; Munk and Wunsch 1998) we assume that ρ and K vary only vertically. Integrating (1) over the volume of an ocean layer and applying the divergence theorem gives, Z

Z (U ρ) · dA = −

(Kρz ) · dA,

(2)

with dA an element of the closed surface that bounds the layer volume. For a density layer bound between two isoneutral surfaces, one with lower density ρl , and another with upper density ρu , and one open lateral boundary, we write, ZZ v(x, z)ρ(x, z)dxdz + ρ

l

ZZ

l

w (x, y)dxdy − ρ

u

ZZ

u  wu (x, y)dxdy = − Kρz A l ,

(3)

where we ignored lateral diffusion and used the overbar to indicate spatial averaging over isopycnal area A. Introducing T ≡

RR

w(x, y)dxdy for vertical advective volume transport

and F ≡ Kρz A for vertical turbulent mass transport we get, ZZ

v(x, z)ρ(x, z)dxdz + ρl T l − ρu T u = F u − F l ,

(4)

where the vertical integration runs from the depth corresponding to ρl to the depth of ρu . We solve (4) for F u starting at the bottom density layer and assuming F l = 0 and T l = 0 at the seafloor. The volume transport through the upper density interface follows from continuity, that is

RR

v(x, z)dxdz + T l − T u = 0. In this study, we calculated the density

field ρ(x, z) from measurements along 32◦ S in the Indian Ocean and we used inverse-solutions for the meridional velocity field v(x, z) based on the same hydrography. 4

The advection–diffusion balance (1) hinges on the assumption that density is a conserved variable. But this is not strictly the case. Salt and heat are conserved, but density is not due to nonlinearities in the equation of state of seawater. These nonlinearities can lead to significant dianeutral advection at low latitudes and particularly in the Southern Ocean (Klocker and McDougall 2010). Based on (Klocker and McDougall 2010) we expect that our ‘traditional’ linearized balance (1) holds to good approximation in the deep (subtropical) Indian Ocean below 1500m. The mean diapycnal mass flux, Kρz may be written as K × ρz assuming that K and ρz are spatially uncorrelated. This is not obvious, but the scatter of K versus N 2 estimates from our finescale data set (Section 3) appears uncorrelated. Applying the Osborn relation (Osborn 1980) to basin-averaged quantities, K = ΓN −2 ,

(5)

we obtain a relation between F and the spatial mean dissipation rate  [W kg−1 ]. The spatial mean density gradient, ρz , cancels out when we substitute N 2 = gρ−1 ρz and we obtain, ρ F = Γ, A g

(6)

with F the turbulent, diffusive mass transport through isopycnal surface ρ, A the area of the isopycnal surface, g = 9.81 ms−2 the gravitational acceleration and Γ the mixing efficiency. For simplicity, and to enable comparison with previous studies, we will ignore evidence for the variability of Γ (Moum 1996; Ruddick et al. 1997; Smyth et al. 2011) and assume the mixing efficiency to be constant and equal to its theoretical upper limit of 0.2 (Osborn 1980). The above relation shows that the dissipation rate is proportional to the turbulent

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mass flux. Conceptually, Γ is equivalent to the work against gravity done by the turbulent mass transport.

b. Transport across 32◦ S

The 32◦ S zonal section has been repeatedly sampled by hydrographic expeditions in 1936, 1965, 1987 and 2002. Figure 2 shows a map of the station positions of the most recent occupation in 2002. This occupation closely follows the 1987 occupation in the western basin, but slightly deviates in the east to avoid complex topography. Figure 3 shows the bathymetry at 32◦ S and the density layers used in our Indian Ocean model. The strength and vertical structure of the Indian Ocean MOC are notoriously weakly constrained (Table 1), although more recent estimates converge towards a strength of ∼10 Sv. The MOC strength is defined as the maximum of the bottom-up integrated transport across 32◦ S. Most studies find a MOC depth in the range between 2000 and 2600m, except for the most recent inverse model solution based on the new 2002 data, which finds a deeper overturning cell with a depth of about 3300m (McDonagh et al. 2008). This study explores the energetics of five previously published solutions for the Indian Ocean circulation. The three-letter abbreviations used to identify these solutions are listed in Table 1. We focus on the four most recent hydrography based inverse solutions, three based on the 1987 observations along 32◦ S, and one on the new 2002 data. The fifth solution is from a data assimilating general circulation model (GCM). Many ocean GCMs tend to produce a unrealistically weak Indian Ocean overturning when run to equilibrium (Palmer et al. 2007). For this study we picked a model solution with a strength comparable to the

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observational estimates.

c. Indonesian Throughflow (ITF)

The bulk of the ITF transport enters the Indian Ocean in shallow density layers, well above the closing density level of the MOC. We include the ITF in this study, despite its marginal influence on the deep Indian Ocean MOC, to make our box-model divergence free, so that the overturning streamfunction adds up to zero when integrated to the surface (Fig. 4). The inverse solutions for the Indian Ocean MOC used in this study implicitly impose or resolve the ITF and the strength of the implicit ITF is equal to the net transport across 32◦ S. The net flow across 32◦ S ranges from 10 to 15Sv for the flow fields we use and is southward, which means that the ITF flows from the Pacific– into the Indian Ocean. Including the ITF in our box-model requires knowledge of its the density structure when it enters the Indian Ocean, which is not obvious from the velocity field at 32◦ S. Since we do not know the density distribution of the implicit ITF we choose to impose the distribution from a recent but unrelated regional model study (Koch-Larrouy et al. 2006). We realize that inconsistencies between the imposed density distribution and the distribution implicit in the inverse models will lead to some degree of misrepresentation of the water mass transformation in the upper 1000m, but, as stated earlier, we expect this to have a negligible effect on total energy budget of deep MOC.

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d. Results

Given the advective transport and the density of the water flowing in and out of our Indian Ocean box, we calculated the diapycnal turbulent mass transport assuming mass conservation in arbitrary density layers and a balance between advection and diffusion. Figure 4 shows the advective layer transport T and the resulting isoneutral mean turbulent mass transport F when a balance between advection and diffusion is assumed (4). The figure also shows the overturning streamfunction, ψ, which is the bottom-up integrated layer transport. The vertical axis in the figure shows the ‘typical depth’ of the isoneutral layers in box-model, based on the mean isoneutral depth in a 10 by 10 degree box in the central Indian Ocean. The panel with overturning streamfunctions in Fig. 4 shows that the most recent inverse model solution for the Indian Ocean circulation, based on the new 2002 data, has a distinctly different profile compared to previous solutions. The new (McDonagh et al. 2008) solution, ‘MCD’ hereafter, has two cells, a deep upwelling cell below 2000m, and a downwelling cell at shallower depth. This results in F becoming negative around 1000m, implying net downward mass transport, which could be driven by deep convection, for example due to the strong net evaporation in the Red Sea and the Persian Gulf. The very saline, high density outflows plumes from these marginal seas are small initially, with an annual mean of 0.06-0.37Sv (Murray and Johns 1997; Bower et al. 2000; Beal et al. 2000), but will entrain surrounding watermasses during their descent. Signatures of Red Sea Water have been up to a maximum depth of about 1300m in the Indian Ocean (Beal et al. 2000), which roughly corresponds to the depth of the MCD downwelling cell (Fig. 4). The isoneutral mean turbulent dissipation rate follows from substituting the obtained F

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values in (6). The isoneutral surface area A in (6) is based on the Hydrobase climatology (Chang and Chao 2000). Hydrobase is also used to calculate the isoneutral mean buoyancy frequency to infer diffusivity using the Osborn relation (5). All the quantities calculated in this section are plotted versus depth in Fig. 4. The depth coordinate is obtained by labelling the layer densities with the isopycnal mean depth in the central Indian Ocean. In Fig. 4 we display all the model layers, including the upper layers that hardly affect the MOC, to show that the overturning streamfunctions integrate to zero at the surface when the ITF is included. The same figure shows the inferred mixing coefficient Kρ . We note that our mixing estimates for the GAN solution compare reasonably well with the Kρ profile shown in (Ganachaud and Wunsch 2000), although we do not reproduce their intensification toward the bottom. We attribute this difference to the lack of resolution in our model below 28.15. We choose not to resolve layers below 28.15, because we find that the neutral density error estimates, as given by the CSIRO neutral density routine (version 3.1) (Jackett and McDougall 1997), blow up at higher densities, leading to large uncertainties in vertical position of density surfaces in deep, weakly stratified waters. The total power to sustain the overturning circulation is calculated by bottom-up integration of the dissipation rate, P ≈

P

 ρ A ∆z, with dissipation rate  [Wkg−1 ], density ρ,

layer area A, and mean layer thickness ∆z. We integrate the power bottom-up to the ‘closing density’, which we define as the density level where the overturning streamfunction crosses zero, or in other words the point in density space where the deep inflow is balanced by the shallower retro-flow. The energy requirements of the various overturning solutions are listed in Table 2. We note that the maxima of the overturning streamfunctions in Table 2 differ up to ∼20% from the previously published overturning strength estimates as listed in Table 9

1. We attribute these differences primarily to the fact that we calculated the overturning maximum in density layers as opposed to depth layers. In addition to this we found some small differences between the published inverse solutions and the solutions we obtained from the respective authors, but we deem these differences to be acceptable because they do not change the main characteristics of the various MOC solutions.

e. Discussion

The estimates of the power needed to sustain the deep Indian Ocean MOC become more meaningful when compared to the available energy. The dynamically important energy sources for the large scale ocean circulation are winds and tides (Wunsch and Ferrari 2004). In an attempt to close the energy budget of the deep Indian Ocean we consider abyssal energy sources only, that is (i) wind power input to the geostrophic flow, (ii) wind power input to downward propagating near-inertial motions, and (iii) tidal energy input to baroclinic internal waves. All published energy inputs have considerable uncertainties and we therefore choose to work with a minimum and a maximum estimate (Table 3). The minimum wind-to-inertial flux is based on a factor 0.5 correction to the (Alford 2003) estimate, as suggested by (Plueddemann and Farrar 2006), integrated over the Indian Ocean north of 32◦ S. The maximum estimate is based on the full (Alford 2003) estimate of energy input to near-inertial motions, integrated over higher southern latitudes, up to 50◦ S, to account for near-inertial waves propagating northward across 32◦ S. Net equatorward propagation is to be expected because near-inertial waves can only propagate to regions with lower or equal planetary vorticity.

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Extending the generation region all the way past the stormy ‘roaring forties’ is not unreasonable because low-mode internal waves can propagate over thousands of kilometers (Alford 2003; Simmons et al. 2004). The lower and upper estimate for the energy transfer between the wind field and the surface geostrophic currents are based on the uncertainty in the global energy transfer estimated by (Scott and Xu 2009). The low and high value for the energy input in baroclinic tides is based on error estimates by (Egbert and Ray 2000). We also calculated the tidal energy based on the (Nycander 2005) global map and found it to be indistinguishable from the (Egbert and Ray 2000) upper estimate. The estimates of the energy going into the Indian Ocean should be enough to balance the implied dissipation needed to sustain the deep Indian Ocean MOC if the energy input is near-locally dissipated. Assuming that the energy flux into or out of the Indian Ocean is small compared to the local sources we may compare the energy inputs in Table 3 with the estimates of dissipated power in Table 2. This comparison tells something about the energetic feasibility of the various MOC solutions. For example, the power, when integrated up to the closing density, varies between 0.17 and 1.19 TW. We note that only the 0.17 TW MCD solution dissipates less than the 0.31 TW estimated maximum energy input. This result suggests that energy budgets may be useful as an additional constraint in inverse models. The energy needed to sustain a particular MOC configuration depends on the amount of diapycnal transport, that is the MOC strength, and the density gradient below the closing density. The most distinct feature of the MCD solution is that it closes at a much higher density, that is deeper, than the other MOC configurations. Deeper closure means that 11

‘fewer’ isopycnals are crossed, and that less diapycnal mixing is needed to maintain the density stratification. In this section we have estimated the levels of turbulent dissipation needed to sustain various published solutions for the Indian Ocean MOC. In the next section we estimate the rate at which internal wave breaking dissipates turbulent kinetic energy, and we assess whether the Indian Ocean MOC can be driven by breaking internal waves.

3. Internal wave dissipation Internal wave breaking is generally considered to be the single most viable mechanism to explain turbulence in the ocean interior, away from the surface boundary layer, the bottom boundary layer and sites of deep convection (Munk and Wunsch 1998; Wunsch and Ferrari 2004; Ferrari and Wunsch 2009). We estimate the spectral energy in the fine scale internal wave field (10–100m) using conventional conductivity, temperature, and depth (CTD) and lowered acoustic Doppler current profiler (LADCP) data and we use a fine scale parameterization to infer the turbulent dissipation rate. The parameterization is based on the notion that nonlinear interactions among internal waves cause an ‘energy cascade’ towards smaller scales (McComas and M¨ uller 1981; Henyey et al. 1986), until they eventually break into turbulent motions when the shear overcomes the stratification. The promise that internal waves hold information about turbulence has motivated the construction of the fine scale parameterization that relates the turbulent dissipation rate to observations of internal wave shear (Gregg 1989; Polzin 1995; Gregg et al. 2003).

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a. Finescale parametization

In this study we use the (Gregg et al. 2003) incarnation of the parameterization to infer turbulent dissipation from fine scale shear variance. The basic scaling at the core of this 2 parameterization is,  ∝ EGM N 2 f (McComas and M¨ uller 1981; Henyey et al. 1986), with

EGM the dimensionless energy level of the Garrett-Munk (GM) internal wave spectrum (Garrett and Munk 1972, 1975; Cairns and Williams 1976), N the buoyancy frequency, and f the inertial frequency. The Henyey scaling (Henyey et al. 1986), with the additional cosh−1 (N/f ) factor, was modified for application to ocean observations by Gregg by allowing for a variable energy level and by inferring the energy from vertical shear variance (Gregg 1989). The shear based parameterization is often referred to as the ‘Gregg-Henyey scaling’, but we will use the more generic ‘fine scale parameterization’. Later add-ons to the fine scale parameterization account for the dependency of the energy cascade rate on the dominant frequency of the wave field. The dominant frequency changes with f (Gregg et al. 2003) and may be inferred from observed shear-to-strain ratio, R, which is a proxy for the internal wave aspect ratio (Polzin 1995). These elements together give the current state-of-the-art fine scale parameterization of turbulent dissipation as used in this study, N 2 hSi2 h(R) L(f, N ), with  = 0 2 N0 hSGM i2 3(R + 1) h(R) = √ √ , and 2 2R R − 1 L(f, N ) =

f cosh−1 (N/f ) , f30 cosh−1 (N0 /f30 )

(7) (8) (9)

and 0 = 6.73 × 10−10 m2 s−3 the canonical GM dissipation rate, S the shear variance spec13

trum normalized by the buoyancy frequency, N0 = 5.24 × 10−3 rad s−1 the canonical GM buoyancy frequency, and f30 the inertial frequency at 30◦ latitude. The h.i-brackets in (7) indicate integration of the shear spectrum over an appropriate vertical wave number band that captures internal wave motion. The GM shear spectrum, SGM , is integrated over the same wave number band as the observed shear spectrum. In this study we use the GM76 expression for the buoyancyfrequency-normalized vertical wavenumber shear spectrum, 3 kz2 , SGM [Vz /N ] = πE0 b j ∗ 2 (kz + kz ∗)2

(10)

with kz the vertical wave number, Vz the vertical shear, i.e. the vertical gradient of the horizontal velocity, N the buoyancy frequency averaged over a data segment, E0 = 6.3×10−5 a dimensionless energy level, b = 1300m the thermocline scaling factor, and j ∗ = 3 the modal scale number, and kz ∗ = πj ∗ N /b/N0 (Garrett and Munk 1972, 1975; Cairns and Williams 1976). Strain enters the parameterization through the shear-to-strain ratio, R, and is defined as the vertical gradient of the displacement of isopycnals by internal waves, which we estimate based on the local change in buoyancy frequency relative to the background stratification, ξz =

N 2 − hN 2 i , N2

(11)

where the brackets indicate spatial smoothing over a data segment and the overline indicates spatial averaging over the same data segment (Polzin 1995). We tried a simple quadratic fit to smooth N 2 , as done by (Kunze et al. 2006) (personal communication), and the adiabatic levelling method (Bray and Fofonoff 1981) and found that differences are generally small. To prevent strain from blowing up when N 2 → 0 we discard segments with N 2 smaller than 14

its uncertainty based on WOCE standard errors for temperature and salinity (Monte Carlo simulation gives an uncertainty of 2×10−10 rad s−1 ). As a final note on strain we caution the reader that the calculation may be contaminated by quasi-permanent density finestructure associated with e.g., the formation of a seasonal thermocline, and other processes capable of injecting density anomalies into the ocean interior, such as potential vorticity anomalies at boundaries (Kunze 1993); internal wave-driven scarring of the thermocline (Polzin and Ferrari 2004), and double diffusion. Following (Kunze et al. 2006) we chop the vertical profiles of shear and strain in 320m half-overlapping profile segments, starting at the bottom. Each segment is tapered using a 10%sin2 window function and Fourier-transformed to obtain the vertical wavenumber power spectra. To reduce potential contaminination by quasi-permanent finestructure we integrate the strain spectrum over wavelengths smaller than 150m, which is smaller than the typical scale of these features (Kunze et al. 2006). The integration wave band has a variable lower limit, λ0 < λ ≤ 150m, with λ0 = 10m or the shortest wavelength for which

R 150 λ0

S[ξz ](λ) dλ ≤

0.1. This criterion prevents the inclusion of noisy strain estimates at small scales and is also derived from (Kunze et al. 2006)). The shear spectrum, on the contrary, is integrated over larger wavelengths between 150m and 320m, to avoid potentially noisier shear estimates at smaller scales (Kunze et al. 2006). Since we use different integration wave bands for shear and strain we cannot simply use, R = hS[Vz /N ]i / hS[ξz ]i, to calculate the shear-to-strain ratio. However, assuming that both the shear and the strain spectrum have GM-like shapes over their respective integration

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bands, we can calculate R by normalization with the GM variance, S[ VNz ]/SGM [ VNz ] R=3 , hS[ξz ]/SGM [ξz ]i

(12)



where the factor 3 corrects for SGM [ξz ]/SGM [ VNz ] ≡ 1/3 when integrated over the same wave number band. The velocity estimation in discrete bins by the LADCP as well as other instrument limitations lead to loss of shear variance for which we correct by applying spectral correction functions. The shear variance spectrum is corrected for loss of variance due to, (i) range averaging, (ii) finite differencing, (iii) interpolation, and (iv) instrument tilting following (Polzin et al. 2002). The strain spectrum S[ξz ] is only corrected for bin-to-bin first differencing using sinc2 (∆zkz /2π) for bin-size ∆z.

b. Data

In our analysis we preferably use the shear method based on LADCP shear estimates, with a variable shear-to-strain ratio inferred from simultaneous CTD data. We also include a minor number (453 out of 1545) of CTD-only casts to improve the data coverage, as shown in Fig. 2. We infer the internal wave spectral energy level from strain only, when LADCP data is missing, assuming a fixed shear-to-strain ratio, R = 7 (Mauritzen et al. 2002; Kunze et al. 2006). Table 4 lists the data sets we used including some additional information such as the year and month of the field operations and the number of casts.

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c. Results

Internal waves are ubiquitous in the ocean, but not uniformly distributed, as for example the GM model assumes, because both forcing and sinks are non-uniform. Figure 5 shows the dissipation inferred along the main zonal hydrographic sections in the Indian Ocean. The main topographic features are the Southwest Indian Ridge (SWIR), the Central Indian Ridge (CIR) and the Ninetyeast Ridge (NER). These features are labelled in Fig. 2. All sections show a 2–3 orders of magnitude elevated dissipation rates above the SWIR and the CIR, and only slightly elevated dissipation above the NER. We think that this is primarily due to the less fractured structure of the NER and the eastern basin in general, as previously noted by (Kunze et al. 2006; Drijfhout and Garabato 2008). This observation however may be partially biased, because the 2002 occupation of the I05 section avoided complex topography in the east. The meridional sections displayed in Figure 6 show fewer dissipation features and also less obvious correlation to the bottom topography. The Seychelles in section I07 is perhaps an exception to this general observation. The very smooth Ganges sediment cone (lower panel of Fig. 6) supports the general notion that weak mixing is to be expected above topography with little or no roughness.

d. Discussion

Apart from using shear everywhere, we generally use a model configuration similar to (Kunze et al. 2006). The (Kunze et al. 2006) study is hybrid in the sense that it uses the strain method in weakly stratified waters (N < 4.510−4 rad s−1 ) and shear variance and the shear17

to-strain ratio everywhere else. They avoid using shear variance in deep, weakly stratified waters, because of concerns about the potentially poor performance of the LADCP in these waters, where the concentration of acoustical scatterers is often low. Although we share these concerns, we find that strain inferred from CTD-data is also noisy at low stratification, and therefore we prefer using shear variance consistently throughout the water column. The accuracy of the fine scale method discussed in this section is typically to within a factor 3–4 (Gregg 1989; Polzin 1995; Polzin et al. 2002; Gregg et al. 2003). This ‘rule of thumb’ applies to the interior ocean away from abrupt topographic features, but the method is found to underestimate dissipation in a number of specific environments, such as above the continental shelf (MacKinnon and Gregg 2003a,b), in a submarine canyon (Carter and Gregg 2002; Kunze et al. 2002), and in the close proximity to generation sites, such as abrupt topography (Klymak et al. 2006, 2008a; Legg and Klymak 2008; Klymak et al. 2008b, 2010b,a). The break down of internal waves in these environments is dominated by processes other than the gentle energy cascade towards turbulence by wave–wave interactions. The fine scale parameterization is based on this cascade and therefore fails to adequately capture internal wave dissipation in these regimes. The underestimation of internal wave dissipation is local and at most a factor 6 in exotic environments, such as submarine canyons (Carter and Gregg 2002; Kunze et al. 2002). This bias however is bound to be less severe when we spatially average the dissipation rate over the abyssal ocean, because most measurement locations are sufficiently remote from canyons and potential generation sites. In the next section we discuss potential sampling biases and we calculate the isopycnal mean dissipation rate for comparison with the large scale energetics of the Indian Ocean MOC. 18

4. Large scale versus fine scale energetics This section compares the energetics required to explain basin-integrated diapycnal transports (Section 2) with spatially averaged internal wave dissipation estimates (Section 3). Obtaining a reliable spatial average of the internal wave estimates is challenging, because (i) the scarcity of data, (ii) the large spatial and temporal variability of the internal wavefield, and (iii) the non-Gaussian distribution of turbulent dissipation. This section addresses the question of whether there is enough energy in the internal wave field to sustain the Indian Ocean MOC, but we first consider and discuss several potential sampling biases that may affect the spatial average of internal wave dissipation.

a. Potential sampling biases

Scattering of internal waves over rough topography is one of the major reasons to expect localized internal wave breaking and dissipation. The notion that interactions with topography facilitate the breaking of internal waves is supported by observations of elevated levels of turbulence above submarine mountain ridges and other topographic features (Polzin et al. 1997; Toole et al. 1997; Eriksen 1998; Ledwell et al. 2000; Klymak et al. 2006; Carter et al. 2006). The dissipation rate at these so-called ‘mixing hotspots’ is typically a factor 100–1000 higher than the canonical GM value and it is critically important to adequately capture these sites in our analysis. Following Morris et al. (2001) we define bottom-roughness as the square root of the mean square distance between a smooth second order polynomial surface and the Smith and Sandwell bathymetry (Smith and Sandwell 1997). The 2D polynomial is fitted to onethirtieth 19

degree bathymetric data (SSv8.2) in 0.5×0.5 degree, non-overlapping patches. Given the resolution of the bathymetry and the patch size we expect the roughness parameter to reflect variance at 15-50km length scales. Figure 7 shows that mixing hotspots are associated with topographic features, such as the SWIR, the western edge of the Mascarene Plateau, the Amirante Passage (between Mascarene and Somali Basin), the NER, the Java Ridge, and Broken Plateau (see Fig. 2). The mixing hotspots in the figure are defined as locations where the inferred fine scale dissipation rate exceeds the median value of the dissipation rates based on large scale inverse methods (see Section 2). As expected we find dissipation to be correlated to bottom roughness, although only weakly (the linear correlation coefficient is 0.48). This correlation implies that non-random sampling with respect to roughness, that is under– or over sampling of areas with high roughness, will bias the mean dissipation rate. We test the hypothesis that locations of hydrographic stations are random with respect to roughness, by comparing the empirical probability density distribution of roughness at all Indian Ocean grid points with the distribution of roughness at the station locations. The left panel of Fig. 8 shows the probability distribution of all grid cells and the roughness at station locations, where the roughness at station locations is estimated from the roughness grid cells by triangle-based linear interpolation. Both distributions look similar, suggesting random sampling. This notion is enforced by comparing the cumulative density functions and applying a two-sample KolmogorovSmirnov test. The test confirms that the samples are from the same underlying population with 95% likelihood. We therefore accept our hypothesis and conclude that there is no significant roughness bias. An important source of internal wave energy is the conversion of the barotropic tide to 20

baroclinic tidal waves. Sites of internal tide generation are also locations of elevated internal wave breaking, because higher mode waves dissipate locally and some of the waves are unstable from their onset (Klymak et al. 2006, 2008a; Legg and Klymak 2008; Klymak et al. 2008b, 2010b,a). The fine scale parameterization is known to underestimate dissipation in proximity to generation sites (Klymak et al. 2006), but will still produce elevated dissipation rates. To check if our data set adequately captures these sites we test whether sampling is random with respect barotropic-to-baroclinic tidal energy conversion, as estimated by (Nycander 2005) using a linear wave model. Again we find no significant bias, which perhaps is no great surprise because both roughness and tidal energy conversion scale with topographic variance. Another spatial variable correlated to internal wave dissipation is latitude. The rate at which internal waves are Doppler shifted towards dissipative length scales depends on their aspect ratio, which in turn depends on f . The energy transfer rate is smaller for smaller f , leading to the generally observed lower internal wave dissipation rates near the equator. It therefore matters how our internal wave observations are distributed with respect to latitude. Just a glance at Fig. 2 shows that this distribution is not random, because of the WOCE sampling strategy with zonal sections. Our analysis shows that the mean dissipation rate may be biased low by at most 25% due to this effect.

b. Spatial averaging

The above discussion gives us the confidence that a meaningful spatial average can be obtained if we can trust the inferred dissipation rates to be representative of the actual

21

dissipation. Another point of concern is the inherent sensitivity of the dissipation distribution to outliers in the high-end tail. The probability density function (pdf) of the (isopycnal) ensemble of fine scale dissipation estimates is strongly skewed to the right because of the positive definiteness of dissipation rates. This asymmetry, and the high kurtosis (peakiness), makes the distribution more sensitive to outliers than the bell-shaped normal distribution. In fact the distribution looks close to lognormal, making it tempting to assume lognormality. The advantage of making this parametric assumption, and fitting a lognormal distribution to the data, is that the sensitivity to outliers is reduced. However, problems arise when the actual distribution is not really lognormal as is shown to be the case for oceanic turbulent dissipation by (Davis 1996). Examination of the effects of small departures from lognormality led (Davis 1996) to the conclude that direct arithmetic averaging is preferable when analyzing observations of turbulent dissipation.

c. Results

We interpolated the fine scale dissipation estimates onto the same neutral densities we used in the layer model presented in Section 2. For each of the isopycnal dissipation ensembles we calculated the mean by direct arithmetic averaging and by fitting a lognormal distribution to the data. Figure 9 shows both fine scale mean values and the large scale dissipation estimates. The uncertainty of the arithmetic mean is calculated using bootstrap methods. The width of the horizontal red lines corresponds to two standard deviations as is obtained from 1000 bootstrap re-samples from the data. The uncertainty of the lognormal mean in Fig. 9 corresponds to the 95% confidence interval of a maximum likelyhood fit. The agreement

22

between both methods is remarkable and suggests that the data is close to lognormal and not contaminated by outliers. Figure 9 provides the answer to our main question and shows that the Indian Ocean MOC cannot be sustained turbulent dissipation as inferred from fine scale internal wave shear and strain. We find a shortfall of internal wave dissipation to support any of the MOC solutions considered in this study at densities between γ = 26.94 and γ = 28.12. Internal wave breaking as a sole provider of turbulent energy in the abyssal ocean is only sufficient at the deepest density level for the (Bryden and Beal 2001) and (Sloyan and Rintoul 2001) solution. In general we find that the Indian Ocean MOC cannot be supported primarily by internal wave breaking. Figure 9 shows that internal wave dissipation in the interior ocean is about one order of magnitude too weak to support the Indian Ocean MOC.

d. Discussion

Can we reconcile the estimated energy needed to sustain the Indian Ocean MOC with published estimates of energy input in the Indian Ocean, and with dissipation estimates inferred from internal wave observations? Table 5 shows the various energy estimates in the deep ocean below ∼1100m, ∼2000m, and ∼3000m. Regarding the energy put into the Indian Ocean we find that the estimated energy input exceeds the energy required by the BRY solution below ∼2000m (assuming that the energy input is dissipated uniformly in the ocean volume below density level 26.26 (∼300m)). We find enough available energy for the other solutions below ∼2000m, except for the more vigorous FER overturning. When integrating up to ∼1100m there is enough energy for the MCD, GAN, and BRY solution and

23

when integrated up to ∼300m only for the MCD solution. This agrees with the discussion in Section 2, where we conclude there is insufficient energy for all overturning configurations when integrated up to the closing depth, except for the MCD solution. The MCD solution requires less energy because it closes deeper, around 1500m, whereas the other solutions close at depths shallower than 800m. Most of the energy put into the deep Indian Ocean is contained in internal wave motions. Table 3 shows that about 22% is put into sub-inertial geostrophic current, about 60% into internal tides and the remainder into near-inertial internal waves. Table 5 and Fig. 9 show that most internal wave energy is dissipated within the upper ocean, above ∼1100m. The dissipation of internal wave energy in the deep Indian Ocean below 1100m is only 14% of the total (Table 5) and insufficent to support any of the MOC solutions, except for the BRY and SLO solution near the bottom, below ∼3000m. We find that internal wave dissipation is falling short at the interior ocean density layers to support any of the overturning solutions (Fig. 9). Dissipation levels near the bottom and near the surface are large enough to support some of the overturning solutions, but this is also where we have least confidence in our methods. Estimates of fine scale shear based on LADCP measurements are often noisier in deeper waters, because there are usually fewer acoustical scatterers. And, in our large scale box-model we expect larger mixing uncertainties in the upper layers because of the influence of the ITF. The fine scale method likely produces a lower bound on the average mixing in the abyssal ocean, because it does not adequately capture some sites of elevated dissipation, as discussed in Section 3. However, when integrated over the entire basin we expect this bias to be within the factor 3–4 typical uncertainty of the fine scale method (Gregg 1989; Polzin 1995; Gregg et al. 2003). This 24

uncertainty is significantly smaller than the factor 8–12 discrepancy beween our internal wave dissipation estimates and our large scale circulation estimates (Fig. 9). The shortfall of internal wave energy below ∼1100m is about 0.18TW compared to what is needed to sustain the energetically least demanding MCD solution and about 0.56TW for the strong FER overturning circulation (Table 5). This is substantially more than the estimated 0.06TW going into geostrophic surface currents in the Indian Ocean (Table 3). But, work done on general circulation elsewhere, e.g. in the Southern Ocean, may conceivably be dissipated in the Indian Ocean. Bottom boundary drag on the general circulation can be significant when abyssal flows are accelerated through deep passages (Ferron et al. 1998; Hogg et al. 1982). Hydraulic jumps at sill overflows in canyons can cause intense mixing and this mixing process has been hypothesized to be important, perhaps even dominant in the abyssal ocean (Bryden and Nurser 2003; Thurnherr et al. 2005; Thorpe 2007; St Laurent and Thurnherr 2007). This mixing mechanism could be particularly relevant to the Indian Ocean because of the abundant fractured topography with numerous canyons. We identified FZs in the Indian Ocean using a spectral algorithm that filters typical FZ-wavelenghts and amplitudes (Fig. 10). Many observational studies find strong flows and significant mixing in narrow passages between deep Indian Ocean basins. Recent observations in the Atlantic II FZ, an important passageway in the SWIR, revealed a strong and persistent, jet-like, northward flow of about 3Sv (3 × 106 m3 s−1 ) and an estimated mixing rate of 10–100×10−4 m2 s−1 (MacKinnon et al. 2008). Previous studies in Indian Ocean passages found mixing rates of 10×10−4 m2 s−1 in Amirante Passage between the Madagascar and Somali Basin (Barton and Hill 1989), 13– 105×10−4 m2 s−1 at the 28◦ S gap in the NER (McCarthy et al. 1997), and 35×10−4 m2 s−1 at 25

the same passage (Warren and Johnson 2002). The notion that sill overflows in canyons may cause significant mixing is also supported by the modification of the bottom layer in the Hydrobase climatology. Figure 10 shows that bottom water masses flowing northward are modified when passing through ridges that separate one deep basins from another. For example, the density jumps from ∼28.28 to ∼28.23 from the Crozet Basin, south of the SWIR, to the Madagascar Basin, and there is a similar jump across the Amirante Passage between the Madagascar Basin and the Somali Basin. We assess the potential importance of ‘canyon mixing’ by considering the fraction of density layers in proximity to FZs. For illustratie purposes we borrow an argument from (Bryden and Nurser 2003). In their paper they argue that ‘missing mixing’ of one order of magnitude could be provided by vigorous mixing in canyons covering 0.1% of the seafloor. We find that at least 0.1% of observations at density levels larger than 27.75 is in FZs within 200m from the bottom. Extending the height above bottom to 500m we find that the >0.1% criterion applies to layers denser than 27.53. Based on this exploratory analysis we conclude that less dense layers are too distant from FZs to undergo significant mixing by sill overflow processes in sumarine canyons. Can ‘canyon mixing’ close the energy budgets of the various Indian Ocean circulation solutions? Regarding the MCD solution it is interesting that the ‘influence horizon’ of canyon mixing approximately matches the MOC closing density at 27.92. This suggests that a deep overturning cell, such as the MCD overturning, may be driven primarily by boundary mixing. Canyon mixing is of course also available to the other MOC solutions, but they close at lower densities (≤ 27.07), shallower than the expected influence of canyon mixing, although only 26

by a few hundred meters (Fig. 9). In summary, this study shows that mixing caused by breaking internal waves is insufficient to sustain the Indian Ocean MOC. Based on fine scale shear and strain observations we find that internal wave mixing in the interior ocean falls short by about one order of magnitude. Another abyssal mixing process considered in this study is ‘hydraulic mixing’ near sill overflows in canyons. This mechanism is potentially important in the Indian Ocean because of its fractured topography, with many deep, narrow passages between ocean basins. Our exploratory analysis of mixing in passages and canyons suggests that this process could be dominant in the abyssal Indian Ocean. However, whether it is enough to support the deep Indian Ocean MOC remains inconclusive. Observations near sill overflows targeted at quantifying the intensity and vertical structure of hydraulic mixing are key to address this question.

Acknowledgments.

We would like to thank and acknowledge Bernadette Sloyan, Alexandre Ganachaud, Bob Molinari, Graham Quartly, Bruno Ferron, Ariane Koch-Larouy, Gary Egbert, Jonas Nycander, and Robert Scott for valuable discussions and for generously sharing their data with us. Discussions with Eric Kunze, Andreas Thurnherr, Jen MacKinnon and Kurt Polzin have been very helpful to gain understanding about fine scale measurements, parameterizations and analysis techniques. TNH’s PhD scholarship was supported by the University of Southampton and the Ocean Observing and Climate Research Group at the National Oceanography Centre, Southampton. ACNG was supported by the Natural Environment

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Research Council (NERC) under an Advanced Fellowship NE/C517633/1, ELM by NERC under the Oceans 2025 programme, and HLB by NERC grant NER/A/S/2000/00438. We would also like to express our gratitude to the PI’s involved in WOCE/CLIVAR for collecting the data and making them publicly available.

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List of Tables 1

Published estimates of the overturning strength, defined as the maximum zonally and bottum-up integrated meridional transport across 32◦ S. The three letter abbreviations indicate the solutions used in this study.

2

41

Estimates of the total dissipated power, P , needed to sustain the deep Indian Ocean MOC. Also shown are, the overturning maximum Ψmax , the depth of the overturning maximum zmax , the closing density γ0 , and the approximate depth of the closing density, z0 . The power is calculated by integrating the dissipation rate from the bottom up to the closing density. The closing density corresponds to the zero-crossing of the overturning streamfunction and represents the density level where the inflow of dense bottom and deep water is balanced by the more shallow and less dense retro-flow.

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3

Estimates of the energy input in the deep Indian Ocean north of 32◦ S.

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4

Hydrographic sections used for estimation of turbulent dissipation. The LADCP bin size is given in the ∆z column and the asterisk means that both up– and mean cast data are available. All sections with CTD and LADCP data are part of the World Ocean Circulation Experiment (WOCE) or the Climate Variability and Predictability (CLIVAR) program, except for the ACSEX series, which was organised and funded by the Netherlands Institute for Sea Research (NIOZ). The data sets I, II and III contain additional CTD-only profiles from NIOZ, Syst`emes d’Informations Scientifiques pour la Mer (SISMER), and the United States National Oceanographic Data Center (NODC).

39

44

5

Total power integrated bottom-up over density layers. All power values are in tera-Watts (1012 W). The input is based on the energy sources listed in Table 3 assuming uniform dissipation of the total input in the ocean volume below density layer 20 (26.26). The required dissipation for the MCD solution when integrated up to layer 15 is printed between brackets because it includes layers shallower than the closing density, which is between layer 10 and 11. The dissipation integrated over 20 layers is omitted for the MCD solution because the diapycnal transport becomes negative between layer 15 and 16. The internal wave (IW) estimates are inferred from fine scale shear and strain (Section 3).

45

40

Hydrography Strength (Sv) (Toole and Warren 1993) 27 SLO (Sloyan and Rintoul 2001) 23 ± 3 (Macdonald 1998) 17 ± 5 (Robbins and Toole 1997) 12 ± 3 GAN (Ganachaud and Wunsch 2000) 11 ± 4 BRY (Bryden and Beal 2001) 10.1 MCD (McDonagh et al. 2008) 10.1 (Fu 1986) 3 Modelling (Wacongne and Pacanowski 1996) < 0a (Lee and Marotzke 1997) 2 (Zhang 1999) 2 (Garternicht and Schott 1997) 3 FER (Ferron and Marotzke 2003) 17 Table 1. Published estimates of the overturning strength, defined as the maximum zonally and bottum-up integrated meridional transport across 32◦ S. The three letter abbreviations indicate the solutions used in this study. a

no deep northward flow at 32◦ S.

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Ψmax [Sv] zmax [m] γ0 [kg m−3 ] z0 [m] P [TW] MCD 10.1 4100 27.92 1900 0.17 FER 19.0 4100 25.04 100 1.19 SLO 19.2 2100 27.07 700 0.94 GAN 10.2 2100 26.93 500 0.68 BRY 11.1 2000 24.12 100 0.78 Table 2. Estimates of the total dissipated power, P , needed to sustain the deep Indian Ocean MOC. Also shown are, the overturning maximum Ψmax , the depth of the overturning maximum zmax , the closing density γ0 , and the approximate depth of the closing density, z0 . The power is calculated by integrating the dissipation rate from the bottom up to the closing density. The closing density corresponds to the zero-crossing of the overturning streamfunction and represents the density level where the inflow of dense bottom and deep water is balanced by the more shallow and less dense retro-flow.

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energy source wind inertial wind geostrophic baroclinic tide total

reference Plo (Alford 2003) (Scott and Xu 2009) (Egbert and Ray 2000)

[TW] Phi 0.02a 0.05 0.11 0.18

[TW] 0.09b 0.06 0.18c 0.31

Table 3. Estimates of the energy input in the deep Indian Ocean north of 32◦ S. a

factor 0.5 correction to (Alford 2003) based on (Plueddemann and Farrar 2006). b (Alford 2003) extended to 50◦ S. c same as (Nycander 2005) estimate.

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no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 I II III

dataset I09N* ISS01/10* IR03 IR01W I4-I5W-I7C* I01W I01E IR04 I10 I02* ACSEX1 ACSEX2 ACSEX3 I05 I03/I04 I09N 2007 nioz sismer nodc

chief scientist A.L. Gordon H.L. Bryden A. Ffield R. Molinari J. Toole J.M. Morrison H.L. Bryden R. Molinari N. Bray B. Warren H. Ridderinkhof H.M. van Aken H. Ridderinkhof H.L. Bryden M. Fukasawa J. Sprintall – – –

year/month 1995/1 1995/2 1995/3 1995/5 1995/6 1995/8 1995/9 1995/9 1995/11 1995/12 2000/3 2001/3 2001/3 2002/3 2003/12 2007/3 – – –

∆z # casts 20.0 129 20.0 15 10.0 114 10.0 93 20.0 134 20.0 105 20.0 53 10.0 92 20.0 61 20.0 168 19.5 55 19.4 63 19.6 79 19.5 133 20.0 141 8.4 110 – 80 – 196 – 177

Table 4. Hydrographic sections used for estimation of turbulent dissipation. The LADCP bin size is given in the ∆z column and the asterisk means that both up– and mean cast data are available. All sections with CTD and LADCP data are part of the World Ocean Circulation Experiment (WOCE) or the Climate Variability and Predictability (CLIVAR) program, except for the ACSEX series, which was organised and funded by the Netherlands Institute for Sea Research (NIOZ). The data sets I, II and III contain additional CTD-only profiles from NIOZ, Syst`emes d’Informations Scientifiques pour la Mer (SISMER), and the United States National Oceanographic Data Center (NODC).

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levels depth input MCD FER SLO GAN BRY IW

1–5 3000m 0.08±0.02 0.07±0.02 0.14±0.04 0.03±0.01 0.05±0.02 0.01±0.00 0.02±0.00

1–10 1-15 1–20 2000m 1100m 300m 0.14±0.04 0.20±0.05 0.25±0.07 0.16±0.05 (0.23±0.07) – 0.32±0.10 0.61±0.18 1.07±0.32 0.13±0.04 0.44±0.13 0.82±0.25 0.14±0.04 0.34±0.10 0.61±0.18 0.07±0.02 0.26±0.08 0.64±0.19 0.02±0.00 0.05±0.00 0.35±0.06

Table 5. Total power integrated bottom-up over density layers. All power values are in tera-Watts (1012 W). The input is based on the energy sources listed in Table 3 assuming uniform dissipation of the total input in the ocean volume below density layer 20 (26.26). The required dissipation for the MCD solution when integrated up to layer 15 is printed between brackets because it includes layers shallower than the closing density, which is between layer 10 and 11. The dissipation integrated over 20 layers is omitted for the MCD solution because the diapycnal transport becomes negative between layer 15 and 16. The internal wave (IW) estimates are inferred from fine scale shear and strain (Section 3).

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List of Figures 1

Schematic zonal cross-section of the isoneutral layer model with advective transport T , density ρ, and turbulent mass transport F .

2

49

Indian Ocean map with a 4000m depth contour and the hydrographic stations used in this study. Open circles/diamonds indicate depth profiles with simultaneous CTD and LADCP data and the plus signs mark the locations of CTD only measurements. Legend: B.=Basin; DFZ=Diamantina Fracture Zone; FZ=Fracture Zone; P.=Plateau; R.=Ridge; SEIR=Southeast Indian Ridge; SWIR=Southwest Indian Ridge.

3

50

Vertical cross-section along ∼32◦ S with bathymetry and neutral density layers based on the 2002 occupation of the I05 section. The dotted isopycnal indicates the deepest density class of the ITF (Koch-Larrouy et al. 2006). Note however that the bulk of the ITF is contained in the most shallow layers.

4

51

Vertical profiles of (1) the isoneutral mean density ρ and the logarithm of the isoneutral mean buoyancy frequency log10 (N 2 ), (2) transport T , consisting of the geostrophic and Ekman transport at 32◦ S plus the ITF, (3) the overturning streamfunction ψ, (4) the turbulent mass transport F , (5) the isopycnal surface area A, (6) the dissipation rate  (note the logarithmic scale), and (7) turbulent diffusivity, with the horizontal black lines indicating neutral density levels.

5

52

Dissipation estimates [Wkg−1 ] for zonal sections. The color scale is logarithmic and white spaces indicate missing data or noisy data.

46

53

6

Dissipation estimates [Wkg−1 ] for meridional sections. The color scale is logarithmic and white spaces indicate missing.

7

54

Mixing hotspots and bottom roughness. Open black circles indicate locations of hydrographic measurements at 28.12 density level. Red diamonds indicate mixing hotspots, which are defined as locations where the dissipation rate inferred from internal waves is larger than the median of the large scale dissipation estimates inferred from the five MOC solutions considered in this study.

8

55

Comparison of roughness at all Indian Ocean grid points with roughness at the location of hydrographic stations. Left panel: empirical probability density histogram. Right panel: empirical cumulative density function.

9

56

Large scale and fine scale dissipation estimates. The red cross indicates the arithmetic mean of the fine scale dissipation estimates at a given density level. The width of the red cross corresponds to the mean plus/minus two standard deviations as obtained from bootstrap re-sampling. The black cross is the fine scale mean based on a maximum likelihood fit of the dissipation estimates to a lognormal distribution. The width of the black cross indicates the 95% confidence interval. The large scale dissipation estimates are based on various solutions for Indian Ocean overturning circulation (refer to Table 1). The large scale uncertainty is assumed to be 30% at all density levels. The Garrett-Munk background dissipation rate 0 is plotted for reference.

47

57

10

Neutral density at bottom as calculated from the Hydrobase climatology. Thick white contours indicate areas with Fracture Zones as identified by our algorithm. Black diamonds mark station locations. Thin black contours show the depth at 500m intervals.

58

48

Fig. 1. Schematic zonal cross-section of the isoneutral layer model with advective transport T , density ρ, and turbulent mass transport F .

49

Fig. 2. Indian Ocean map with a 4000m depth contour and the hydrographic stations used in this study. Open circles/diamonds indicate depth profiles with simultaneous CTD and LADCP data and the plus signs mark the locations of CTD only measurements. Legend: B.=Basin; DFZ=Diamantina Fracture Zone; FZ=Fracture Zone; P.=Plateau; R.=Ridge; SEIR=Southeast Indian Ridge; SWIR=Southwest Indian Ridge.

50

Fig. 3. Vertical cross-section along ∼32◦ S with bathymetry and neutral density layers based on the 2002 occupation of the I05 section. The dotted isopycnal indicates the deepest density class of the ITF (Koch-Larrouy et al. 2006). Note however that the bulk of the ITF is contained in the most shallow layers.

51

Fig. 4. Vertical profiles of (1) the isoneutral mean density ρ and the logarithm of the isoneutral mean buoyancy frequency log10 (N 2 ), (2) transport T , consisting of the geostrophic and Ekman transport at 32◦ S plus the ITF, (3) the overturning streamfunction ψ, (4) the turbulent mass transport F , (5) the isopycnal surface area A, (6) the dissipation rate  (note the logarithmic scale), and (7) turbulent diffusivity, with the horizontal black lines indicating neutral density levels.

52

Fig. 5. Dissipation estimates [Wkg−1 ] for zonal sections. The color scale is logarithmic and white spaces indicate missing data or noisy data.

53

Fig. 6. Dissipation estimates [Wkg−1 ] for meridional sections. The color scale is logarithmic and white spaces indicate missing.

54

Fig. 7. Mixing hotspots and bottom roughness. Open black circles indicate locations of hydrographic measurements at 28.12 density level. Red diamonds indicate mixing hotspots, which are defined as locations where the dissipation rate inferred from internal waves is larger than the median of the large scale dissipation estimates inferred from the five MOC solutions considered in this study.

55

Fig. 8. Comparison of roughness at all Indian Ocean grid points with roughness at the location of hydrographic stations. Left panel: empirical probability density histogram. Right panel: empirical cumulative density function.

56

Fig. 9. Large scale and fine scale dissipation estimates. The red cross indicates the arithmetic mean of the fine scale dissipation estimates at a given density level. The width of the red cross corresponds to the mean plus/minus two standard deviations as obtained from bootstrap re-sampling. The black cross is the fine scale mean based on a maximum likelihood fit of the dissipation estimates to a lognormal distribution. The width of the black cross indicates the 95% confidence interval. The large scale dissipation estimates are based on various solutions for Indian Ocean overturning circulation (refer to Table 1). The large scale uncertainty is assumed to be 30% at all density levels. The Garrett-Munk background dissipation rate 0 is plotted for reference.

57

Fig. 10. Neutral density at bottom as calculated from the Hydrobase climatology. Thick white contours indicate areas with Fracture Zones as identified by our algorithm. Black diamonds mark station locations. Thin black contours show the depth at 500m intervals.

58