Turbulent Isopycnal Mixing dominates Thermohaline Transformations of Intermediate Ocean Waters

Turbulent Isopycnal Mixing dominates Thermohaline1 Transformations of Intermediate Ocean Waters2 Florian S´evellec1,2, Nicolas Kolodziejczyk1, and Esther Portela1 3 1 Laboratoire d’Oc´eanographie Physique et Spatiale, Univ Brest CNRS IRD Ifremer, Brest, France 4 2 ODYSSEY Team-Project, INRIA CNRS, Brest, France 5 The ocean, because of its ability to store heat and as the biggest mediator of water exchanges6 on Earth, modulates the climate from years to centuries. By combining Water Mass trans-7 formation and the Temporal-Residual-Mean frameworks, together with a direct estimation8 of turbulent diffusivity (computed through an artificial intelligence method), we determine9 temperature and salinity transformations along density surfaces. Because isopycnal trans-10 formations barely alter the density field, they remain hidden from the ocean dynamics. Here11 we unveil these hidden, isopycnal transformations from in situ observations at 1,000-m depth.12 We shows that these isopycnal transformations are 5 times as large as their diapycnal coun-13 terpart and are occurring for ∼67% in the Southern Ocean. Our estimations stress the role14 of the spatially-varying and anisotropic characteristics of isopycnal diffusion, often not con-15 sidered in ocean models. This has major consequences for our understanding of the role of16 the ocean in response to anthropogenic climate changes.17 Correspondence Correspondence and requests for materials should be addressed to FS (email: florian.18 [email protected]).19 1 Ocean circulation transports a vast amount of water over the globe (up to 150 Sv, where20 1 Sv≡106m3s−1, in the Antarctic Circumpolar Current, for instance)1. This large-scale ocean cir-21 culation is also associated with transport of heat (up to 1.5 PW northward at 20◦N)2and freshwater22 (around 0.5 Sv southward at 35◦N in the North Atlantic)3. The former is a fundamental component23 of the climate equilibrium and adjustment by transporting the excess of heat from the tropics to the24 poles; whereas the latter indirectly reflects the geographical pattern of evaporation, precipitation,25 river discharge, and ice melting, all taking part in the water cycle. In particular, the ocean is the26 most important region of precipitation and evaporation (i.e., 75% and 85%, respectively), making27 it particularly relevant for the Earth water cycle4.28 Beyond this equilibrated view, the Earth is experiencing changes since the pre-industrial29 era, with a significant amount of anthropogenically-induced greenhouse gazes released into the30 atmosphere5. As a consequence, the surface atmospheric temperature is increasing5, despite a31 significant mitigation by the ocean, with an ocean absorption of about 90% of the Earth’s heat32 excess5–7. Together with this warming, the water cycle is also affected8. This is reflected by33 changes in the evaporation and precipitation patterns and amplitudes5. These changes, either34 directly (when over the ocean) or indirectly through runoffs (when over land), are imprinted35 in the ocean freshwater transport9, 10 through, for instance, modification of the ocean salinity36 distribution11. Hence, the ocean heat and freshwater transports are central actors of the Earth37 equilibrium and climate changes.38 Mesoscale eddies are ubiquitous worldwide in the ocean12 and, unlike the mean transport,39 2 they contribute to the heat and freshwater transport in two folds. Firstly, equivalently to the lami-40 nar component, they move ocean water properties (i.e., its temperature and salinity) in a conserv-41 ing manner within the ocean. Secondly, eddies also induce a transformation of these properties42 through turbulent diffusion13 (e.g., mixing cold and warm waters or salty and fresh ones). Trans-43 formations of seawater properties can occur either through interactions with the atmosphere at the44 ocean surface or through turbulent diffusion in the ocean interior. Whereas the former is easier to45 etimate8, 14, the latter has always been more difficult to assess and is often deduced using inverse46 methodology15–18. Assessing the role of turbulent eddy diffusion for heat and freshwater trans-47 ports and for the transformation of seawater properties is a timely question of ocean and climate48 sciences, as demonstrated by numerous numerical model studies19–21.49 There has been a large range of studies on Water Mass Transformations22–28. These studies50 often assess the transformations in term of temperature and salinity changes, without specifically51 separating the respective role of isopycnal and diapycnal transformations. In parallel, the role52 of diapycnal diffusion on temperature and salinity transformations in the ocean interior has been53 well established16, 29. More recently, studies have suggested the key role of isopycnal processes54 on heat and freshwater uptakes30, 31, opening the possibility of an important role of the isopycnal55 diffusion. This has been further confirmed as potentially important in the North Atlantic for the56 maintenance of the mean temperature and salinity structure32. However these studies rely on either57 numerical models or inverse methods, both intrinsically depending on a chosen closure scheme58 (and sometimes imposed parameters). Hence it is key to use direct observations to assess whether59 isopycnal or diapycnal diffusion is dominant in the ocean interior. Indeed, in ocean science where60 3 reproducible controlled experiments are not possible, the use of direct observations is the only way61 to validate or invalidate hypotheses derived from these numerical or inverse modeling approaches.62 In this work, we use direct observations to assess the changes and transformations of tem-63 perature and salinity induced by mesoscale eddy turbulence, which acts as an equivalent isopycnal64 turbulent diffusion. We shows that, at 1,000-m depth, these temperature and salinity changes65 mainly occurred in the Southern Ocean and along the Gulf Stream. These isopycnal changes in-66 duces temperature and salinity transformations significantly more important than their diapycnal67 equivalents. We also conclude that the spatially-variable and anisotropic natures of the isopycnal68 turbulent diffusion are keys for an accurate estimation of the temperature and salinity transforma-69 tions.70 Results71 The major difficulty of obtaining robust, direct estimations of heat and freshwater transforma-72 tions by eddies comes from the need of knowing turbulent diffusive coefficients independently of73 temperature and salinity fields (to avoid the dependence of the results to a closure scheme)33, 34.74 Here, to circumvent this difficulty, we have used the recently estimated diffusivity coefficients35 75 derived from Argo float deep displacements36. This dataset has been obtained using a class of76 data driven Artificial Intelligence methods: the Analog Method37, 38. There, the spatially-varying77 and anisoptropic diffusivity coefficients were estimated through local tracer dispersion induced by78 a turbulent velocity field reconstructed from deep Argo displacements. This dataset provides the79 4 full diffusivity tensor, explicitly acknowledging the anisotropy, rather than a single diffusivity co-80 efficient, as most commonly done33, 34, 39. These resulting diffusivity coefficients are strong where81 the flow is strong (Fig. 1d and e), but with a slight spatial-offset with the core of the currents40, 41,82 hence with the largest density gradients. This could be rationalized by the existence of Kinetic83 Energy transfers42. These coefficients (Fig. 1d and e) together with temperature and salinity fields84 from gridded ISAS17 product43 (Optimal Interpolation44 from Argo profiles, Fig. 1a and b) allow85 us to have a direct estimation of isopycnal heat and freshwater transformations and uncover an86 unobserved facet of deep ocean circulation.87 Effect of Isopycnal Turbulent Diffusion. In the present study we assess the global effect of the88 turbulent diffusion on temperature and salinity fields. However, because of observational con-89 straints (i.e., the typical parking depth of Argo float deep displacements), our study focuses at90 1,000-m depth. This depth is particularly relevant for estimating heat and freshwater transports91 and seawater property transformations for two reasons. (1) It is close to the depth of the maximum92 of the Atlantic Meridional Overturning Circulation (depth of no-motion for this circulation, as es-93 timated at 26.5◦N in the North Atlantic by RAPID)45. (2) It is the depth with largest contrast in94 salinity46, 47, but also includes signatures of the coldest waters47 (Fig. 1).95 The transformation of seawater properties works hand in hand with the concept of Water96 Masses48. Water Masses are volumes of water with consistent seawater properties (Fig. 1f) that are97 set through ocean-atmosphere exchange at the ocean surface where water masses originate. They98 then spread within the ocean through advection and mixing and are transformed by the latter. At99 5 1,000-m depth, we will consider three intermediate water masses: Red Sea–Persian Gulf Inter-100 mediate Water (RSPGIW) formed in the Red Sea and Persian Gulf49, the Mediterranean Water50 101 (MW) reaching the Atlantic through the Strait of Gibraltar, and the AntArctic Intermediate Water51 102 (AAIW) intersecting the 1,000-m depth along the the Polar Front52. We will also consider more103 dense Water Masses, namely the North Atlantic Deep Water (NADW), its transformed southern104 extension, the Circumpolar Deep Water53 (CDW), and the Antarctic Bottom Water54 (AABW).105 Despite not being their depth of maximum intrusion, these Water Masses are present at 1,000-m106 depth in the high latitudes of the North Atlantic and of the Southern Ocean (Fig. 1f).107 To estimate the impact of the turbulent diffusion on the temperature and salinity of these108 water masses we follow the Temporal-Residual-Mean framework (see Methods – Isopycnal Tur-109 bulent Transformation Framework)13. This framework disentangles advective and mixing effects110 when eddy turbulence is averaged. This allows for an accurate attribution of eddy-induced trans-111 port and transformation. Also, this framework acknowledges that transformations acts within112 isopycnal layers as epineutral flux (Fig. 2). To this purpose averaging are done along-isopycnal,113 so that fictitious diapycnal transport, due to incorrect estimates of the isopycnal slopes, can be114 limited55. This transformation-induced process has almost no signature on the density field (ex-115 cept for the weak cabbeling and thermobaricity components, although they remain crucial for the116 density transformations56), nor pressure, nor circulation. As a consequence, there is no impact on117 Potential Energy and it can act passively, as long as Eddy Kinetic Energy remains to maintain the118 turbulent diffusion. In this sense, for the ocean dynamics, it remains hidden along the isopycnals119 (Fig. 1c). However it still contributes to heat and freshwater transport from cold to warm and from120 6 salty to fresh regions, respectively. This process can be described in the form of temperature and121 salinity rates of change or of water-mass transformation rates (Methods – Water Mass Transfor-122 mation Rates). The rates of change of a material property (temperature or salinity) measures the123 amount of warming/cooling or salinification/freshening induced by the isopycnal turbulent diffu-124 sion; whereas the transformation accounts for the amount of seawater that have their properties125 transformed by this process.126 Rates of temperature and salinity change. As mentioned above, the isopycnal diffusion of tem-127 perature and salinity can be assessed as the induced rates of change in terms of temperature and128 salinity [Methods – (10)]. High magnitudes of the rates of change are due to high diffusivity co-129 efficients, sharp isopycnal temperature or salinity gradients, or a combination of both. At 1,000-m130 depth, we find that they are of the order of kelvins per year or tenth of (g kg−1) per year [or a131 few 10−8K s−1and 10−9g kg−1s−1] for temperature and salinity, respectively. These rates of132 change are mainly located in the Southern Ocean, along the Antarctic Circumpolar Current, and,133 to a lesser extent, in the North West of the North Atlantic (Fig. 3a and 4a). Indeed the Southern134 Ocean account for 67% of the global rates of change for temperature and salinity [as measured by135 the R2of the transformations described in (11) ], despite representing only 31% of the global ocean136 area. When including North Atlantic it reaches 95% for temperature and salinity rates of change.137 A local maximum of these rates of change can be seen in the Zapiola gyre, which corresponds to a138 local maximum of diffusivity coefficients (Fig. 1d and e). There is also significant rates of change139 along the Agulhas return current and its merging with the Antarctic Circumpolar Current, which140 also corresponds to a local maximum of diffusivity coefficients. Indeed, between South Africa and141 7 the Kerguelen plateau, there is a warming and salinification of the relatively cold and salty AAIW142 (Fig. 3a and 4a), a cooling and freshening of the relatively warm and fresh AAIW, and a warming143 and salinification of the warm and salty residual of RSGPIW (trapped in the Agulhas system57,144 Fig. 1b).145 Unlike the geographical map that reveals where the rates of change are located, the TS-146 diagram (i.e., representation with temperature-salinity axes) reveals which water masses are sub-147 jected to the isopycnal diffusion (i.e., change along isopycnal surfaces). This can be represented148 globally (insets in Fig. 3a and 4a), or displayed for each relevant basin (following the division of149 Fig. 1f), which allows a simpler relation with local Water Masses (Fig. 3b-e and 4b-e). In the150 North Atlantic, despite the weak isopycnal turbulent diffusion coefficients in the subtropical gyre151 interior (Fig. 1d and e), temperature and salinity rates of change within the MW (along the 27.6-152 27.8 kg m−3density class) are visible with a slight cooling and a freshening of MW (Fig. 3b). A153 more important cooling and freshening is also visible at the edge between MW and NADW. In the154 Southern Ocean the geographical separation is quite revealing. It suggests different water masses155 at play for each of the three sectors (Atlantic, Indian, and Pacific). In the Atlantic sector of the156 Southern Ocean, we observe a cooling and freshening of CDW and a warming and salinification157 of AAIW and AABW (Fig. 3c and 4c). In the Indian and Pacific sectors, the rates of change158 correspond to a warming and salinification of the AABW, a cooling and freshening of the CDW,159 a warming and salinification of the coldest and freshest portion of the AAIW, and a cooling and160 freshening of the warmest and saltiest portion of the AAIW (Fig. 3d and e and 4d and e). In the161 Indian sector, there is also a warming and salinification of the warmer portion of the AAIW, which162 8 derives from RSPGIW57.163 Water Mass Transformations. To further quantify these effects, the isopycnal turbulent diffu-164 sion can also be expressed as Water Masses Transformation (see Methods – Water Mass Trans-165 formation Rates). As discussed earlier, since the turbulent eddy-induced diffusion acts along166 isopycnals13 it cannot modify density (except for weak nonlinear effects, which affect density167 and hence the circulation)56. Hence we will focus on transformations induced by temperature and168 salinity changes. We use the traditional Water Mass Transformation framework48, 58, often defined169 across density layers. Here, we compute transformation rates induced by temperature and salinity170 changes along the isopcycnals [see Methods – (11)]. They are computed both globally and for each171 region defined earlier (Fig. 1f). These two transformations are evidences of heat and freshwater172 transport by isopycnal turbulent diffusion.173 We find density transformations of the order of ±2 Sv (i.e., density-class standard deviation)174 for density changes induced by either temperature and salinity, respectively (colored – red and blue175 – bars in Fig. 5a and c, respectively). This is important as these transformations correspond to a 70-176 m layer only (i.e., the typical density layer thickness due to the stratification at our studied depth,177 see Method – Water Mass Transformation Rates and Supplementary Fig. 1). For comparison, the178 buoyancy transformations are of the order of a few tens of Sverdrup when computed over the full179 ocean depth56. We rationalize the importance of the temperature and salinity transformations over180 the density ones because of their strong thermohaline compensating effect on density (i.e., the so181 called spiciness). The Water Masses located at our studied depth exhibit particularly intense spici-182 9 depth of no-motion for this circulation) and it is where some of the most saline waters reside303 and where the coldest waters also exist. This makes this depth particularly relevant for heat and304 freshwater transports. However, given the intensity of the circulation and transformation identified305 in our study, it is important to acknowledge it at other depths. In particular, diapycnal mixing306 could become more prevalent near the seabed, mitigating the key role of isopycnal mixing for307 temperature and salinity transformations. Hence, building a robust 3-dimensional picture, fully308 constrained by observations, of the isopycnal turbulent transformations of the global ocean will be309 a direction for future work.310 Methods311 Isopycnal Turbulent Transformation Framework. Starting from the advection equation for a312 tracer (which could be temperature or salinity) away from forcing (mainly occurring at the ocean313 surface) and for high P´eclet number (Pe≫1, measuring the advection to diffusion ratio), we have:314 DtC= 0,(1) where Cis the tracer concentration and Dtis the material derivative (=∂t+u∂x+v∂y+w∂z, where315 tis time, x,yand zare the zonal, meridional, and vertical coordinates, and u,v, and ware the316 zonal, meridional, and vertical velocities).317 This equation can be modified to show the evolution of the large-spatial scale or long-time318 scale by splitting each terms in an Eulerian mean (¯.) and its associated anomaly (.′). This reads:319 16 Dt¯ C=−∂xu′C′−∂yv′C′−∂zw′C′,(2) where Dtis the mean material derivative (=∂t+¯u∂x+¯v∂y+¯w∂z).320 This shows that several mean ( ¯ C,¯u,¯v, and ¯w) and turbulent (u′C′,v′C′, and w′C′) terms321 contribute to the maintenance of the mean state. In this context, we can redistribute the terms13, 64 322 so that the evolution of the tracer becomes:323 b Dtˆ C=dˆ C,(3) where ˆ Cis the modified tracer, b Dtis the modified material derivative [=∂t+ˆu∂x+ˆv∂y+ ˆw∂z, and324 ˆu=¯u+˜u,ˆv=¯v+˜v, and ˆw= ¯w+ ˜w, where ˜u,˜v, and ˜ware the zonal, meridional and vertical eddy-325 induced velocities, respectively], and dˆ Cis the transformation term. This expression suggests that326 the modified tracer is advected by both the mean and the eddy-induced velocity65 and transformed.327 In this Temporal-Residual-Mean framework, the eddy-induced advection and the transformation328 are consequences of the skew-symmetric and symmetric components of the turbulent flux, respec-329 tively. This framework is particularly useful to accurately separate and attribute the advection and330 mixing effects of averaged eddy turbulence. The advection effect only displaces tracer properties,331 whereas the mixing effect changes tracer properties. Hence, this framework avoids the misinter-332 pretation of eddy-induced transport by horizontal turbulence as transformation.333 In the ocean interior (i.e., below the ocean mixed layer), the transformation term can take the334 form56 of335 17 dˆ C=diso ˆ C+ddia ˆ C,(4) where diso ˆ Cand ddia ˆ Care the transformation along the isopycnal and the diapycnal direction. Here,336 by being in the ocean interior (i.e., below mixed layer depth), we have neglected the potential337 effect of horizontal transformation (important within the mixed layer). In the rest of the study,338 we will focus on the isopycnal component of these fluxes and compare it to the diapycnal one.339 Note that isopycnal heat and freshwater transformations act along constant density surface, thus,340 by construction they avoid density gradients. Although, the diapycnal component, induced by341 small-scale mixing processes66, will be used as a reference. It is worth noting that the use horizon-342 tal diffusion instead of isopycnal diffusion outside of the mixed layer is fundamentally flawed55.343 With this approximation, we would find transformations that are completely missing the correct344 warming/cooling freshening/salinification. Also, as expected for such flawed approximation, the345 compensation between temperature and salinity changes are missed. This would result in unreal-346 istic transformations.347 Following a downgradient flux closure13, 67 (i.e., Fick’s law), the density-weighted isopycnal348 transformation reads:349 diso ˆ C=∂zγ∇n· K·∇nˆ C ∂zγ!,(5) where ∇nrefers to gradient along the neutral density (γ) and Kis the, possibly spatially-varying,350 anisotropic diffusivity tensor acting along the neutral density (or anisotropic epineutral diffusivity351 18 tensor). Here the gradient is computed using the projected nonorthogonal approach68, 69. The352 diffusivity tensor is expressed as:353 K=    κ˜x˜xκ˜x˜y κ˜x˜yκ˜y˜y    ,(6) where ˜xand ˜yare the zonal and meridional direction along neutral density, respectively, and κ˜x˜x,354 κ˜y˜y, and κ˜x˜yare the zonal, meridional, and cross diffusivities along the neutral density, respectively.355 Hence the isopycnal transformations for a spatially-varying and anisotropic diffusivity tensor read:356 diso ˆ C=∂zγ ∂˜xκ˜x˜x ∂zγ∂˜xˆ C+∂zγ ∂˜xκ˜x˜y ∂zγ∂˜yˆ C+∂zγ ∂˜yκ˜x˜y ∂zγ∂˜xˆ C+∂zγ ∂˜yκ˜y˜y ∂zγ∂˜yˆ C.(7) This expression shows that the diffusivity is dependent on 3 scalars that measured both the357 intensity of the diffusivity and its orientation. Indeed, since the off-diagonal term are strictly358 identical in (6), it simply induces a rotation of diffusivity, which will acts independently along its359 two orthogonal natural directions (directions after rotation). Here it becomes apparent that the use360 of a single coefficient cannot fully represent the complexity of this isopycnal transformations, both361 in term of intensity and directionality.362 Computation of Epineutral Flux. One last difficulty is to estimate the gradient along neutral363 density69 (or epineutral gradient) as expressed in (7): computing the ∇n(or ∂˜xand ∂˜y). As an364 19 example, but it would be equivalent for the meridional direction, for the zonal direction, we have:365 ∂˜xσ≃∆σ|γ ∆˜x≃∆σ|z+ ∆σ|x √∆x2+δz2≃∂xσ∆x+∂zσ δz ∆xq1 + δz2 ∆x2 , ≃∂xσ+sx∂zσ−1 2s2 x∂xσ−1 2s3 x∂zσ+. . . , ≃∂xσ+sx∂zσ, (8) where σis any scalar quantity (e.g., Temperature or Salinity), sx=δz/∆xis the zonal component366 of the isopycnal slope, ∆σ|{γ,x,z}is the difference in σat constant γ,x, and z, respectively, ∆˜x367 is the distance at constant γalong the zonal direction, and ∆xand δz are the zonal and vertical368 distances, respectively, covered by the neutral density surface.369 In the last calculation a few approximations have been done: (i) ∆˜x≃√∆x2+δz2, assum-370 ing that the epineutral displacement can be geometrically approximated by the zonal and verti-371 cal displacement; (ii) δz≪∆x, assuming that the vertical displacement of the epineutral is weak372 compared to the zonal one (i.e., small slope approximation65) allowing a Taylor expansion of the373 denominator; and (iii) ∂xσand ∂zσare constant over ∆xand δz, respectively. Equivalently we374 have ∂˜yσ≃∂yσ+sy∂zσ, where syis the meridional component of the isopycnal slope. Note that375 there exists more complex but more accurate computation methods of the neutral slopes and gradi-376 ents, which are key when the slopes become important70, 71. However, in our application the slopes377 remain weak, with a maximum slope magnitude of 0.08 and a median value of 0.0001.378 The slope is defined through the horizontal gradients of Absolute Salinity (SA) and Conser-379 vative Temperature (Θ), by setting ∂˜xγ=0 and ∂˜yγ=0, such as:380 20     sx sy    =−α∇Θ−β∇SA α∂zΘ−β∂zSA ,(9) where ∇is the horizontal gradient, and αand βare the thermal expansion and haline contraction381 coefficients, respectively. s2is the magnitude of the slope measured through the components inner382 product (=s2 x+s2 y),383 This epineutral formulation for the gradients allows us to compute an approximation of the384 isopycnal diffusion, described in (5) and (7), for any tracer ˆ Cas a function of Cartesian coordinates.385 This reads:386 diso ˆ C≃∂zγ∂xκ˜x˜x ∂zγ∂xˆ C+sx∂zˆ C+κ˜x˜y ∂zγ∂yˆ C+sy∂zˆ C +sx∂zκ˜x˜x ∂zγ∂xˆ C+sx∂zˆ C+κ˜x˜y ∂zγ∂yˆ C+sy∂zˆ C +∂yκ˜x˜y ∂zγ∂xˆ C+sx∂zˆ C+κ˜y˜y ∂zγ∂yˆ C+sy∂zˆ C +sy∂zκ˜x˜y ∂zγ∂xˆ C+sx∂zˆ C+κ˜y˜y ∂zγ∂yˆ C+sy∂zˆ C.(10) This is this formulation, which includes anisotropic, isopycnal diffusivities, that is used in our387 study.388 Water Mass Transformation Rates. Building on (10), the action of the isopycnal turbulent term389 could be further estimated in terms of transformation rates56, 72 as:390 Ψ# Θ=∂γZZΣ(γ′≤γ)−αdiso ΘdΣ ∆z, (11a) Ψ# SA=∂γZZΣ(γ′≤γ) βdiso SAdΣ ∆z, (11b) 21 391 where Σ(γ′≤γ)is the surface of a tracer class below the threshold value γat 1,000-m392 depth. Here Ψ# Θand Ψ# SArepresent neutral density transformations through temperature or salinity393 changes over a layer of thickness ∆z, respectively. These transformations are expressed in Sv,394 where 1 Sv≡106m2s−1. In practice, the transformations are estimated using neutral density395 increment (we chose: ∆γ=0.03 kg m−3). For consistency, the layer thickness can be estimated396 though the scaling: ∆z≃∆γ(∂zγ)−1(which derives from dγ=∂xγdx+∂yγdy+∂zγdz). Compution397 over the globe at 1,000-m depth shows values from 10 m to more than 3,000 m (Supplementary398 Fig. 1a). In particular the thickness is significantly more important in the Southern Ocean (e.g., the399 Weddell Sea) and in the subpolar North Atlantic (e.g., Labrador Sea) than in the rest of the globe.400 However extrapolating our computation over more than 3,000 m is inconsistent with our knowledge401 of vertical variations of diffusivity coefficient: existence of a steering level40, 41 and variations with402 Eddy Kinetic Energy36. Hence we have chosen to restrict the layer thickness amplitude. We have403 used a uniform layer thickness based on the median value: ∆z=70 m (Supplementary Fig. 1b),404 regardless of the local stratification (∂zγ). Hence our results, despite being in Sverdrup, only405 reflects a slice of the ocean at 1 000-m depth.406 These transformations mathematically expressed a probability density function of density407 changes induced by cooling/warming or freshening/salinification per neutral density classes, re-408 spectively. They physically correspond to the volume of water at a given density that is gain-409 ing/loosing density by cooling/warming or by salinification/freshening, respectively.410 22 These transformation rates (Ψ# Θand Ψ# SA) can be interpreted as the component of the total411 transformation induced by isopycnal turbulence. Other components exist23, such as the one in-412 duced by the vertical turbulence73 [w′C′, visible in (2)] and the small scale diffusion [neglected in413 (1), by assuming Pe≫1].414 To summarize, (11) shows the existence of transformations when both isopycnal oceanic415 turbulence and isopycnal tracer gradients are present (Fig. 2). In this framework, one can compute416 transformations associated to temperature and salinity (Fig. 5). The sum of the two transformations417 with respect to neutral density classes can also be defined as: Ψ# Θ+Ψ# SA. This sum is expected to418 be zero and, therefore, reflects the computation errors (Fig. 5e and f).419 Tracer Fields, Diffusivity Data, and Computation Method. One can compute a tracer transfor-420 mation and transformation rates by knowing two properties:421 1. ˆ Cand ∂zˆ C(as well as ∂zγ) at all locations [∀(x, y)] along the surface (defined by z=z0,422 where z0is a constant depth). This can be obtained after assuming ˆ C≃¯ Cfrom relevant re-423 analyses at any depth, but primarily above the maximum Argo depth sampling of ∼2,000 m424 for robustness. In this study, Ccan be Conservative Temperature or Absolute Salinity425 (Fig. 1a-b);426 2. Kat all locations [∀(x, y)] along the same surface (defined by z=z0, where z0is a constant427 depth), which can be estimated by Argo deep displacements at their parking depth36 (Fig. 1d-428 f).429 23 Hence the main constraint occur through Kwhich is only determined at Argo float parking depth430 (mainly located at ∼1,000 m) and determine the focused depth of our study.431 We have used the two-dimensional gridded direct estimate of the turbulent anisotropic, isopy-432 cnal diffusivity coefficients derived from Argo deep displacements36, which are available35 at433 https://doi.org/10.17882/91335, and the global three-dimensional ISAS17 gridded434 temperature and salinity data derived from objective anaylis of in situ observations43 and available435 at https://doi.org/10.17882/52367.436 The spatially-varying and anisotropic diffusivity coefficients were obtained by reconstruct-437 ing an analogue turbulent field from deep Argo displacement. This reconstructed turbulent field438 was used to determine the local dispersion of a locally-injected spike of passive tracer, the rates of439 dispersion estimating the local diffusivity coefficients along the zonal, meridional, and cross direc-440 tions. This allows for the full determination of the diffusivity tensor, rather than a single coefficient441 as often done33, 34, 39.442 In practice, after conversion of the data to Conservative Temperature and Absolute Salinity,443 as well as the computation of neutral density, all the computations are done using 3◦×3◦cells (i.e.,444 the native cell of the diffusivity coefficients) on 1◦×1◦grid (i.e., the native grid of the diffusiv-445 ity coefficients). Data are vertically averaged over 40 m bins and vertical levels (needed for the446 computation of vertical gradients) are separated by 20 m. All conversion to Conservative Temper-447 ature and Absolute Salinity, as well as computation of neutral density, are done using the Gibbs448 SeaWater Oceanographic Toolbox of TEOS-10 code.449 24 For the water masses framework, we have identified six Water Masses located at the depth of450 the study49. They are defined through their temperature and salinity range. They are the Mediter-451 ranean Water (MW), the Red Sea-Persian Gulf Intermediate Intermediate Water (RSPIGIW), the452 Antarctic Intermediate Water (AAIW), the North Atlantic Water (NADW), the Circumpolar Deep453 Water (CDW), and the AntArctic Bottom Water (AABW).454 Alternative Diffusivity Coefficients. To test the importance of using spatially-varying and anisotropic455 isopycnal diffusivity coefficients we have tested a range of less complex diffusivity coefficients:456 1. Spatially-uniform and isotropic isopycnal diffusivity coefficients: the diffusivity coefficients457 are set to κUni & Iso ˜x˜x=κUni & Iso ˜y˜y=(hκ˜x˜xi+hκ˜y˜yi)/2 and κUni & Iso ˜x˜y=0. These coefficients are applied458 to (5).459 2. Spatially-varying and isotropic isopycnal diffusivity coefficients: the diffusivity coefficients460 are set to κVar & Iso ˜x˜x=κVar & Iso ˜y˜y=(κ˜x˜x+κ˜y˜y)/2 and κVar & Iso ˜x˜y=0. These coefficients are applied to461 (5).462 To compare transformations using the different versions of the diffusivity we used a relative463 error (RE) using the most complete version as the reference. This reads:464 RE = sign "log Ψ# comp Ψ# ref !#var Ψ# comp −Ψ# ref var Ψ# ref,(12) where Ψ# ref is the reference transformation (i.e., most complete diffusivity), Ψ# comp is the transfor-465 mation used for comparison (i.e., less complete diffusivity), and the log term allows to estimate the466 25 27. Evans, D. G., Zika, J. D., Naveira Garabato, A. C. & Nurser, A. J. G. The cold transit of582 Southern Ocean upwelling. Geophys. Res. Lett. 45, 3,386–13,395 (2018).583 28. Zika, J. D., Gregory, J. M., McDonagh, E. L., Marzocchi, A. & Cl´ement, L. Recent water mass584 changes reveal mechanism of ocean warming. J. Phys. Oceanogr. 34, 3461–3479 (2021).585 29. Hieronymus, M., Nilsson, J. & Nycander, J. Water mass transformation in salinity-temperature586 space. J. Phys. Oceanogr. 44, 2547–2568 (2014).587 30. Clement, L. et al. Mechanisms of ocean heat uptake along and across isopycnals. J. Phys.588 Oceanogr. 35, 4885–4904 (2022).589 31. Zou, M. S., S. amd Lozier & Li, F. Density-compensated overturning in the Labrador Sea.590 Nat. Geosci. 13, 121–126 (2020).591 32. Evans, D. G., Holliday, N. P., Bacon, S. & Le Bras, I. Mixing and air-sea buoyancy fluxes set592 the time-mean overturning circulation in the subpolar north atlantic and nordic seas. Ocean593 Sci. 19, 745–768 (2023).594 33. Cole, S. T., Wortham, C., Kunze, E. & Brechner Owens, W. Eddy stirring and horizontal595 diffusivity from Argo float observations: Geographic and depth variability. Geophys. Res.596 Lett. 42, 3989–3997 (2015).597 34. Groeskamp, S., LaCasce, J. H., McDougall, T. J. & Rog´e, M. Full-depth global estimates598 of ocean mesoscale eddy mixing from observations and theory. Geophys. Res. Lett. 47,599 e2020GL089425 (2020).600 32 35. S´evellec, F., Colin de Verdi`ere, A. & Kolodziejczyk, N. Deep horizontal turbulent diffusivity.601 SEANOE https://doi.org/10.17882/91335 (2022).602 36. S´evellec, F., Colin de Verdi`ere, A. & Kolodziejczyk, N. Estimation of horizontal turbulent603 diffusivity from deep Argo float displacements. J. Phys. Oceanogr. 52, 1509–1529 (2022).604 37. Lorenz, E. N. Atmospheric predictability as revealed by naturally occurring analogues. J.605 Atmos. Sci. 26, 636–646 (1965).606 38. Ayet, A. & Tandeo, P. Nowcasting solar irradiance using an analog method and geostationary607 satellite images. Solar Energy 164, 301–315 (2018).608 39. Roach, C. J., Bawada, D. & Speer, K. Global observations of horizontal mix-609 ing from Argo float and surface drifter trajectories. J. Geophys. Res.: Oceans 123,610 doi:10.1029/2018JC013750 (2018).611 40. Smith, K. S. & Marshall, J. Evidence for enhanced eddy mixing at middepth in the Southern612 Ocean. J. Phys. Oceanogr. 39, 50–69 (2009).613 41. Abernathey, R., Marshall, J. & Mazloff, M. Enhancement of mesoscale eddy stirring at steer-614 ing levels in the Southern Ocean. J. Phys. Oceanogr. 40, 170–184 (2010).615 42. S´evellec, F., Colin de Verdi`ere, A. & Kolodziejczyk, N. Global observations of deep ocean616 kinetic energy transfers. J. Phys. Oceanogr. 54, 1633–1654 (2024).617 43. Kolodziejczyk, N., Prigent-Mazella, A. & Gaillard, F. ISAS temperature, salinity, dissolved618 oxygen gridded fields. SEANOE https://doi.org/10.17882/52367 (2023).619 33 44. Bretherton, F. P., Davis, R. & Fandry, C. Technique for objective analysis and design of620 oceanographic experiment applied to MODE-73. Deep-Sea Res. Oceanogr. Abstr. 23, 559–621 582 (1976).622 45. Stepanov, V. N., Iovino, D., Masina, S., Storto, A. & Cipollone, A. Methods of calculation of623 the atlantic meridional heat and volume transports from ocean models at 26.5◦n. J. Geophys.624 Res.: Oceans 121, 1459–1475 (2016).625 46. Talley, L. D. Freshwater transport estimates and the global overturning circulation: Shallow,626 deep and throughflow components. Prog. Oceanogr. 78, 257–303 (2008).627 47. Talley, L. D., Pickard, G. L., Emery, W. J. & Swift, J. H. Descriptive physical oceanography:628 An introduction (sixth edition). Elsevier 560 pp (2011).629 48. Walin, G. On the relation between sea-surface heat flow and thermal circulation in the ocean.630 Tellus 34, 187–195 (1982).631 49. Emery, W. J. Ocean circulation — Water Types and Water Masses. In Holton, J. R. (ed.)632 Encyclopedia of Atmospheric Sciences, 1556–1567 (Academic Press, Oxford, 2018).633 50. Iorga, M. C. & Lozier, M. S. Signatures of Mediterranean outflow from North Atlantic clima-634 tology – 1. Salinity and density fields. J. Geophys. Res. 104, 25985–26009 (1999).635 51. Carter, L., McCave, I. N. & M., W. M. J. Circulation and water masses of the southern ocean:636 A review in anatractic climate evolution. Developments in Earth & Environmental Science 8,637 85–114 (2009).638 34 52. Orsi, A. H., Whitworth, T. & Nowlin, W. D. On the meridional extent and fronts of the639 Antarctic Circumpolar Current. Deep-Sea Res. 42, 641–673 (1995).640 53. Defant, A. Physical Oceanography (Pergmon Press, 1961).641 54. Emery, W. J. & Meincke, J. Global water masses: summary and review. Oceanologica Acta642 9, 383–391 (1986).643 55. Veronis, G. (The role of models in tracer studies. Numerical Models of the Ocean Circulation,644 Natl. Acad. Sci., 133-146, 1975).645 56. Groeskamp, S., Abernathey, R. P. & Klocker, A. Water mass transformation by cabbeling and646 thermobaricity. Geophys. Res. Lett. 43, 10,835–10,845 (2016).647 57. Roman, R. E. & Lutjeharms, J. R. E. Red Sea Intermediate Water at the Agulhas current648 termination. Deep-Sea Res. 54, 1329–1340 (2007).649 58. Groeskamp, S. et al. The Water Mass Transformation framework for ocean physics and bio-650 geochemistry. Annu. Rev. Mar. Sci. 11, 271–305 (2019).651 59. de Lavergne, C. et al. A parameterization of local and remote tidal mixing. J. Adv. Model.652 Earth Syst. 12, e2020MS002065 (2020).653 60. de Lavergne, C. Global tidal mixing maps. SEANOE https://doi.org/10.17882/73082 (2020).654 61. Fern´andez Castro, B. et al. Isopycnal eddy stirring dominates thermohaline mixing in the655 upper subpolar north atlantic. J. Geophys. Res. 129, e2023JC020817 (2024).656 35 62. Eyring, V. et al. Overview of the coupled model intercomparison project phase 6 (CMIP6)657 experimental design and organization. Geosci. Model Dev. 9, 1937–1958 (2016).658 63. Beech, N. et al. Long-term evolution of ocean eddy activity in a warming world. Nature Clim.659 Change 12, 910–917 (2022).660 64. Young, W. R. An exact Thickness-Weighted Average formulation of the boussinesq equations.661 J. Phys. Oceanogr. 42, 692–707 (2012).662 65. Gent, P. R. & McWilliams, J. C. Isopycnal mixing in ocean circulation model. J. Phys.663 Oceanogr. 20, 150–155 (1990).664 66. de Lavergne, C., Madec, G., Le Sommer, J., Nurser, A. J. G. & Naveira Garabato, A. C. The665 impact of a variable mixing efficiency on the abyssal overturning. J. Phys. Oceanogr. 46,666 663–681 (2016).667 67. Redi, M. H. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr. 12, 1154–668 1158 (1982).669 68. Starr, V. P. A quasi-lagrangian system of hydrodynamical equations. J. Meteor. 2, 227–237670 (1945).671 69. McDougall, T. J., Groeskamp, S. & Griffies, S. M. On geometrical aspects of interior ocean672 mixing. J. Phys. Oceanogr. 44, 2164–2175 (2014).673 36 70. Groeskamp, S., Barker, P. M., McDougall, T. J., Abernathey, R. P. & Griffies, S. M. Venm:674 An algorithm to accurately calculate neutral slopes and gradients. J. Adv. Model. Earth Syst.675 11, 1917–1939 (2019).676 71. Shao, A. E., Adcroft, A., Hallberg, R. & Griffies, S. M. A general-coordinate, nonlocal neutral677 diffusion operato. J. Adv. Model. Earth Syst. 12, e2019MS00199 (2020).678 72. Maze, G., Forget, G., Buckley, M. & Marshall, J. Using transformation and formation maps to679 study the role of air-sea heat fluxes in north atlantic eighteen degree water formation. J. Phys.680 Oceanogr. 39, 1818–1835 (2009).681 73. Holmes, R. M., Zika, J. D. & England, M. H. Diathermal heat transport in a global ocean682 model. J. Phys. Oceanogr. 49, 141–161 (2019).683 Acknowledgements This work was supported by ARVOR and OASIS projects from LEFE IMAGO and684 GMMC program, respectively, by the OceaniX project funded through the French ANR program, and by the685 ISblue project, Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015) co-funded by a686 grant from the French government under the program “Investissements d’Avenir”. These data were collected687 and made freely available by the International Argo Program and the national programs that contribute to688 it (https://argo.ucsd.edu and https://www.ocean-ops.org). The Argo Program is part of689 the Global Ocean Observing System. FS is supported by the EERIE project (Grant Agreement 101081383)690 funded by the European Union. Views and opinions expressed are, however, those of the authors only and do691 not necessarily reflect those of the European Union or the European Climate Infrastructure and Environment692 Executive Agency (CINEA). Neither the European Union nor the granting authority can be held responsible693 for them.694 37 Author Contribution All three authors (FS, NK, and EP) contributed equally to the experimental design695 and the writing of the manuscript. FS initiated the analysis and developed the data analysis.696 Competing Interests The authors declare no competing interests.697 38 Figure 1 Climatological tracer fields and horizontal diffusivity at 1,000-m depth. (a) Con-698 servative Temperature, (b) Absolute Salinity, and (c) neutral density at 1,000-m depth699 from the climatological-annual mean of gridded ISAS17 product43. (d) Primary and (e)700 secondary diffusivity, as well as their respective directions, estimated from deep Argo dis-701 placements at 1,000-m depth from the ANDRO dataset36. (f) Six Water Masses are identi-702 fied at 1,000-m depth49 and denoted through color patches. These Water Masses are the703 Mediterranean Water (MW), the Red Sea–Persian Gulf Intermediate Water (RSPGIW),704 the AntArctic Intermediate Water (AAIW), the North Atlantic Deep Water (NADW), the705 Circumpolar Deep Water (CDW), and the AntArctic Bottom Water (AABW). Four key re-706 gions are also highlighted and used in the rest of the study : North Atlantic (NA), Atlantic707 sector of Southern Ocean (SO-A), Indian sector of Southern Ocean (SO-I), and Pacific708 sector of Southern Ocean (SO-P).709 Figure 2 Distribution of temperature and salinity along 25◦E and potential transforma-710 tion induced by the oceanic isopycnal turbulence. (a) Conservative Temperature and (b)711 Absolute Salinity along 25◦W from the climatological-annual mean of gridded ISAS17712 product43. The light grey lines indicates neutral density contour of 26.5, 27.25, 27.85, and713 28.02 kg m−3. Because existence of Temperature and Salinity (TS) gradients along isopy-714 cnal, the oceanic isopycnal turbulent diffusion (grey arrow) can transform TS-properties715 (black spiral). This is especially true at 1 000-m depth (denoted by the horizontal black716 line) where isopycnal temperature and salinity gradients are important given the range717 39 of different Water Masses. At 25◦E we have: AntArctic Bottom Water (AABW), AntArc-718 tic Intermediate Water (AAIW), Mediterranean Water (MW), North Atlantic Deep Water719 (NADW), and Circumpolar Deep Water (CDW). As suggested by the schematic (a and b),720 it is possible to compute the rates of change, following (10), and the corresponding water721 mass transformation, following (11), associated to a tracer (e.g., temperature or salinity).722 Figure 3 Temperature rates of change at 1,000-m depth. Rates of Change in (a) Conser-723 vative Temperature at 1,000-m depth induced by the isopycnal turbulence. Inset show the724 same rates of change but as a Temperature-Salinity diagram, with neutral density in con-725 tours (in kg m−3with intervals of 0.2 kg m−3). (b-e) same as the inset but for regional es-726 timations of the rates of change for Conservative Temperature. The four selected regions727 are North Atlantic (NA), Atlantic sector of Southern Ocean (SO-A), Indian sector of South-728 ern Ocean (SO-I), and Pacific sector of Southern Ocean (SO-P), as separated by the lines729 and represented in Fig. 1f. In the scatter plots, the values are ordered in absolute rates730 of change (potentially hiding weaker rates of change of the same Temperature-Salinity731 class). The color patches show properties of selected Water Masses49: Mediterranean732 Water (MW), Red Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermedi-733 ate Water (AAIW), North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW),734 and AntArctic Bottom Water (AABW).735 Figure 4 Salinity rates of change at 1,000-m depth. Rates of Change in (a) Absolute Salin-736 ity at 1,000-m depth induced by the isopycnal turbulence. Inset show the same rates of737 40 change but as a Temperature-Salinity diagram, with neutral density in contours (in kg m−3 738 with intervals of 0.2 kg m−3). (b-e) same as the inset but for regional estimations of the739 rates of change for Absolute Salinity. The four selected regions are North Atlantic (NA),740 Atlantic sector of Southern Ocean (SO-A), Indian sector of Southern Ocean (SO-I), and741 Pacific sector of Southern Ocean (SO-P), as separated by the lines and represented in742 Fig. 1f. In the scatter plots, the values are ordered in absolute rates of change (poten-743 tially hiding weaker rates of change of the same Temperature-Salinity class). The color744 patches show properties of selected Water Masses49: Mediterranean Water (MW), Red745 Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermediate Water (AAIW),746 North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW), and AntArctic Bot-747 tom Water (AABW).748 Figure 5 Temperature and Salinity water mass transformations at 1,000-m depth for den-749 sity classes. Water mass transformations in term of density changes for (a and b) Con-750 servative Temperature and for (b and d) Absolute Salinity, and (c and d) their sum for751 density classes. Positive or negative values show warming or salinification and cooling752 or freshening, respectively. (a, c, and e) Red and blue bars show positive and negative753 transformations for the anisotropic and spatially-varying diffusivity, respectively; dark and754 light grey bars show transformations for the isotropic and spatially-varying and for the755 isotropic and for the globally-uniform diffusivity (set as the local-mean and global-mean of756 the anisotropic diffusivity), respectively. The cyan lines are the transformations induced757 by diapycnal diffusion. (e, d, and f) The transformations are split in geographical sectors:758 41 Figure 1:Climatological tracer fields and horizontal diffusivity at 1,000-m depth. (a) Conservative Temperature, (b) Absolute Salinity, and (c) neutral density at 1,000-m depth from the climatological-annual mean of gridded ISAS17 product43. (d) Primary and (e) secondary diffusivity, as well as their respective directions, estimated from deep Argo displacements at 1,000m depth from the ANDRO dataset36. (f) Six Water Masses are identified at 1,000-m depth49 and denoted through color patches. These Water Masses are the Mediterranean Water (MW), the Red Sea–Persian Gulf Intermediate Water (RSPGIW), the AntArctic Intermediate Water (AAIW), the North Atlantic Deep Water (NADW), the Circumpolar Deep Water (CDW), and the AntArctic Bottom Water (AABW). Four key regions are also highlighted and used in the rest of the study : North Atlantic (NA), Atlantic sector of Southern Ocean (SO-A), Indian sector of Southern Ocean (SO-I), and Pacific sector of Southern Ocean (SO-P). 4 !"#$%&'(%")*"+,-$./0,1-+20$ !"#.034'$-5 +&,6&5($'( !"#$ %$ &#$ ""'$ ""($ !"#$ %$ &#$ ""'$ ""($ Figure 2:Distribution of temperature and salinity along 25◦W and potential transformation induced by the oceanic isopycnal turbulence. (a) Conservative Temperature and (b) Absolute Salinity along 25◦W from the climatological-annual mean of gridded ISAS17 product43. The light grey lines indicates neutral density contour of 26.5, 27.25, 27.85, and 28.02 kg m−3. Because existence of Temperature and Salinity (TS) gradients along isopycnal, the oceanic isopycnal turbulence (grey arrow) can transform TS-properties (black spiral). This is especially true at 1 000m depth (denoted by the horizontal black line) where isopycnal temperature and salinity gradients are important given the range of different Water Masses. At 25◦E we have: AntArctic Bottom Water (AABW), AntArctic Intermediate Water (AAIW), Mediterranean Water (MW), North Atlantic Deep Water (NADW), and Circumpolar Deep Water (CDW). As suggested by the schematic (a and b), it is possible to compute the rate of changes, following (10), and the corresponding water mass transformation, following (11), associated to a tracer (e.g., temperature or salinity). 5 Figure 3:Temperature rate of changes at 1,000-m depth. Rate of Changes in (a) Conservative Temperature at 1,000-m depth induced by the isopycnal turbulence. Inset show the same rate of changes but as a Temperature-Salinity diagram, with neutral density in contours (in kg m−3 with intervals of 0.2 kg m−3). (b-e) same as the inset but for regional estimations of the rate of changes for Conservative Temperature. The four selected regions are North Atlantic (NA), Atlantic sector of Southern Ocean (SO-A), Indian sector of Southern Ocean (SO-I), and Pacific sector of Southern Ocean (SO-P), as separated by the lines and represented in Fig. 1f. In the scatter plots, the values are ordered in absolute rate of changes (potentially hiding weaker rate of changes of the same Temperature-Salinity class). The color patches show properties of selected Water Masses49: Mediterranean Water (MW), Red Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermediate Water (AAIW), North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW), and AntArctic Bottom Water (AABW). 6 Figure 4:Salinity rate of changes at 1,000-m depth. Rate of Changes in (a) Absolute Salinity at 1,000-m depth induced by the isopycnal turbulence. Inset show the same rate of changes but as a Temperature-Salinity diagram, with neutral density in contours (in kg m−3with intervals of 0.2 kg m−3). (b-e) same as the inset but for regional estimations of the rate of changes for Absolute Salinity. The four selected regions are North Atlantic (NA), Atlantic sector of Southern Ocean (SO-A), Indian sector of Southern Ocean (SO-I), and Pacific sector of Southern Ocean (SO-P), as separated by the lines and represented in Fig. 1f. In the scatter plots, the values are ordered in absolute rate of changes (potentially hiding weaker rate of changes of the same Temperature-Salinity class). The color patches show properties of selected Water Masses49: Mediterranean Water (MW), Red Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermediate Water (AAIW), North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW), and AntArctic Bottom Water (AABW). 7 27 27.2 27.4 27.6 27.8 28 28.2 -10.5 -7 -3.5 0 3.5 7 10.5 14 # (Sv) WATER MASS TRANSFORMATION (a) MW RSPGIW AAIW NADW CDW AABW Var & Aniso - pos Var & Aniso - neg Var & Iso Uni & Iso Diapycnal 27 27.2 27.4 27.6 27.8 28 28.2 -10.5 -7 -3.5 0 3.5 7 10.5 14 # SA (Sv) (c) MW RSPGIW AAIW NADW CDW AABW 27 27.2 27.4 27.6 27.8 28 28.2 NEUTRAL DENSITY (kg m-3) -10.5 -7 -3.5 0 3.5 7 10.5 14 # + # SA (Sv) (e) MW RSPGIW AAIW NADW CDW AABW 27 27.2 27.4 27.6 27.8 28 28.2 -4.2 -2.8 -1.4 0 1.4 2.8 4.2 5.6 REGIONAL DECOMPOSITION (b) MW RSPGIW AAIW NADW CDW AABW GLOBAL NA SO-A SO-I SO-P 27 27.2 27.4 27.6 27.8 28 28.2 -4.2 -2.8 -1.4 0 1.4 2.8 4.2 5.6 (d) MW RSPGIW AAIW NADW CDW AABW 27 27.2 27.4 27.6 27.8 28 28.2 NEUTRAL DENSITY (kg m-3) -10.5 -7 -3.5 0 3.5 7 10.5 14 (f) MW RSPGIW AAIW NADW CDW AABW Figure 5:Temperature and Salinity water mass transformations at 1,000-m depth for density classes. Water mass transformations in term of density changes for (a and b) Conservative Temperature and for (b and d) Absolute Salinity, and (c and d) their sum for density classes. Positive or negative values show warming or salinification and cooling or freshening, respectively. (a, c, and e) Red and blue bars show positive and negative transformations for the anisotropic and spatially-varying diffusivity, respectively; dark and light grey bars show transformations for the isotropic and spatially-varying and for the isotropic and for the globally-uniform diffusivity (set as the local-mean and global-mean of the anisotropic diffusivity), respectively. The cyan lines are the transformations induced by diapycnal diffusion. (e, d, and f) The transformations are split in geographical sectors: global (black lines), North Atlantic (NA, orange line), Atlantic sector of Southern Ocean (SO-A, blue line), Indian sector of Southern Ocean (SO-I, yellow line), and Pacific sector of Southern Ocean (SO-P, green line), as represented in Fig. 1f. The curves have been smoothed using a moving average window of 0.06 kg m−3and re-interpolated on regular 0.012 kg m−3grid with a spline interpolation. The horizontal color patches show neutral density classes of selected Water Masses49: Mediterranean Water (MW), Red Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermediate Water (AAIW), North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW), and AntArctic Bottom Water (AABW). (e and f) Non-zero values for the sum of isopycnal temperature and salinity transformations correspond to the computational error. 8 Figure 6:Other estimations of isopycnal diffusivity and induced Temperature and Salinity water mass transformations at 1,000-m depth for density classes. (a and b) Isopycnal diffusivity coefficients at 1,000-m estimated with alternative methods34,39 (denoted as Groeskamp and Roach, respectively). Water mass transformations in term of density changes for (c) Conservative Temperature and for (d) Absolute Salinity for density classes. Blue lines show transformations for the isotropic and spatially-varying diffusivity. Solid and dashed blue lines show results for the average between primary and secondary diffusivities and secondary diffusivities, respectively. The former is strictly identical to the dark grey bars of Fig. 5. Orange and red lines show transformations for the Groeskamp and Roach diffusivities, respectively. The curves have been smoothed using a moving average window of 0.06 kg m−3re-interpolated on regular 0.012 kg m−3 grid with a spline interpolation. The horizontal color patches show neutral density classes of selected Water Masses49: Mediterranean Water (MW), Red Sea–Persian Gulf Intermediate Water (RSPGIW), AntArctic Intermediate Water (AAIW), North Atlantic Deep Water (NADW), Circumpolar Deep Water (CDW), and AntArctic Bottom Water (AABW). 9 Turbulent Isopycnal Mixing dominates Thermohaline Transformations of Intermediate Ocean Waters Florian S´ evellec, Nicolas Kolodziejczyk, and Esther Portela Supplementary Information Supplementary Figure 1:Vertical layer thickness estimated for a density increment of 0.03 kg m-3 based on local stratification. (a and b) Map and distribution of thickness, respectively. The median value is 68 m. Hence we have used ∆z=70 m in (11) as a scaling of the vertical layer thickness in our estimated transformations. 1 Supplementary Figure 2:Vertical diffusivity at 1,000-m depth. Vertical diffusivity coefficients59,60 at 1,000-m used to assess the temperature and salinity diapycnal transformations. 2