The Origin and Fate of Antarctic Intermediate Water in the Southern Ocean

Zhi Li; Sjoerd Groeskamp; Ivana Cerovečki; Matthew H. England

doi:10.1175/JPO-D-21-0221.1

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Fig. 1.

Horizontal distribution of the annual mean (a) AAIW thickness (m), (b) geostrophic streamlines (m² s⁻²) on the neutral density surfaces of γⁿ = 27.35 kg m⁻³ (red-brown lines) and γⁿ = 27.6 kg m⁻³ (blue lines), and (c) AASW thickness (m). Gray contours in (a) and (c) show the mean position of the Subantarctic and Polar Fronts from Sokolov and Rintoul (2009). Yellow contours indicate the region with both thick AASW and AAIW over the South Pacific and Drake Passage. All data obtained from the WOA18 product for 2005–17.

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Fig. 2.

Horizontal distribution of the (a) meridional and (b) zonal components of lateral advection, (c) meridional and (d) zonal components of eddy-induced subduction, (e) the net Ekman pumping and beta advection, and (f) the annual mean subduction rate as a sum of components shown in (a)–(e) [Eq. (2), all in m yr⁻¹]. The eddy-induced subduction in (c) and (d) is calculated using $K$ ₀ from Groeskamp et al. (2020). Gray lines, as in Fig. 1, show the mean position of the Subantarctic and Polar Fronts from Sokolov and Rintoul (2009). Subduction is positive downward.

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Fig. 3.

Monthly mean potential vorticity (×10⁻¹¹ m⁻¹ s⁻¹; color) in September as a function of depth and latitude averaged over the longitude range of (a) 80°–90°E, (b) 100°–90°W, and (c) 30°–20°W. Monthly mean Absolute Salinity (g kg⁻¹; color) in September averaged over (d) 80°–90°, (e) 100°–90°W, and (f) 30°–20°W. The superimposed white solid lines in (a)–(c) indicate PV = 8 × 10⁻¹¹ and 7 × 10⁻¹¹ m⁻¹ s⁻¹, and light gray lines in (d)–(f) indicate S_A = 34.6 g kg⁻¹. The yellow solid line shows the monthly mean MLD in September. Black dashed lines show the neutral surfaces γⁿ = 27.1 and 27.4 kg m⁻³. Black boxes in (b) indicate locations of the property overlap of SAMW and AAIW described in section 4c. Monthly mean water mass transformation (WMT) due to cabbeling and thermobaricity (Sv; color) in September zonally integrated over (g) 30°–150°E, (h) 150°E–70°W, and (i) 70°W–30°E. Here cabbeling and thermobaricity are computed using the suppressed eddy diffusivity $K$ from Groeskamp et al. (2020). Monthly mean water mass transformation due to vertical mixing (Sv; color) in September zonally integrated over (j) 30°–150°E, (k) 150°E–70°W, and (l) 70°W–30°E. Here vertical mixing is computed using a constant vertical diffusion coefficient of D = 5 × 10⁻⁵ m² s⁻¹. Positive water mass transformation (red shading) corresponds to transformation toward increasing density.

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Fig. 4.

Geographical distribution of (a) the thickness of water with both low PV (PV < 7 × 10⁻¹¹ m⁻¹ s⁻¹) and low salinity (S_A ≤ 34.6 g kg⁻¹) characteristics within the density range of γⁿ = (27.1–27.4) kg m⁻³, and water mass transformation (m yr⁻¹) by (b) cabbeling, (c) thermobaricity, and (d) vertical mixing on the neutral surface γⁿ = 27.25 kg m⁻³ in the annual mean. Red shading corresponds to transformation toward increasing density, i.e., transformation from the SAMW layer into the AAIW layer. Gray lines shown are as in Fig. 1. Note that different scales of the color bar are used in (b)–(d).

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Fig. 5.

Geographical distribution of (a) PV (×10⁻¹¹ m⁻¹ s⁻¹) and water mass transformation (m yr⁻¹) by (b) cabbeling, (c) thermobaricity, and (d) vertical mixing on the neutral surface γⁿ = 27.7 kg m⁻³ in the annual mean. Gray lines are as shown in Fig. 1. Red shading in (b)–(d) corresponds to transformation from the AAIW layer into the UCDW layer, and blue shading from UCDW into AAIW. Note that different scales of the color bar are used in (b)–(d).

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Fig. 6.

(top) Time–density diagram of the monthly (a) water volume tendency, (b) subduction rate by lateral advection and Ekman pumping, (c) eddy-induced subduction rate, (d) water mass formation rate due to cabbeling and thermobaricity, (e) water mass formation rate due to vertical mixing, and (f) volume transport of water by geostrophic mean flow and eddy-induced flow at 70° and 20°S (all in Sv). All data have been binned into 0.05 kg m⁻³ wide density bins. Positive values (red shadings) represent an increase and negative values (gray shading) a decrease of water volume for each density bin. (bottom) The density integral of (a)–(f) within a zonally fixed density range of γⁿ = [27.25–27.7] kg m⁻³: monthly rate (Sv) of (g) volume tendency of water within the AAIW layer (black line) and AAIW volume tendency (yellow line), (h) subduction rate induced by lateral advection and Ekman pumping (black line) and Ekman pumping term alone (gray line), (i) eddy-induced subduction rate using the suppressed $K$ (black line) and the unsuppressed $K$ ₀ (gray dashed line) from Groeskamp et al. (2020), (j) cabbeling and thermobaricity using $K$ (black line) and $K$ ₀ (gray dashed line), (k) vertical mixing using D = 5 × 10⁻⁵ m² s⁻¹, (l) volume transport of water by geostrophic mean flow and eddy-induced flow using $K$ (black solid line), and (m) the residual of the volume budget. Red shadings in (h), (l), and (m) represent uncertainties from computing the geostrophic velocity by using different choices of reference velocity.

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Fig. 7.

Monthly evolution of the residual term derived from Eq. (1) (all in Sv). (a) Residual terms estimated using a constant value of D = 5 × 10⁻⁵ m² s⁻¹ and different eddy-diffusion coefficient fields, i.e., $K$ and $K$ ₀ taken from Groeskamp et al. (2020) and constant values K = 500 and 1000 m² s⁻¹. (b) Residual terms estimated using the eddy-diffusion coefficient $K$ taken from Groeskamp et al. (2020) but changing the vertical diffusion coefficient from constant values of D = 3 × 10⁻⁵ and 5 × 10⁻⁵ m² s⁻¹ to the diffusivity field taken from de Lavergne et al. (2020). (c) As in in (b), but changing $K$ to $K$ ₀.

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Fig. 8.

A sketch of the volume budget within the AAIW density layer in the Southern Ocean (Sv). Blue arrows indicate subduction and red arrows upwelling, both across the deepest mixed layer base. Black anticlockwise arrows indicate isopycnal mixing on the neutral density surfaces of γⁿ = 27.25 and 27.7 kg m⁻³, respectively. The subduction estimates are given in Table 1. The water mass transformation and volume transport estimates are based on Eqs. (5a)–(5c) and (7), respectively. The range of each estimate reflects the choice of different eddy-diffusion coefficients (i.e., K = $K$ , $K$ ₀, 500 m² s⁻¹, and 1000 m² s⁻¹) and vertical diffusion coefficients (i.e., D = 3 × 10⁻⁵ m² s⁻¹, 5 × 10⁻⁵ m² s⁻¹ and D from de Lavergne et al. 2020) used in the calculation. DMLW represents the deep mixed layer water of the SAMW subduction.

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Editorial Type:: Article

Article Type:: Research Article

The Origin and Fate of Antarctic Intermediate Water in the Southern Ocean

Zhi Li

Zhi Li ^aClimate Change Research Centre, University of New South Wales, New South Wales, Australia
^bAustralian Centre for Excellence in Antarctic Science, University of New South Wales, New South Wales, Australia

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https://orcid.org/0000-0002-0166-9289

Sjoerd Groeskamp

Sjoerd Groeskamp ^cDepartment of Ocean Systems, NIOZ Royal Netherlands Institute for Sea Research, Den Burg, Texel, Netherlands

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Ivana Cerovečki

Ivana Cerovečki ^dScripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Matthew H. England

Matthew H. England ^aClimate Change Research Centre, University of New South Wales, New South Wales, Australia
^bAustralian Centre for Excellence in Antarctic Science, University of New South Wales, New South Wales, Australia

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Online Publication:: 02 Nov 2022

Print Publication:: 01 Nov 2022

DOI:: https://doi.org/10.1175/JPO-D-21-0221.1

Page(s):: 2873–2890

Received:: 29 Sep 2021

Accepted:: 12 Jul 2022

Published Online:: 02 Nov 2022

Displayed acceptance dates for articles published prior to 2023 are approximate to within a week. If needed, exact acceptance dates can be obtained by emailing amsjol@ametsoc.org.

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Abstract

Using observationally based hydrographic and eddy diffusivity datasets, a volume budget analysis is performed to identify the main mechanisms governing the spatial and seasonal variability of Antarctic Intermediate Water (AAIW) within the density range γⁿ = (27.25–27.7) kg m⁻³ in the Southern Ocean. The subduction rates and water mass transformation rates by mesoscale and small-scale turbulent mixing are estimated. First, Ekman pumping upwells the dense variety of AAIW into the mixed layer south of the Polar Front, which can be advected northward by Ekman transport into the subduction regions of lighter-variety AAIW and Subantarctic Mode Water (SAMW). The subduction of light AAIW occurs mainly by lateral advection in the southeast Pacific and Drake Passage as well as eddy-induced flow between the Subantarctic and Polar Fronts. The circumpolar-integrated total subduction yields from −5 to 19 Sv (1 Sv ≡ 10⁶ m³ s⁻¹) of AAIW volume loss. Second, the diapycnal transport from subducted SAMW into the AAIW layer is predominantly by mesoscale mixing (2–13 Sv) near the Subantarctic Front and vertical mixing in the South Pacific, while AAIW is further replenished by transformation from Upper Circumpolar Deep Water by vertical mixing (1–10 Sv). Last, 3–14 Sv of AAIW are exported out of the Southern Ocean. Our results suggest that the distribution of AAIW is set by its formation due to subduction and mixing, and its circulation eastward along the ACC and northward into the subtropical gyres. The volume budget analysis reveals strong seasonal variability in the rate of subduction, vertical mixing, and volume transport driving volume change within the AAIW layer. The nonzero volume budget residual suggests that more observations are needed to better constrain the estimate of geostrophic flow and mesoscale and small-scale mixing diffusivities.

Corresponding author: Zhi Li, zhi.li4@unsw.edu.au

Abstract

Corresponding author: Zhi Li, zhi.li4@unsw.edu.au

Keywords: Southern Ocean; Diapycnal mixing; Ekman pumping/transport; Upwelling/downwelling; Intermediate waters; Isopycnal mixing

1. Introduction

Subantarctic Mode Water (SAMW) and Antarctic Intermediate Water (AAIW) are the dominant middepth (500–1000 m) water masses in the Southern Hemisphere oceans (Hanawa and Talley 2001). They play a vital role in Earth’s climate system due to their importance in effecting the global-scale oceanic transport of carbon, heat, and salt (McCartney 1977, 1982; Gruber et al. 2009; Iudicone et al. 2011; Gao et al. 2018; Morrison et al. 2021). Understanding and quantifying processes controlling the variability of SAMW and AAIW is thus necessary for understanding the global ocean’s ventilation and longer-term variability. The goal of this study is to advance our understanding of the spatial and seasonal variability of AAIW using observationally based datasets.

The formation of SAMW in the ocean interior (below the deepest mixed layer base) is dominated by wintertime subduction (Sallée et al. 2010; Li et al. 2021). SAMW is thus characterized by an oxygen maximum, and due to its homogeneity also by the potential vorticity (PV) minimum. AAIW is denser than SAMW and is generally identified by the salinity minimum (Talley 1996). Thus far, a variety of mechanisms have been proposed to play an important role in AAIW formation, but no agreement has been reached.

In the southeast Pacific, SAMW and AAIW share similar salinity and temperature characteristics (McCartney 1977; Hanawa and Talley 2001). Due to this property overlap, it has been suggested that AAIW is a result of the subduction of the densest type of SAMW in the southeast Pacific, feeding AAIW northward into the South Pacific subtropical gyre and eastward via the Drake Passage to the southwest Atlantic (McCartney 1977; England et al. 1993; Talley 1996; Sallée et al. 2010). In contrast to this noncircumpolar view of AAIW formation, some studies proposed that AAIW is instead formed by circumpolar cross-frontal mixing and subsequent subduction of low-salinity Antarctic and Subantarctic Surface Water along the Antarctic Polar Front Zone (Marsh et al. 2000; Sørensen et al. 2001; Sloyan and Rintoul 2001; Santoso and England 2004).

The circumpolar-averaged subduction over the Southern Ocean suggests broad upwelling of Circumpolar Deep Water and AAIW by Ekman pumping, which is then transported northward into a subduction zone of dense SAMW (Sallée et al. 2010). This strong northward Ekman transport is balanced by vigorous processes of eddy diffusion and a southward eddy-induced advection around the Antarctic Circumpolar Current (ACC) region (Sallée et al. 2010; Portela et al. 2020). The eddy-induced advection can contribute to AAIW subduction by transporting the surface water into the ocean interior when entering a region of shoaling mixed layers (see Fig. 3a in Li et al. 2021). Even though the eddy-induced component of subduction was shown to play a key role in AAIW formation, especially in the Drake Passage (Sallée et al. 2010; Sallée and Rintoul 2011; Canuto and Cheng 2019; Naveira Garabato et al. 2009; Hiraike et al. 2016), it is still poorly understood due to the complexities in estimating diffusivities from observations (de Lavergne et al. 2020; Groeskamp et al. 2020). In this study, we use updated observations of hydrography and mesoscale eddy diffusivity to estimate subduction in the AAIW density range using the approach of Sallée et al. (2010).

Other than subduction, the diapycnal volume exchange between the AAIW layer and the Upper Circumpolar Deep Water (UCDW) and SAMW layers has been proposed to be vital for the renewal of AAIW (e.g., Sloyan and Rintoul 2001; Talley et al. 2003; Iudicone et al. 2008a,b, 2011; Downes et al. 2011; Katsumata et al. 2013; Carter et al. 2014; Evans et al. 2014; Portela et al. 2020). These studies have suggested that both isopycnal and diapycnal mixing could induce diapycnal volume transport (quantified by water mass transformation) from the SAMW layer into AAIW and emphasized the importance of cabbeling and thermobaricity for AAIW formation (e.g., Cerovečki and Mazloff 2016; Groeskamp et al. 2016). Cabbeling is the process in which the mixing of two water parcels with equal density, but different temperature and salinity, results in a water parcel denser than the original density. Groeskamp et al. (2016) showed that cabbeling yields a transformation rate of 10–15 Sv (1 Sv ≡ 10⁶ m³ s⁻¹) from the SAMW layer into AAIW and a formation rate of 8.7 Sv within the AAIW layer. Thermobaricity is the process in which the mixing of two water parcels with equal density, but different temperature and pressure, results in a water parcel either lighter or denser than the original density. Cabbeling and thermobaricity are both a consequence of a combination of eddy mixing and the nonlinear equation of state (McDougall 1984, 1987) and considered in the estimate of water mass transformation by isopycnal mixing in this study.

Turbulent mixing from breaking oceanic internal waves drives a vertical transport of freshwater, heat, carbon, and other tracers in the ocean, thereby playing an important role in mixing over the global ocean (de Lavergne et al. 2020; Whalen et al. 2020). Small-scale turbulent mixing is also found to be significant in the Southern Ocean overturning circulation and for AAIW formation (Meyer et al. 2015). The resulting diapycnal transport from UCDW into AAIW can yield 20 Sv of volume increase in the AAIW layer (Meyer et al. 2015). The importance of diapycnal processes for AAIW formation is also supported by the overall upwelling in the AAIW density range (Sallée et al. 2010; Portela et al. 2020), i.e., the diapycnal volume transport into the AAIW layer can compensate the volume loss of the interior AAIW due to upwelling into the mixed layer. Despite all this progress, a number of inconsistences and open questions remain related to the diapycnal exchanges between SAMW, AAIW, and UCDW. For instance, the sign of diapycnal exchanges of AAIW with SAMW and UCDW obtained in past studies, using different model outputs and observations, remains inconsistent. Comparison of past results is further complicated by the fact that different density ranges have been considered in the water mass transformation analysis. Furthermore, in previous work, the water mass transformation within the mixed layer and in the ocean interior were usually not considered separately, and relatively few studies have directly reconciled volumetric changes of AAIW with AAIW formation mechanisms. In short, the mechanisms and rate of AAIW formation remain unclear.

The above studies have provided insights and identified where we lack observational-based constraints in estimating and understanding the mechanisms controlling AAIW variability. For example, relatively little attention has been paid to AAIW formation on monthly time scales (Evans et al. 2014, 2018). This was partly due to the scarcity of data and a short observational record in the Southern Ocean. The goals of the present study are therefore 1) to document the spatial variability of AAIW and compare it with the distribution of subduction and water mass transformation due to isopycnal mixing (i.e., cabbeling and thermobaricity), and diapycnal mixing (i.e., vertical mixing) using observationally based datasets, and 2) to evaluate the mechanisms controlling the seasonality of the AAIW formation in the ocean interior by conducting a monthly mean volume budget analysis within the AAIW density range. The seasonal volume budget focuses only on the ocean interior due to complicated mixing processes within the mixed layers. Thus, the variability in water mass transformation due to meltwater (Close et al. 2013; Abernathey et al. 2016) and atmospheric freshwater fluxes (Evans et al. 2018) are not included in the volume budget analysis. Instead, we focus on quantifying and comparing the subduction process and the interior diapycnal exchanges in the seasonal cycle of AAIW formation.

The hydrographic data used in this study are described in section 2. The methods of the volume budget analyses are described in section 3. We compare the spatial variability of AAIW with formation processes by subduction and water mass transformation and conduct a seasonal volume budget analysis within the AAIW density range in section 4. A discussion and a summary of our findings are provided in sections 5 and 6, respectively.

2. Hydrographic and diffusivity data

We use monthly means of the World Ocean Atlas 2018 (WOA18), which is a set of objectively analyzed (1° grid) climatological fields (2005–17) of in situ temperature, practical salinity, and other tracers at standard depth levels for the World Ocean (Boyer et al. 2018). WOA18 provides data for all latitudes of the global ocean and depths down to 5500 m, covering all locations with AAIW, unlike Argo, which is limited to regions north of 65°S and above 2000 m. Having a global coverage hydrography enables us to identify and track the volumetric change of AAIW and estimate subduction and water mass transformation rates for studying AAIW formation. The TEOS-10 software (IOC et al. 2010; McDougall and Barker 2011) is applied to convert WOA18 data to Conservative Temperature (Θ; McDougall 2003) and Absolute Salinity (S_A; McDougall et al. 2012) and achieve static stability on time scales of months by applying a vertical stabilization algorithm (Barker and McDougall 2017). Then the surface-referenced potential density σ₀ and neutral density γⁿ are calculated (Jackett and McDougall 1997).

The horizontal wind stress vector τ averaged for the period 2005–17 is obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) to estimate the monthly mean Ekman pumping velocity, w_EK = −curl[τ/(ρ₀f )], where f is the planetary vorticity and ρ₀ is used as the surface-referenced spatially varying potential density, ρ₀ = σ₀ + 1000 kg m⁻³, at 10-m depth. Since the penetration of shortwave radiation changes the temperature and density of seawater, thus affecting water mass transformation (Groeskamp and Iudicone 2018), the shortwave radiative heat flux Q_SW is obtained from ERA-Interim to include the penetrative effects of shortwave radiation below the mixed layer.

Water mass transformation by cabbeling and thermobaricity depends strongly on the spatial structure and magnitude of the mesoscale eddy diffusivity K. To examine this sensitivity, we employ four different choices of K. Results are first obtained using a recent estimate of K from Groeskamp et al. (2020) (hereafter referred to as “ $K$ ”), who extended a mixing length theory with a mean-flow suppression theory (Ferrari and Nikurashin 2010) to estimate the full-depth mesoscale eddy diffusivity from WOA18 and altimeter measurements. Both the suppressed diffusivity $K$ and the unsuppressed diffusivity $K$ ₀ have been considered. For a more detailed sensitivity test, we then use constant values of K = 500 and 1000 m² s⁻¹ (e.g., Groeskamp et al. 2016, 2017). For internal consistency, once selected, we use the same mesoscale eddy diffusivity when estimating eddy-induced mixing, eddy-induced transport, and eddy-induced subduction. The spatially varying $K$ and $K$ ₀ from Groeskamp et al. (2020) were originally constructed to quantify eddy-induced mixing, rather than eddy-induced transport and subduction. The constant values of K = 500 and 1000 m² s⁻¹ provide a sensitivity test for the estimate of eddy-induced transport and subduction using $K$ and $K$ ₀ (e.g., Sallée and Rintoul 2011). As seen from Fig. 1 of Groeskamp et al. (2020), the value of $K$ is close to the constant value of K = 500 m² s⁻¹ and the value of $K$ ₀ is close to 1500 m² s⁻¹, but spatially varying coefficients can significantly improve the regional distribution of eddy-induced mixing and subduction (Sallée and Rintoul 2011).

Calculating the effects of small-scale turbulent mixing requires an estimate of full-depth turbulent diffusivity D. In this study, we make use of a constant value of D = 5 × 10⁻⁵ m² s⁻¹ and also provide estimates by employing a constant value of D = 3 × 10⁻⁵ m² s⁻¹ and a geographically varying vertical diffusion coefficient D based on tidal mixing (de Lavergne et al. 2020) for comparison (Groeskamp et al. 2016). The turbulent diffusivity from de Lavergne et al. (2020) is obtained by applying a tidal mixing parameterization to an observational climatology of stratification, accounting for both bottom-intensified local mixing and stratification-dependent remote mixing. The value of this diffusivity varies widely in the horizontal and vertical, from 10⁻⁶ up to 10⁻³ m² s⁻¹ in localized hotspots, and sharply increases near 2500-m depth from order 10⁻⁵ m² s⁻¹ above to order 10⁻⁴ m² s⁻¹ below, depending on both the bottom topography and stratification (Fig. 17 of de Lavergne et al. 2020).

3. Volume budget

Based on WOA18 data, we performed a seasonal volume budget analysis for the AAIW density layer in the interior ocean within a domain between 20° and 70°S. The monthly water mass volume tendency [∂(ΔV)]/∂t within two isosurfaces γⁿ − (Δγⁿ)/2 and γⁿ + (Δγⁿ)/2 is assessed as a combination of 1) the inflow of volume crossing the upper boundary, i.e., monthly subduction ΔS through the base of the deepest mixed layer, 2) the interior water mass formation ΔG = G(γⁿ − Δγⁿ/2) − G(γⁿ+ Δγⁿ/2), and 3) the outflow of volume crossing the interior domain boundary via ocean circulation, Δψ (see Walin 1982; Nurser et al. 1999; Groeskamp et al. 2019b; Portela et al. 2020).

The volume budget can be expressed as

\underset{volume tendency}{\underset{︸}{\partial (Δ V) / \partial t}} = \underset{subduction}{\underset{︸}{Δ S Δ A_{ML}}} + \underset{water mass formation}{\underset{︸}{Δ G}} + \underset{volume transport}{\underset{︸}{Δ ψ}},

(1)

where ΔA_ML is the surface area of the deepest mixed layer base. G is the water mass transformation due to isopycnal mixing (i.e., cabbeling and thermobaricity), diapycnal mixing (i.e., vertical mixing), and shortwave penetration fluxes, and ΔG is the convergence of G, which quantifies the water mass formation (or destruction) within the layer bounded by (γⁿ − Δγⁿ/2, γⁿ + Δγⁿ/2). The term Δψ is the exchange volume transport across the domain boundaries: 20°S to the north and 70°S to the south. Since our control volume considered in the budget calculation is located below the deepest mixed layer, the water mass transformation by air–sea buoyancy fluxes, sea ice melting, and mixing within the mixed layer are not included. Instead, the imprint of the atmospheric fluxes into the ocean is accounted for by diagnosing subduction (as also seen in Portela et al. 2020). Consequently, the water mass transformation term excludes the exchanges between the MLD and interior waters.

a. Subduction

Subduction can be thought of as an injection of fluid from the surface mixed layer into the ocean interior (Cushman-Roisin 1987). The rate of subduction is usually computed using a kinematic approach that estimates the rate at which fluid passes between the surface mixed layer and the ocean’s interior (Cushman-Roisin 1987; Williams 1991; Marshall et al. 1993; Marshall et al. 1999). Equation (2) from Sallée et al. (2010) distinguishes the three main components of the total mean subduction rate

\underset{Subduction}{\underset{︸}{Δ S}} = \underset{Lateral advection}{\underset{︸}{u_{ml} \cdot \nabla h + u_{sth} \cdot \nabla (H - h)}} + \underset{Vertical}{\underset{︸}{w_{H}}} + \underset{Eddy induced}{\underset{︸}{\nabla \cdot (u_{H}^{*} H)}},

(2)

where h is the monthly MLD and H is the maximum MLD, and

u_{H}^{*}

indicates the eddy-induced velocity within the deepest mixed layer (see section 3c; Gent and McWilliams 1990; Gent et al. 1995). The lateral advection term is given by monthly mixed layer geostrophic velocity u_ml and velocity in the seasonal thermocline, between the base of the monthly mixed layer and the base of the deepest mixed layer u_sth, and horizontal gradients of the monthly mixed layer h and the seasonal thermocline H − h.

The vertical velocity w_H is comprised of the Ekman pumping (w_EK) and the vertical velocity component estimated using the linear vorticity balance (Sverdrup balance) within the mixed layer (Marshall et al. 1993; Sallée et al. 2010), namely,

w_{H} = w_{EK} - \frac{β}{f} [υ_{ml} h + υ_{sth} (H - h)],

(3)

where β is the meridional gradient of the planetary vorticity f, and υ_ml and υ_sth are the meridional velocity within the mixed layer and seasonal thermocline, respectively.

The eddy-induced subduction is defined as the convergence of the horizontal eddy-induced transport above the base of the deepest mixed layer. Following Sallée et al. (2010), the eddy-induced transport in the mixed layer can be parameterized as

u_{H}^{*} H = {[K S l^{nloc}]}_{z = H}

. To minimize numerical error, Sl^nloc is the neutral slope estimated following a vertically nonlocal method based on a search algorithm (VENM) in Groeskamp et al. (2019a). The eddy-induced subduction is then expressed as (Sallée et al. 2010)

Δ S_{eddy} = \nabla \cdot {[K S l^{nloc}]}_{z = H} = \frac{\partial}{\partial x} {[K {Sl}_{x}^{nloc}]}_{z = H} + \frac{\partial}{\partial y} {[K {Sl}_{y}^{nloc}]}_{z = H},

(4)

where

{Sl}_{x}^{nloc}

and

{Sl}_{y}^{nloc}

are neutral slopes in the zonal and meridional directions. In this study, subduction is positive downward, indicating the volume flux of downwelling water entering the permanent thermocline. Following Sallée et al. (2010), the processes opposing subduction, which transfer water from the interior thermocline into the mixed layer, will be called upwelling in this study, similar to the terms “obduction” and “entrainment” used in some past studies (e.g., Qiu and Huang 1995; Li et al. 2021).

b. Water mass transformation

The water mass transformation due to cabbeling G_Cb, thermobaricity G_Tb, vertical mixing G_Ve, and shortwave radiation depth penetration G_SW is given by (Groeskamp et al. 2019b)

G_{Cb} (γ^{n}) = \frac{\partial}{\partial γ^{n}} {\int \int \int}_{V (γ_{*}^{n} \leq γ^{n})} \frac{b γ_{*}^{n}}{ρ} [ρ K C_{b} {| \nabla_{N} Θ |}^{2}] d V,

(5a)

G_{Tb} (γ^{n}) = \frac{\partial}{\partial γ^{n}} {\int \int \int}_{V (γ_{*}^{n} \leq γ^{n})} \frac{b γ_{*}^{n}}{ρ} [ρ K T_{b} \nabla_{N} P \cdot \nabla_{N} Θ] d V,

(5b)

G_{Ve} (γ^{n}) = \frac{\partial}{\partial γ^{n}} {\int \int \int}_{V (γ_{*}^{n} \leq γ^{n})} \frac{b γ_{*}^{n}}{ρ} [α \nabla \cdot (- ρ D \frac{\partial Θ}{\partial z}) - β \nabla \cdot (- ρ D \frac{\partial S_{A}}{\partial z})] d V, and

(5c)

G_{SW} (γ^{n}) = \frac{\partial}{\partial γ^{n}} {\int \int \int}_{V (γ_{*}^{n} \leq γ^{n})} \frac{b γ_{*}^{n}}{ρ} {\frac{α}{C_{p}} \nabla \cdot [Q_{SW} F (z)]} d V .

(5d)

Here b = |∇γⁿ|/|∇ρ_ℓ| is the ratio required to construct an approximate global neutral surface from surfaces that are only locally defined (Iudicone et al. 2008a), ρ_ℓ is the locally referenced potential density and is used as the in situ density ρ in this study, P is the sea pressure, dV is the volume of water within the density range of

γ_{*}^{n} \leq γ^{n}

, C_b is the cabbeling coefficient, T_b is the thermobaricity coefficient, C_p is the specific heat, and α and β are the thermal and haline expansion coefficients, respectively. The terms ∇_NΘ and ∇_NP indicate the gradients of Θ and P, respectively, along a neutral surface. For the WOA18 dataset we calculate monthly neutral slopes and tracer gradients using the VENM algorithm (Jackett and McDougall 1997; Groeskamp et al. 2019a). The exponential decay function,

F (z) = R \exp (- z / h_{1}) + (1 - R) \exp (- z / h_{2})

, in which R = 0.58, h₁ = 0.35 m, and h₂ = 23 m, redistributes the incoming shortwave radiation with depth (Paulson and Simpson 1977). In deep mixed layer regions of SAMW and AAIW, the effects of shortwave radiation penetration below the deepest mixed layer are relatively small (Fig.3c of Groeskamp and Iudicone 2018) but are included for completeness in the budget. In the discrete approximations of Eqs. (5a)–(5d) in the calculation, water mass transformation is partitioned into Δγⁿ = 0.05 kg m⁻³ density bins, i.e.,

γ_{*}^{n} \in [γ^{n} - Δ γ^{n} / 2, γ^{n} + Δ γ^{n} / 2]

. Positive values indicate transformation toward increasing density.

c. Geostrophic and eddy-induced transport

Geostrophic velocity is obtained from the thermal-wind relation by assuming a level of no motion at 1500, 2500, and 4000 m, respectively. We also repeat calculations by adding the mean reference velocity at 1000 m, obtained using data of the trajectories from Argo floats (Lebedev et al. 2007), to the derived geostrophic velocity by assuming a level of no motion at 1000 m, to get a full-depth geostrophic velocity field. The geostrophic velocity presented in this paper uses the mean of these four derived velocity fields. The absolute geostrophic velocity at 1000 dbar (Gray and Riser 2014) was also used to repeat the calculations for lateral advection, and the results were found to be overall robust to this choice. We use the approximate isopycnal geostrophic streamfunction defined in McDougall and Klocker (2010) [see Eq. (3.30.1) of IOC et al. 2010; Herraiz-Borreguero and Rintoul 2011] to indicate the geostrophic circulation of AAIW on neutral density surfaces. This is derived from Θ, S_A, and P fields using the TEOS-10 software (IOC et al. 2010). Note that the geostrophic streamlines shown in Fig. 1b are in contrast estimated based on a 2500-m level depth of no motion. This may slightly impact the representativeness of the streamfunction in portraying the actual circulation if a different depth of no motion is assumed (Herraiz-Borreguero and Rintoul 2011).

Following Gent and McWilliams (1990) and Gent et al. (1995), the eddy-induced horizontal velocity is expressed as

u^{*} = - \frac{\partial}{\partial z} (K {Sl}_{x}^{nloc}), υ^{*} = - \frac{\partial}{\partial z} (K {Sl}_{y}^{nloc}),

(6)

where u^* and υ^* are the eddy-induced flow velocity in the zonal and meridional directions. Here the volume transport across a vertical section in the ocean interior is calculated as

Δ ψ = \iint (υ + υ^{*}) d A,

(7)

where υ is the geostrophic flow velocity in the meridional direction and dA is the area of a vertical section. Positive values indicate transport into the domain of consideration, yielding volume increase.

4. Results

a. Mean features of the AAIW distribution

In this study we define AAIW as low-salinity (S_A ≤ 34.6 g kg⁻¹) water within the density range of γⁿ = (27.25–27.7) kg m⁻³. We additionally adopt a “below the deepest mixed layer” criterion for identifying AAIW (e.g., Portela et al. 2020). Low-salinity water (S_A ≤ 34.6 g kg⁻¹) within the deepest mixed layer and within the AAIW density range of γⁿ = (27.25–27.7) kg m⁻³ is identified as Antarctic Surface Water (AASW), which is suggested to be the major source of AAIW formation both by direct subduction and indirectly via cross-frontal mixing at the Antarctic Polar Front Zone (e.g., Sørensen et al. 2001; Santoso and England 2004; Naveira Garabato et al. 2009; Holte et al. 2013; Carter et al. 2014; Evans et al. 2014). Here we refer to the AAIW formation by subduction of AASW as “AAIW subduction” for simplicity. The SAMW has been defined as low-PV water [PV < 7 × 10⁻¹¹ m⁻¹ s⁻¹; PV = (f/ρ₀)(∂ρ₀/∂z)] within the density range of γⁿ = (26.6–27.25) kg m⁻³ (Li et al. 2021). Since light AAIW isopycnals gradually disappear to the south of the Polar Front, we show geostrophic streamlines on the neutral density surfaces of γⁿ = 27.35 and 27.6 kg m⁻³ in Fig. 1 to separately indicate the geostrophic circulation of light and dense layers of AAIW.

AASW mainly resides poleward of the Polar Front, with wide regions of thick AASW layers that extend to the Antarctic continent (e.g., 60°–150°E and 160°–70°W) (Fig. 1c). The geostrophic streamlines on the south side of the Polar Front, especially the streamlines from the Amundsen Sea and the Bellingshausen Sea to the Drake Passage, suggest that AASW can be transported to the Drake Passage (Fig. 1b) and possibly subduct around the Drake Passage (e.g., Sallée et al. 2010). The cross-frontal exchange of cool, fresh AASW also contributes to the formation of SAMW and AAIW over the southeast Pacific (Sloyan and Rintoul 2001; Holte et al. 2013; Carter et al. 2014) and over the circumpolar Southern Ocean (Santoso and England 2004).

Below the AASW, only thin layers of AAIW are found south of the Polar Front (Fig. 1a). Thick AAIW layers (blue shading in Fig. 1a) mainly reside north of the Subantarctic Front, with the thickness increasing from the central Indian Ocean toward the Drake Passage and the Atlantic Ocean. AAIW thickness can be up to ∼600 m, reaching its maximum in the southeast Pacific and Atlantic Ocean (see also Portela et al. 2020, their Fig. 7a). The overlap of AASW and AAIW thickness indicates possible hotspots of AAIW subduction, which occurs mainly over the South Pacific from 180° to the Drake Passage and between the Subantarctic and the Polar Fronts (yellow contours in Fig. 1; Fig. 2; see also Sallée et al. 2010, their Fig. 8). The AAIW thickness (Fig. 1a) and the geostrophic streamlines (Fig. 1b) north of the Subantarctic Front suggest that branches of AAIW could be advected from the northern limit of the ACC toward the subtropical gyres, such as from northwest of the Kerguelen Plateau (∼70°E) to the west of Tasmania (∼150°E), 140°–70°W north of 50°S in the central and southeast Pacific Oceans, and 30°W–15°E to the west of Africa (Santoso and England 2004). In the southeast corner of the Pacific basin, the location of the northern AAIW branch extending to the subtropical Pacific consists of the “exchange window” located east of 90°W, identified by Iudicone et al. (2007). The Pacific AAIW that reaches the Tasman Sea could reenter the Southern Ocean via either the Tasman Leakage or north of New Zealand, after completing a circuit of the southern subtropical gyres (Ridgway and Dunn 2007; Bostock et al. 2013). South of the exchange window, the ACC transports the southern branch of AAIW and AASW eastward though the Drake Passage, turning northward in the South Atlantic (Hanawa and Talley 2001; Santoso and England 2004; Sallée et al. 2010), which could possibly explain the increase in AAIW thickness after leaving the Drake Passage.

In this section, we aim to advance our understanding of the climatological features of AAIW distribution, as determined by its circulation and formation. By combining the AAIW distribution with geostrophic streamlines, our results show that AAIW is transported both eastward along the ACC and northward through the exchange windows into the subtropical gyres, in agreement with past work (e.g., Sloyan and Rintoul 2001; Santoso and England 2004). Our results also suggest that the geostrophic streamlines within the light AAIW layer are mainly restricted to the region equatorward of the Polar Front (red-brown lines in Fig. 1b) and the geostrophic circulation of the dense AAIW and AASW occurs mainly poleward of the Polar Front and zonally along the ACC (blue lines in Fig. 1b). The AAIW formation processes via subduction over the South Pacific and via diapycnal exchange with SAMW and UCDW layers are described below.

b. Spatial structures in the Southern Ocean subduction

Subduction of AAIW is often identified as subduction of the densest variety of SAMW because of the similarities in their low PV and salinity characteristics in the southeast Pacific (McCartney 1977; Hanawa and Talley 2001). However, the SAMW density layer is mostly located within and north of the region of deepest wintertime mixed layers (see Fig. 2 in Li et al. 2021), while the subduction/upwelling of AAIW occurs further poleward in the region of southward shoaling mixed layers [see also Fig. 3a in Li et al. (2021) and Fig. 9a in Sallée et al. (2010)]. Thus, northward Ekman transport and the southward eddy-induced transport play opposite roles in the subduction of SAMW and AAIW. The subducted low-salinity water in the dense SAMW layer could supply AAIW via diapycnal exchanges (Hanawa and Talley 2001; Downes et al. 2011), which makes it difficult to differentiate between the subduction of AAIW and SAMW. In this section we focus on the subduction of SAMW and AAIW, while the analysis of the diapycnal exchange between the SAMW and AAIW is presented in the next section.

The meridional component of lateral advection reveals large regional variability south of the Subantarctic Front but shows strong uniform subduction to the north over the SAMW formation region (Fig. 2a). The zonal component of lateral advection caused by the eastward-flowing ACC dominates the SAMW subduction and significantly contributes to AAIW subduction around the Drake Passage (Fig. 2b, Table 1) (England et al. 1993; Santoso and England 2004; Naveira Garabato et al. 2009). The meridional component of eddy-induced subduction reveals a downwelling south of the Subantarctic Front and upwelling north of the Subantarctic Front (Fig. 2c), in agreement with Sallée et al. (2010). This meridional sign change is largely associated with strong meridional MLD gradients around the ACC region, which also suggests that the subduction of AAIW by eddy-induced flow could be circumpolar. The circumpolar eddy-induced subduction of AASW (Fig. 2c, Table 1) could supply AAIW within the ACC, but the injection of AAIW from the ACC region into the subtropical gyres is limited to certain exchange windows, as discussed in section 4a. Zonal variability of the eddy-induced subduction has a smaller magnitude compared to that of lateral advection (Figs. 2b,d).

Table 1

Estimates of the annual mean lateral advection, eddy-induced subduction, and Ekman pumping within the SAMW and AAIW density ranges, respectively, as a function of choices of geostrophic velocity (top section) and mesoscale eddy diffusivity K (middle section). All values are given in Sverdrups. Positive values indicate subduction. Geostrophic velocity is obtained from either the thermal-wind relation by assuming a level of no motion at 1500, 2500, and 4000 m, respectively, or using the mean reference velocity at 1000 m obtained from Argo float trajectories (Lebedev et al. 2007).

Ekman pumping has a zonally symmetric pattern over the Southern Ocean (Fig. 2e). The total subduction exhibits opposite sign patterns meridionally distributed over the region of AAIW subduction, with downwelling due to both the eddy-induced flow and the mean flow occurring between the Subantarctic and Polar Fronts, and upwelling driven by Ekman pumping dominating further poleward (Fig. 2f). The downwelling by lateral advection and eddy-induced subduction over the South Pacific and Drake Passage exhibits a similar distribution to the thick layers of overlap between AASW and AAIW and thus contributes to the subduction of AAIW (Figs. 1 and 2).

The circumpolar integral of Ekman pumping is estimated to induce 17.8 Sv of subduction within the SAMW density range and 24.7 Sv of upwelling within the AAIW density range (Table 1), consistent with the estimate of 25 Sv of subduction north of the ACC to 35°S and 34 Sv of upwelling south of the ACC in Sallée and Rintoul (2011). As a result, Ekman pumping [Eq. (2)] is the dominant subduction and upwelling term in the spatial integral for the SAMW and AAIW density classes, respectively.

The lateral advection estimates [Eq. (2)] require calculations of the MLD and geostrophic velocities. The horizontal velocity is obtained from the thermal-wind relation as described in section 3c. The MLD is defined as the depth at which σ₀ is 0.03 kg m⁻³ greater than the value of σ₀ at 10-m depth (de Boyer Montégut et al. 2004). Previous studies using the same computation method have reported that subduction estimates are sensitive to the MLD field and a smoothing of the MLD is needed to obtain subduction estimates similar to Sallée et al. (2010) (Portela et al. 2020). We have tested a 3-grid and 5-grid point spatial smoothing of the MLD field and found that the spatial smoothing can reduce lateral advection estimates by 20%–50%, making the lateral advection estimate strongly dependent on the somewhat arbitrary choice of the spatial smoothing scale. Therefore, we only use the original MLD field to estimate the lateral advection (Table 1). The resulting lateral advection estimates yield −13.5 ± 4.4 and 3.4 ± 1.7 Sv of subduction within the SAMW and AAIW density ranges, respectively, and both estimates are comparable with those of Sallée et al. (2010).

Eddy-induced subduction depends strongly on the magnitude and spatial structure of the mesoscale eddy diffusivity (Sallée and Rintoul 2011; Hiraike et al. 2016; Canuto and Cheng 2019; Groeskamp et al. 2020) as well as on the neutral slope calculation [Eq. (4)]. Thus, regional intensifications of the eddy-induced subduction occur in the high eddy kinetic energy regions along the ACC (Sallée and Rintoul 2011). In this study, we combine a time and spatially varying neutral slope estimate (Groeskamp et al. 2019a) with spatially varying mesoscale diffusion coefficients $K$ and $K$ ₀ from Groeskamp et al. (2020) to estimate the eddy-induced flux across the mixed layer base. We have additionally carried out sensitivity tests, using constant values of K = 500 and 1000 m² s⁻¹. The eddy-induced subduction rates obtained within the AAIW density range are 3.3 Sv using $K$ , 4.4 Sv using K = 500 m² s⁻¹, 8.8 Sv using K = 1000 m² s⁻¹, and 23.9 Sv using K = $K$ ₀ (presented in Fig. 2). Estimates of the eddy-induced subduction within the AAIW density range are comparable with the eddy-induced subduction rate of 17 Sv integrated south of 35°S in Sallée and Rintoul (2011) and summarized in Table 1.

c. Diapycnal exchange with SAMW and UCDW

The diapycnal exchange of AAIW with SAMW and UCDW has been suggested to be one of the main sources for the formation and renewal of AAIW (Sloyan and Rintoul 2001; Iudicone et al. 2008b; Downes et al. 2011; Cerovečki et al. 2013; Carter et al. 2014). Within the light AAIW layer of γⁿ = (27.25–27.4) kg m⁻³, low-PV waters can be found in the South Pacific within 63°–52°S and in the subtropical Pacific within 45°–20°S (black boxes in Fig. 3b), suggesting possible diapycnal exchange between SAMW and AAIW. On the other hand, the northward decreasing PV and increasing salinity near the neutral density surface of γⁿ = 27.7 kg m⁻³, especially north of 40°S (Figs. 3a–f), suggest mixing between AAIW and UCDW. To determine the diapycnal exchange of AAIW with SAMW and UCDW, here we provide the estimates of water mass transformation by isopycnal mixing and vertical mixing as a function of depth and latitude (Figs. 3g–l) and on the neutral surfaces γⁿ = 27.25 and 27.7 kg m⁻³, identified as the boundaries between these water masses (Figs. 4 and 5). All the water mass transformation estimates provided in this section and in Table 2 are obtained using K = $K$ and D = 5 × 10⁻⁵ m² s⁻¹.

Table 2

Water mass transformation rate (Sv) due to cabbeling, thermobaricity, and vertical mixing on the neutral surfaces of γⁿ = 26.6, 27.25, and 27.7 kg m⁻³ in the annual mean. All estimates are based on K = $K$ and D = 5 × 10⁻⁵ m² s⁻¹, and are zonally integrated over the circumpolar Southern Ocean. Positive corresponds to transformation toward increasing density.

The SAMW formation within the mixed layer is predominantly driven by diapycnal volume transport due to wintertime surface buoyancy loss (Kwon 2013; Li et al. 2021). Positive water mass transformation by cabbeling, thermobaricity, and vertical mixing between the mixed layer SAMW and AASW (Figs. 3g–l, Table 2) would further redistribute a large portion of the effects of direct air–sea forcing on SAMW to AASW and result in the renewal of AAIW by subduction of AASW (Sloyan and Rintoul 2001). Beneath the mixed layer, the diapycnal transport from SAMW to AAIW still takes place over the course of the year (Figs. 3g–l, Table 2). Here we show that positive water mass transformation, i.e., diapycnal transport toward denser layers, by isopycnal mixing is mainly restricted to the ACC region, with a transformation rate of 2.5 Sv dominated by cabbeling on the neutral surface γⁿ = 27.25 kg m⁻³ (2 Sv; Table 2; Figs. 3g–i and 4b–d). Positive water mass transformation by vertical mixing on the neutral surface γⁿ = 27.25 kg m⁻³ occurs mainly in the South Pacific (Figs. 3j–l and 4d) and resembles the pathway of South Pacific AAIW (Fig. 1b).

Because of the similar salinity and temperature characteristics of SAMW and AAIW in the southeast Pacific (e.g., McCartney 1977; Hanawa and Talley 2001; Sloyan et al. 2010; Portela et al. 2020), here we use both low-PV (PV < 7 × 10⁻¹¹ m⁻¹ s⁻¹) and low-salinity (S_A ≤ 34.6 g kg⁻¹) constraints within the density range of γⁿ = (27.1–27.4) kg m⁻³ to approximately indicate this property overlap of SAMW and AAIW, which can be considered as a transition layer between SAMW and AAIW (Portela et al. 2020). The thickness of the property overlap reveals two branches starting from the southeast corner of the Pacific basin and extending to the subtropical Pacific and Atlantic, respectively (Fig. 4a). The northern branch of the property overlap extends from the southeast Pacific to the subtropical Pacific and exhibits a similar distribution to the positive water mass transformation by vertical mixing (Figs. 4a,d). The westward branch of the property overlaps near the Subantarctic Front, which extends over the South Pacific and Atlantic Oceans, exhibits a similar distribution to the positive water mass transformation by cabbeling and thermobaricity (Figs. 4a–c). These similarities in spatial pattern suggest that ocean mixing plays a key role in the existence of the property overlap by transforming SAMW into the AAIW layer, while the subduction of low-PV water within the layer γⁿ = (27.25–27.4) kg m⁻³ can be another possible means to form the property overlap in the southeast Pacific (Figs. 2 and 3b).

We next consider the water mass transformation on the neutral surface γⁿ = 27.7 kg m⁻³ to examine the diapycnal exchange between AAIW and UCDW. The diapycnal transport from the AAIW layer into UCDW by cabbeling and thermobaricity occurs mainly near the Polar Front (red shading in Figs. 5b,c). On the other hand, positive water mass transformation by vertical mixing takes place close to the Antarctic continent, where the stratification is relatively strong near the neutral surface γⁿ = 27.7 kg m⁻³ (Figs. 3a–c,j–l and 5a,d). In contrast, wide regions of negative water mass transformation by vertical mixing can be found in the rest of the Southern Ocean and in the subtropics (blue shading in Figs. 3j–l and 5d), transforming ∼10 Sv of UCDW into the AAIW layer (Table 2). The UCDW has relatively low PV and high salinity characteristics compared to AAIW (Figs. 3a–f). Therefore, the northward decreasing PV and increasing salinity near γⁿ = 27.7 kg m⁻³ as well as the northward shoaling isopycnals near γⁿ = 27.7 kg m⁻³ suggest that vertical mixing plays a role in increasing the volume of the AAIW layer by transforming water from the UCDW layer (Figs. 3j–l and 5a,d).

d. Seasonal volume budget for AAIW layer

We next consider the density distribution of the spatial integral (over 70°–20°S) of individual terms in the monthly mean volume budget given by Eq. (1), namely, volume tendency, subduction, water mass formation, and meridional volume transport rates (Figs. 6a–f). These terms are subsequently integrated over the AAIW density range of γⁿ = (27.25–27.7) kg m⁻³ (Figs. 6g–l). Positive values indicate a volume increase. The residual term (Fig. 6m) is computed as the difference between the monthly volume tendency and all the terms on the right-hand side of Eq. (1). The water mass formation by shortwave penetration is included in the volume budget but not shown in Fig. 6 due to its relatively small magnitude (−0.8 Sv in the annual mean). Lateral advection and volume transport are computed using the average of horizontal velocities derived from the thermal-wind relation (as described in section 3c), while the uncertainties obtained using different choices of the reference velocity are shown as shadings in Figs. 6h,l,m. The most remarkable pattern is the strong seasonal change in the rate of subduction (Figs. 6h–i), vertical mixing (Fig. 6k), and volume transport (Fig. 6l) in driving the volume tendency (Fig. 6g).

The volume tendency of water within the AAIW density range reveals a period of volume increase of increasingly denser water over June–November (Fig. 6a, black line in Fig. 6g), while the volume of AAIW increases from July to January and decreases from February to June (yellow line in Fig. 6g). Here the salinity constraint used to define AAIW (section 4a) is only imposed when estimating the AAIW volume (yellow line in Fig. 6g). The month-to-month variations of each term in Eq. (1) are then quantified and compared to evaluate the role of each process in determining the volume tendency of water within the AAIW density range.

The subduction by lateral advection and Ekman pumping is the largest term in the monthly volume budget and shows a strong peak in May and a weak peak in September (Figs. 6b,h). The spatial integral of vertical Ekman velocity dominates the upwelling within the AAIW layer (gray line in Fig. 6h), occurring most strongly in the dense AAIW class of γⁿ = (27.5–27.7) kg m⁻³ (Fig. 6b) near the Antarctic continent (Fig. 2e). In contrast, the eddy-induced subduction that occurs mostly between the Subantarctic and Polar Fronts (Fig. 2c) is particularly strong within the light AAIW class of γⁿ = (27.25–27.45) kg m⁻³ (Fig. 6c). Eddy-induced subduction within the AAIW layer reveals a marked seasonal cycle (Figs. 6c,i), which corresponds closely to the monthly AAIW volume tendency (Fig. 6g). The eddy-induced subduction computed from the suppressed eddy diffusivity $K$ (black line in Fig. 6i) is comparable with the lateral advection estimate (e.g., 3.4 versus 3.4 ± 1.7 Sv, Table 1). However, the estimate of eddy-induced subduction depends strongly on the choice of eddy-diffusion coefficient (Sallée and Rintoul 2011; Hiraike et al. 2016; Canuto and Cheng 2019). For example, the eddy-induced subduction computed from the unsuppressed eddy diffusivity $K$ ₀ (gray dashed line in Fig. 6i) shows a greater magnitude than that from $K$ (23.9 versus 3.4 Sv, Table 1). The circumpolar-integrated subduction yields an overall upwelling over the AAIW density range, also depending on the eddy-diffusion coefficient used, as described later (see also Table 1).

The interior water mass formation due to cabbeling and thermobaricity within the AAIW density range of γⁿ = (27.25–27.7) kg m⁻³ is weak (Fig. 6d). In contrast, the formation due to vertical mixing is much stronger and occurs mostly within the light AAIW class of γⁿ = (27.25–27.45) kg m⁻³ and near the neutral surface γⁿ = 27.7 kg m⁻³, indicating formation from both lighter (SAMW) and denser (UCDW) water (Fig. 6e). The formation rate from cabbeling and thermobaricity peaks around August and reaches a minimum in April (Fig. 6j), which resembles the seasonal evolution of AAIW volume tendency seen in Fig. 6g. The formation rate from vertical mixing peaks in April and reaches a minimum around September. Overall, the water mass formation due to isopycnal and diapycnal mixing tends to increase the volume within the AAIW density range. However, similar to the uncertainty in computing eddy-induced subduction, the estimate of water mass formation also relies on the eddy-diffusion coefficient and the vertical diffusion coefficient used in the calculation. In particular, the annual mean formation rates due to isopycnal mixing are estimated as 1.2, −0.1, −0.3, and 8.1 Sv using K = $K$ , 500 m² s⁻¹, 1000 m² s⁻¹, and $K$ ₀, respectively, while the formation rates due to vertical mixing are estimated as 1.5, 8.3, 13.8 Sv using the diffusivity from de Lavergne et al. (2020), D = 3 × 10⁻⁵ and 5 × 10⁻⁵ m² s⁻¹, respectively. However, uncertainties from the water mass formation estimate associated with the choice of diffusivity coefficient are smaller than these of the eddy-induced subduction in determining the residual of the AAIW volume budget (gray dashed lines in Figs. 6i–j).

The volume transport of waters by the geostrophic mean flow and eddy-induced flow at the open boundaries of the domain considered, 70° and 20°S, is mostly negative, representing an outflow leaving the domain. This volume transport occurs mainly within the light AAIW class of γⁿ = (27.25–27.45) kg m⁻³ (Fig. 6f), with a peak in September (Fig. 6l). Two time periods of weaker export in May–June and October–November correspond to the period of positive volume tendency in the same density range (Figs. 6a,f,g,l). Similar to the subduction and mixing terms, the estimate of volume transport also depends on the eddy-diffusion coefficient (12.0 Sv in $K$ ₀ versus 7.7 Sv in $K$ ). The uncertainty in the volume transport estimate, obtained by using different geostrophic velocity fields, is mainly restricted to March–December with a mean value of ±2.3 Sv (shading in Fig. 6l).

Overall, water within the AAIW density class is exported outside of the domain by Ekman pumping and volume transport, which is compensated by the volume increase due to eddy-induced subduction and interior diapycnal volume transport of waters from the SAMW and UCDW layers. With a suppressed eddy-diffusion coefficient $K$ estimate from Groeskamp et al. (2020) and a constant vertical diffusion coefficient of D = 5 × 10⁻⁵ m² s⁻¹ used in computing the volume budget, the annual mean value of the residual term is 11.1 Sv (Fig. 6m). Since the residual is computed as the difference between the volume tendency and the formation estimates, i.e., residual = volume tendency − (subduction + mixing + volume transport), the positive values of the residual over April–November suggest that formation estimates are too small to balance the volume tendency. Furthermore, the nonzero residual term might be due to sparse data coverage in the monthly WOA18 fields, uncertainties in the subduction and volume transport estimates, or uncertainties from the eddy-diffusion coefficient and vertical diffusion coefficient used in the volume budget. Here we show different choices of the geostrophic velocity (see section 3c) give an uncertainty of ±2.8 Sv to the residual term (Fig. 6m). Though improved estimates of the geostrophic velocity are needed to better estimate the subduction and volume transport and therefore, obtain better closure of the volume budget, this is beyond the scope of this study. We now focus on the role of K and D for the closure of the volume budget by repeating the calculations for different K and D estimates.

e. Residual term

Here we evaluate the sensitivity of the residual term to different choices of K and D used in the volume budget. We do so by repeating the calculations for different K and D estimates, respectively (see Fig. 7 and Table 3). To test the uncertainty from the K applied, i.e., the estimate of eddy-induced subduction and isopycnal mixing, we repeat our calculations using the unsuppressed eddy-diffusion coefficient $K$ ₀ as well as constant coefficient values of K = 500 and 1000 m² s⁻¹ when D = 5 × 10⁻⁵ m² s⁻¹ (Fig. 7a). The results obtained show that the choice of K fields does not strongly impact the annual mean residual (i.e., 11.1 Sv using K = $K$ , 10.3 Sv using K = 500 m² s⁻¹, and 7.9 Sv using K = 1000 m² s⁻¹), except for the large differences in the case when using K = $K$ ₀ (−12.2 Sv, Fig. 7a, Table 3). This is because the diffusivity $K$ from Groeskamp et al. (2020) is close to the constant value of K = 500 m² s⁻¹, while the value of $K$ ₀ is much greater than 1500 m² s⁻¹. With the intensification of $K$ ₀ in regions of strong flow, the resulting regional intensification of eddy-induced subduction would yield a much higher value of the circumpolar-integrated transport (Table 1) and thus, significantly change the residual term. Overall, with an increasing value of K used in the volume budget calculation, i.e., a larger estimate of the eddy-induced subduction and isopycnal mixing, the residual estimate shows a substantial decrease (see also Fig. 7c).

Table 3

The residual of the volume budget within the AAIW density class averaged over a year. All values are given in Sverdrups. Different eddy-diffusion coefficients K and vertical diffusion coefficients D are applied to estimate the corresponding residual term.

We then repeat volume budget calculations using the vertical diffusion coefficient field from de Lavergne et al. (2020), and constant values of D = 3 × 10⁻⁵ and 5 × 10⁻⁵ m² s⁻¹, to examine influences of these choices of the D fields on the residual term (Fig. 7b, Table 3). Here the suppressed $K$ field is used in the calculation. The residual term obtained shows that these three D fields yield essentially the same monthly variations in the residual term, except for differences in the magnitude [23.4 Sv using D from de Lavergne et al. (2020), 16.6 Sv using D = 3 × 10⁻⁵ m² s⁻¹, and 11.1 Sv using D = 5 × 10⁻⁵ m² s⁻¹]. Therefore, an increasing value of the D field decreases the residual term. Using larger estimates of the mesoscale eddy subduction and mixing (K = $K$ ₀) along with a larger estimate of vertical mixing, the residual could be significantly reduced [0.1 Sv using D from de Lavergne et al. (2020), −6.7 Sv using D = 3 × 10⁻⁵ m² s⁻¹, and −12.2 Sv using D = 5 × 10⁻⁵ m² s⁻¹], especially during July–December (Fig. 7c, Table 3).

This sensitivity test suggests that the eddy-induced subduction, isopycnal, and vertical mixing terms could significantly influence the residual estimate and the closure of the volume budget, depending on the K and D estimates used. Compared to the isopycnal and vertical mixing, the estimate of volume tendency, subduction and volume transport can bring larger uncertainties to the residual term (Tables 1 and 2, Fig. 6; see the discussion in section 5). Here we considered K and D as the main source of uncertainty and tested their influence on the closure of the budget. But note that uncertainties in the estimate of volume tendency, Ekman pumping, geostrophic circulation, and MLD might create a residual as large as the effects of mixing.

5. Discussion

a. Regional variability in AAIW formation

Our results show large regional variability in the processes controlling AAIW formation, as also indicated in previous work (e.g., Sloyan and Rintoul 2001; Downes et al. 2011; Close et al. 2013; Evans et al. 2014). Here we provide a discussion on the regional variability in the formation, distribution and destruction of AAIW, by synthesizing previous literature with our calculations of subduction [Eq. (2)] and water mass transformation due to mixing [Eqs. (5a)–(5c)] within the SAMW and AAIW density ranges in the ocean interior (summarized in Fig. 8), using different diffusivities (Table 3 and section 4).

The SAMW in the ocean interior is primarily formed by subduction north of the Subantarctic Front (Hanawa and Talley 2001; Sallée et al. 2010; Carter et al. 2014; Li et al. 2021). The subduction estimates in this study (given in Table 1) reveal strong subduction by lateral advection and Ekman pumping at the previously defined hotspots of SAMW subduction (e.g., Sallée et al. 2010; Herraiz-Borreguero and Rintoul 2011; Li et al. 2021) (Fig. 2). The formation of AAIW is, however, more complicated since its outcropping region resides mainly south of the Subantarctic Front where a number of fronts coincide with enhanced meridional gradients of temperature and salinity and with maxima in geostrophic flow (see also Orsi et al. 1995; Sokolov and Rintoul 2009).

Due to steep isopycnals within the ACC frontal area, the strongest eddy-induced flow and subduction occur near the Subantarctic and Polar Fronts according to the Gent and McWilliams (1990) parameterization [Eq. (6)] (Figs. 2c,d). The eddy-induced subduction and lateral advection terms dominate subduction over the South Pacific and Drake Passage regions (as also found by Sallée et al. 2010; Portela et al. 2020) and within the light AAIW layer of γⁿ = (27.25–27.45) kg m⁻³ (Figs. 2, 6c, and 8). The subducted light AAIW is transported either eastward along the ACC or northward through the exchange windows into the subtropical oceans (Fig. 1b). The upwelling by Ekman pumping occurs mainly south of the Polar Front and upwells the dense variety of AAIW into the mixed layer (Figs. 1c, 2e, 6b, and 8), which can be advected northward into the subduction region of AAIW and SAMW (Rintoul and England 2002; Sallée et al. 2010).

The ACC frontal region is characterized by rich mesoscale and small-scale eddy activity. A number of studies using model simulation and/or hydrographic data have suggested cabbeling is essential for AAIW formation (e.g., Marsh 2000; Iudicone et al. 2008a; Urakawa and Hasumi 2012; Carter et al. 2014; Nycander et al. 2015; Cerovečki and Mazloff 2016; Groeskamp et al. 2016). Here we have shown that AAIW formation by cabbeling is induced by the convergence of water mass transformation from the SAMW layer near the Subantarctic Front (2–13 Sv at γⁿ = 27.25 kg m⁻³) and water mass transformation into the UCDW layer near the Polar Front (1–7 Sv at γⁿ = 27.7 kg m⁻³) (Figs. 4, 5, and 8). Our vertical mixing estimates show that small-scale mixing dominates the diapycnal exchange of AAIW with SAMW and UCDW north of the ACC frontal region (Figs. 3–5). More specifically, our results show a strong water mass transformation of 1–10 Sv from the UCDW layer in all three Southern Ocean basins and a weak water mass transformation of 0–1 Sv from the SAMW layer into AAIW within the South Pacific (Figs. 4, 5, and 8), which is overall consistent with the findings of Iudicone et al. (2008b), Katsumata et al. (2013), and Evans et al. (2014, 2018). In contrast, the observationally based work by Meyer et al. (2015) suggested that water mass transformation by vertical mixing transforms AAIW into the SAMW layer. This inconsistency might be due to the different density surfaces considered, and because water mass transformation within the mixed layer and in the ocean interior were not considered separately in that study, as also seen in Downes et al. (2011).

b. Uncertainty in volume budget calculation

A volume budget analysis within the AAIW layer was performed to study the dominant formation processes and the major sources of uncertainty. Subduction and volume transport are the largest formation terms and could thus be the largest source of uncertainty in the residual term, while uncertainties arising from isopycnal and diapycnal mixing estimates likely play a secondary role. The estimate of subduction by lateral advection and volume transport is largely influenced by the MLD and geostrophic mean flow [Eqs. (2) and (7)]. First, the density-based MLD criterion of Δσ₀ ≤ 0.03 kg m⁻³ has been suggested to be appropriate for the Southern Ocean mixed layer and subduction estimates (de Boyer Montégut et al. 2004; Li et al. 2021). Second, different choices of the geostrophic velocity (see section 3c) give an uncertainty of ±2.8 Sv to the residual term (Fig. 6m), which is comparable with the formation rate due to isopycnal mixing. Improved estimates of the geostrophic velocity are needed to better estimate the subduction and volume transport, but remain beyond the scope of this study. Instead, we focus on uncertainties due to the eddy-induced subduction and ocean mixing terms. We do so by testing the sensitivity of the residual term to a variety of mesoscale and small-scale diffusivities and found that uncertainties in the estimate of eddy-induced subduction and ocean mixing could also influence the closure of the volume budget, though the estimate of other terms in the budget might create larger uncertainties. A near-zero residual term in the annual mean is remained from using observationally based diffusivities $K$ ₀ from Groeskamp et al. (2020) and D from de Lavergne et al. (2020), while other choices of diffusivities could induce a larger residual term. Finer hydrographic temperature and salinity fields and improved estimates of geostrophic velocity, turbulent diffusivities and mixing will improve our ability to close the AAIW volume budget and advance our understanding of the role of AAIW in the climate system.

6. Conclusions

In this study we used observationally based WOA18 data to examine the spatial and seasonal variability of AAIW and identify which processes dominate this variability. We quantified and contrasted the effects of subduction by Ekman pumping and geostrophic flow, eddy-induced subduction, and water mass transformation due to mesoscale and small-scale mixing. For the first time, the seasonal variability of waters within the AAIW density range of γⁿ = (27.25–27.7) kg m⁻³ has been quantified using a monthly mean volume budget in the Southern Ocean. A state-of-the-art search algorithm (VENM) for the neutral slope calculation and an observationally based mesoscale eddy diffusivity estimate are combined to estimate the eddy-induced subduction and ocean mixing in a water mass transformation framework.

The subduction of AAIW was found to be dominated by eddy-induced subduction between the Subantarctic and Polar Fronts and lateral advection around the southeast Pacific and Drake Passage, whereas the upwelling of AAIW is dominated by Ekman pumping poleward of the Polar Front. Therefore, the ventilation of AAIW is comprised of subduction by eddy-induced flow that occurs mainly within the light AAIW layer of γⁿ = (27.25–27.45) kg m⁻³ and upwelling by Ekman pumping that occurs mainly within the dense AAIW layer of γⁿ = (27.5–27.7) kg m⁻³ (Fig. 8).

The volume loss of AAIW by upwelling across the mixed layer base and northward volume transport leaving the Southern Ocean are compensated by diapycnal transport from the SAMW and UCDW layers (Fig. 8). First, diapycnal transport from the SAMW layer into AAIW occurs mainly via cabbeling near the Subantarctic Front and vertical mixing over the South Pacific. Second, diapycnal transport from the UCDW layer into AAIW is dominated by vertical mixing over most of the Southern Ocean.

Combined with the circulation of AAIW, our results suggest that AAIW originates from subduction by both eddy-induced and geostrophic flow, and from diapycnal transport from the SAMW and UCDW layers, as described above. The overall circulation of AAIW reveals an eastward branch along the ACC and a northward branch through the exchange windows into the subtropical gyres. The AAIW layer loses volume due to export leaving the Southern Ocean, upwelling by Ekman pumping, and diapycnal transport into the UCDW layer by isopycnal mixing near the Polar Front. All these mechanisms contribute to the mean features of the AAIW distribution, but show strong regional variability in each formation process. For example, lateral advection and vertical mixing at γⁿ = 27.25 kg m⁻³ both show large regional variability and contribute to AAIW formation mainly within the southeast Pacific and Drake Passage, and the South Pacific, respectively. In contrast, the eddy-induced subduction, Ekman pumping, isopycnal mixing, and vertical mixing at γⁿ = 27.7 kg m⁻³ are circumpolar mechanisms and play a role in AAIW formation within different latitudes of the Southern Ocean.

A monthly mean volume budget was then analyzed for a further understanding of the seasonality in AAIW formation. The most remarkable pattern found is the strong seasonal variability in the rate of subduction, vertical mixing, and volume transport in driving the volume tendency. There is still a substantial residual term remaining, even when adopting different values for both mesoscale and small-scale mixing diffusivities. Improved estimates of geostrophic velocity and mixing can improve our ability to close the AAIW volume budget, and better understand its role in the climate system.

Acknowledgments.

Z.L. receives support from the Foundation of China Scholarship Council (201806330075), Climate Change Research Centre (CCRC), University of New South Wales, and the Centre for Southern Hemisphere Ocean Research (CSHOR), a joint research centre between QNLM, CSIRO, UNSW and UTAS. This study was supported by the ARC Australian Centre for Excellence in Antarctic Science (ACEAS; ARC Grant SR200100008). M.H.E. was also suppprted by CSHOR. I.C. received support from National Science Foundation Award OCE-1658001 and NASA grant number 80NSSC19K1115. We thank two anonymous reviewers for their insightful comments that helped to improve this paper.

Data availability statement.

The gridded WOA18 data were downloaded at https://www.ncei.noaa.gov/products/world-ocean-atlas. The ERA-Interim dataset, developed by the European Centre for Medium-Range Weather Forecasts, was obtained from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim. The mesoscale eddy diffusivity $K$ and $K$ ₀ of Groeskamp et al. (2020) was downloaded at https://figshare.com/articles/dataset/Groeskamp_et_al_2020_-_mixing_diffusivities/12554555. The global tidal mixing diffusivities are obtained from de Lavergne et al. (2020): Global tidal mixing maps, SEANOE (doi:10.17882/73082) at https://www.seanoe.org/data/00619/73082/. This study used the data of YoMaHa’07 (Lebedev et al. 2007) dataset of velocities derived from Argo float trajectories provided by APDRC/IPRC. The observationally based velocity fields were downloaded at http://apdrc.soest.hawaii.edu/projects/yomaha/. The GSW toolbox is at http://www.teos-10.org/software.htm.

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EDITORIAL

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The Origin and Fate of Antarctic Intermediate Water in the Southern Ocean

Abstract

Abstract

1. Introduction

2. Hydrographic and diffusivity data

3. Volume budget

a. Subduction

b. Water mass transformation

c. Geostrophic and eddy-induced transport

4. Results

a. Mean features of the AAIW distribution

b. Spatial structures in the Southern Ocean subduction

c. Diapycnal exchange with SAMW and UCDW

d. Seasonal volume budget for AAIW layer

e. Residual term

5. Discussion

a. Regional variability in AAIW formation

b. Uncertainty in volume budget calculation

6. Conclusions

Acknowledgments.

Data availability statement.

REFERENCES