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  • View in gallery

    (top) Surface wind stress and (bottom) “equilibrium” surface density used for restoring. The surface density in the figure corresponds to a case where sea ice extent is set to 2°. In simulations with larger sea ice extent, the meridional coordinate is contracted such that the equilibrium surface density at the sea ice edge remains unchanged.

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    Surface buoyancy flux for the reference simulation with = 1.5 × 10−8 m2 s−3. Positive values indicate surface buoyancy gain by the ocean, while negative values indicate buoyancy loss.

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    Zonal-mean overturning streamfunction (color shading) and potential density (contours) for the reference simulation with = 1.5 × 10−8 m2 s−3. The different panels show (a) the Eulerian-mean overturning transport , (b) the sum of and the parameterized transient eddy transport , (c) the total isopycnal overturning transport , and (c) the residual transport computed by remapping the isopycnal overturning streamfunction back into physical space. Notice that the color scale is saturated in parts of the upper cell.

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    Zonal-mean residual overturning (shading) and potential density (contours) for three simulations with varying extent and rate of high-latitude surface buoyancy loss. (a) A buoyancy loss rate of 1.5 × 10−8 m2 s−3 is prescribed within 2° of the southern boundary. (b) The same buoyancy loss rate per surface area is prescribed within 8° of the southern boundary. (c) A buoyancy loss rate of 6.75 × 10−8 m2 s−3 is prescribed over 2°, yielding about the same integrated buoyancy loss as in (b). The dashed red and blue lines indicate the depth at which the upper and abyssal overturning cells decrease to 25% of their maximum value at the respective latitude, while the black dashed line indicates the cell interface where the streamfunction changes sign. Notice that in particular the cell interface becomes poorly defined at large buoyancy loss rates in the northern part of the domain, where a wide depth range with vanishingly weak circulation develops. Lines are discontinued where their definition becomes ambiguous due to multiple zero crossings.

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    Basin-averaged stratification (solid) and residual overturning (dashed), as a function of depth, for simulations with a varying rate of buoyancy loss around Antarctica. The color of the lines indicates the rate of buoyancy loss, ranging from = 0.5 × 10−8 m2 s−3 (blue) to = 3 × 10−8 m2 s−3 (orange). In all simulations buoyancy loss is applied over 4° of sea ice extent. The black line indicates an exponential stratification profile with an e-folding depth of 300 m.

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    Separation depth between the upper and abyssal cells as a function of the integrated buoyancy loss over the sea ice region around Antarctica. The 75% quantile level of the upper cell (red) is defined such that 75% of the NADW flows southward above this level, while the 75% level of the abyssal cell (blue) is defined such that 75% of AABW returns southward below this level. Also shown is the level where the basin-averaged overturning streamfunction changes sign (black). Pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and squares denote the simulation with 8° sea ice extent. Blue diamonds show the 75% quantile level of the abyssal cell in simulations where the upper cell is suppressed (see text). The black line indicates the predicted dependence of the upper-cell depth on the integrated buoyancy loss rate, using (11) with he = 300 m.

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    Abyssal stratification, averaged over the basin and below 2000-m depth, as a function of the integrated buoyancy loss rate in the sea ice region. Pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and the square denotes the simulation with 8° sea ice extent. The black line indicates a linear relationship.

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    Abyssal density, averaged over the lowest 600 m, for two simulations with 4° of sea ice extent and differing buoyancy loss rates: = (left) 1.5 × 10−8 and (right) 3 × 10−8 m2 s−3 m2 s−3. Black arrows indicate the flow in the lowest model layer (i.e., lowest 200 m). Notice that zonal and meridional density gradients are of similar order, and both increase strongly as the buoyancy loss rate is increased (note different color bars in two panels). Notice also that zonal density gradients change sign in the Northern Hemisphere, as required to maintain an overturning circulation in thermal wind balance.

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    Abyssal overturning transport [evaluated as the maximum of the (negative) isopycnal overturning streamfunction in the basin] against the scaling relation in (14) with LBL = W = 6 × 106 m. The term ΔbBL is computed as the buoyancy contrast between the northern end of the basin and the basin channel interface averaged zonally and vertically over the lowest 600 m. As before, pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and the square denotes the simulation with 8° sea ice extent. The black line indicates a linear relationship.

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    Vertical structure of the diapycnal diffusivity κ used in simulations with vertically varying mixing.

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    As in Fig. 4, but using the vertically varying diapycnal diffusivity shown in Fig. 10.

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The Effect of Southern Ocean Surface Buoyancy Loss on the Deep-Ocean Circulation and Stratification

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  • 1 Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois
  • 2 Institut des Sciences de la Mer de Rimouski, Université du Québec à Rimouski, Rimouski, Québec, Canada
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Abstract

The deep-ocean circulation and stratification have likely undergone major changes during past climates, which may have played an important role in the modulation of atmospheric CO2 concentrations. The mechanisms by which the deep-ocean circulation changed, however, are still poorly understood and represent a major challenge to the understanding of past and future climates. This study highlights the importance of the integrated buoyancy loss rate around Antarctica in modulating the abyssal circulation and stratification. Theoretical arguments and idealized numerical simulations suggest that enhanced buoyancy loss around Antarctica leads to a strong increase in the abyssal stratification, consistent with proxy observations for the last glacial maximum. Enhanced buoyancy loss moreover leads to a contraction of the middepth overturning cell and thus upward shift of North Atlantic Deep Water (NADW). The abyssal overturning cell initially expands to fill the void. However, if the buoyancy loss rate further increases, the abyssal cell also contracts, leaving a “dead zone” with vanishing meridional flow at middepth.

Corresponding author address: Malte F. Jansen, Dept. of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637. E-mail: mfj@uchicago.edu

Abstract

The deep-ocean circulation and stratification have likely undergone major changes during past climates, which may have played an important role in the modulation of atmospheric CO2 concentrations. The mechanisms by which the deep-ocean circulation changed, however, are still poorly understood and represent a major challenge to the understanding of past and future climates. This study highlights the importance of the integrated buoyancy loss rate around Antarctica in modulating the abyssal circulation and stratification. Theoretical arguments and idealized numerical simulations suggest that enhanced buoyancy loss around Antarctica leads to a strong increase in the abyssal stratification, consistent with proxy observations for the last glacial maximum. Enhanced buoyancy loss moreover leads to a contraction of the middepth overturning cell and thus upward shift of North Atlantic Deep Water (NADW). The abyssal overturning cell initially expands to fill the void. However, if the buoyancy loss rate further increases, the abyssal cell also contracts, leaving a “dead zone” with vanishing meridional flow at middepth.

Corresponding author address: Malte F. Jansen, Dept. of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637. E-mail: mfj@uchicago.edu

1. Introduction

The paleoclimate record indicates that the deep-ocean circulation and water masses have likely undergone major rearrangements during past climates (e.g., Curry and Oppo 2005; Lund et al. 2011). These rearrangements may have played a crucial role in the climatic changes between glacial and interglacial periods, due to their potential impact on ocean carbon storage (e.g., Brovkin et al. 2007; Adkins 2013). And they may again play an important role in the modulation of anthropogenic climate change (e.g., Sarmiento and Le Quere 1996). The mechanisms by which the ocean circulation changed (and may change again), however, are still poorly understood and represent a major challenge to our understanding of past and future climates.

Much progress has been made recently toward understanding the deep-ocean circulation based on theoretical arguments and idealized numerical models (Gnanadesikan 1999; Ito and Marshall 2008; Wolfe and Cessi 2009, 2011; Nikurashin and Vallis 2011, 2012; Mashayek et al. 2015). These studies consider the circulation in a single interhemispheric basin connected to a circumpolar channel in the south. Surface forcing is represented by a prescribed wind stress and a restoring of the surface buoyancy to a prescribed profile. The emerging deep-ocean circulation generally consists of two separate cells. The first cell (hereinafter, the “upper cell”) starts with the generation of deep water at the northern end of the basin, which is analog to North Atlantic Deep Water (NADW). The water then flows southward at middepth in the basin before upwelling primarily along isopycnals in the Southern Ocean and eventually flowing back northward as intermediate waters to close the loop. The second cell (hereinafter, the “abyssal cell”) starts with the formation of bottom water at the southern end of the channel, which is analog to Antarctic Bottom Water (AABW). This water mass then upwells (balanced by abyssal diapycnal mixing) to middepth before returning back to the surface along isopycnals in the Southern Ocean, where it eventually is converted back into AABW. The theoretical picture developed in these studies suggests that the upper cell protrudes into the Southern Ocean to about the latitude where the surface buoyancy matches the densest surface waters in the North Atlantic. AABW formation is confined to latitudes where the surface buoyancy is smaller than anywhere in the Northern Hemisphere. The emerging theory provides a powerful tool to predict the structure of the abyssal circulation and stratification, given the wind stress and the surface buoyancy.

Over most of the ocean, surface buoyancy variations are dominated by temperature variations, which in turn are tightly linked to the atmospheric temperature. Heat exchange between the atmosphere and ocean thus amounts to a restoring condition for surface buoyancy. However, at high latitudes, salinity variations become important, and indeed Southern Ocean surface buoyancy fluxes tend to be dominated by freshwater fluxes (e.g., Karstensen and Lorbacher 2011), which cannot be represented by restoring to an atmospheric value. The surface buoyancy itself thus is poorly constrained, and the boundary condition may more adequately be described by a fixed-flux condition.

A buoyancy flux boundary condition lies at the heart of a theory for the difference in the deep-ocean circulation between the present and the Last Glacial Maximum (LGM; ~20 kyr before present) that was recently brought forward by Ferrari et al. (2014) and Watson et al. (2015). Ferrari et al. (2014) show evidence, based on ocean state estimates and coupled climate model results, that the sea ice extent around Antarctica exerts a strong control on the surface buoyancy fluxes in the Southern Ocean. In the regions covered quasi permanently by sea ice, heat fluxes are either small (when sea ice cover is complete) or negative (in the presence of leads), which leads to net buoyancy loss. Moreover, freezing and sea ice export leads to brine rejection, which further contributes to buoyancy loss. Around the ice margin, on the other hand, surface buoyancy fluxes are dominated by ice melting, which leads to a buoyancy gain. Because of this connection between sea ice extent and Southern Ocean surface buoyancy fluxes, Ferrari et al. (2014) hypothesized that the Antarctic sea ice extent exerts a strong control on the deep-ocean circulation. Specifically, it was proposed that a larger sea ice extent would lead to a contraction of the upper overturning cell and expansion of the abyssal overturning circulation cell, which is consistent with the change in the overturning circulation between the present and Last Glacial Maximum indicated by proxy observations (e.g., Curry and Oppo 2005; Adkins 2013). Watson et al. (2015) further argue that the change in circulation can cause a significant drawdown of atmospheric CO2 by up to 40 ppm.

While the argument in Ferrari et al. (2014) and Watson et al. (2015) is geometrical in nature, and thus highlights the importance of the meridional extent of the buoyancy loss region, previous studies have also pointed toward the potential importance of the rate of buoyancy loss around Antarctica (e.g., Adkins et al. 2002; Shin et al. 2003; Adkins 2013; Roberts et al. 2016; Sun et al. 2016). Paleoproxy observations suggest a strong increase in the deep-ocean density stratification, which is most readily attributed to enhanced brine rejection in the Southern Ocean (Adkins et al. 2002). This picture is also supported by climate model simulations discussed by Shin et al. (2003) and Sun et al. (2016). In addition to enhanced stratification, Shin et al. (2003) also find an upward shift of NADW, which again is attributed to enhanced brine rejection in the Southern Ocean. However, the simulations not only show an enhanced rate of sea ice formation and associated brine rejection but also an equatorward expansion of the sea ice cover, making it hard to separate the effect of the enhanced buoyancy loss rate from the purely geometrical effect highlighted by Ferrari et al. (2014) and Watson et al. (2015).

While most theoretical and idealized studies of the deep-ocean circulation have considered surface-restoring boundary conditions, Shakespeare and Hogg (2012) and Stewart et al. (2014) consider models with fixed-flux boundary conditions. Although the study of Stewart et al. (2014) focuses primarily on the sensitivity of the abyssal cell to diapycnal mixing, their analytical results also suggest a sensitivity of the abyssal stratification and circulation on both the magnitude and spatial structure of buoyancy loss around Antarctica. Unfortunately, the interpretation of the results is complicated by a dependence on the stratification below the abyssal cell, which needs to be prescribed. Shakespeare and Hogg (2012) consider an analytical box model as well as an idealized GCM with fixed-surface buoyancy flux boundary conditions. Unlike the approach that will be taken in this study, fixed-surface buoyancy fluxes are prescribed everywhere. The analytical model, as well as numerical simulations, suggests an increase in abyssal stratification for increasing buoyancy loss rates in the Southern Ocean, with the numerical simulation further indicating a strengthening of the abyssal cell. However, analytical solutions are provided only for the adiabatic limit where no abyssal overturning cell exists, and the interpretation of the numerical results is complicated by the fact that the simulations are not integrated to full equilibrium.

In this paper, we systematically analyze the connection between Southern Ocean surface buoyancy fluxes and the deep-ocean circulation and stratification, using a series of idealized numerical simulations. We analyze the role of both the meridional extent of buoyancy loss around Antarctica as well as the rate of buoyancy loss. The results highlight the importance of the integrated buoyancy loss rate around Antarctica. Consistent with previous studies (e.g., Shakespeare and Hogg 2012; Sun et al. 2016), enhanced buoyancy loss around Antarctica leads to a strong increase in the deep-ocean stratification. Enhanced buoyancy loss also leads to a contraction of the upper overturning cell and thus upward shift of NADW, even in the absence of increased sea ice extent (although the latter strengthens the effect). The abyssal overturning cell initially expands to fill the void. However, if the buoyancy loss rate further increases, the abyssal cell starts to contract leaving a “dead zone” with vanishing meridional flow at middepth. The results also point toward some limitations of the scaling relations derived in recent idealized studies. Apart from the common assumption of a fixed-surface buoyancy profile, which naturally does not apply here, previous scaling relations generally presume that circulation changes in the basin are largely slaved to the dynamics in the circumpolar channel. Instead, we argue that understanding the response of the deep-ocean circulation to changes in the buoyancy loss rate around Antarctica requires us to consider the dynamics in the basin.

2. Theoretical background

Progress has been made recently toward understanding the deep-ocean circulation based on 2D scaling arguments (e.g., Gnanadesikan 1999; Ito and Marshall 2008; Nikurashin and Vallis 2011, 2012; Mashayek et al. 2015). Generally, the idea behind these arguments is to separate the domain into a channel (representing the Southern Ocean) and a basin (typically thought to represent the Atlantic). The flow in the basin is generally assumed to be governed by a vertical advective–diffusive balance, augmented by a closure for NADW production in the north of the basin. Except in the NADW production region, isopycnals in the basin are assumed to be flat, such that the stratification in the basin can be directly connected to the circumpolar channel.

The flow in the channel is controlled by a balance between wind-driven Ekman pumping, which acts to steepen the isopycnal slopes, and an eddy-driven circulation, which acts to flatten the isopycnals. Wind-driven Ekman transport drives an Eulerian overturning circulation, which below the Ekman layer and above any topographic barrier can be expressed as
e1
where is the meridional overturning circulation, is the zonal-mean zonal wind, ρ is the density of seawater, and f is the Coriolis parameter. Using the Gent and McWilliams (1990, hereinafter GM) closure for mesoscale eddy effects, the eddy-driven meridional overturning streamfunction can be parameterized as
e2
where K is an eddy diffusivity, and s is the meridional isopycnal slope.
For a zonally symmetric flow, the residual overturning cell, responsible for the net transport of mass and tracers, is given by the sum of the wind-driven Eulerian overturning and this eddy-driven overturning. The residual overturning is generally understood to change sign in the Southern Ocean, where the upper cell gives way to the abyssal cell (e.g., Nikurashin and Vallis 2011). At the interface between the two cells, the eddy-driven overturning thus exactly cancels the wind-driven overturning, which allows us to derive an equation for the isopycnal slope as
e3
Ferrari et al. (2014) and Watson et al. (2015) argue that the direction of the overturning transport at the surface is constrained by the sign of the surface buoyancy fluxes, with buoyancy loss associated with southward transport (and thus ψ < 0 below the surface) and buoyancy gain associated with northward transport (and thus ψ > 0 below the surface). The latitude at which the surface buoyancy flux changes sign thus provides the northernmost outcrop of the abyssal cell at the surface. If the circulation in the channel is adiabatic, we can integrate (3) to obtain the depth of the isopycnal that separates the two cells at the northern end of the channel:
e4
where θb denotes the latitude where the surface buoyancy flux changes sign, θc denotes the northern end of the circumpolar channel, and a is Earth’s radius.

In a 3D ocean, the Antarctic Circumpolar Current meanders, which leads to an additional contribution to the zonal-mean meridional transport of buoyancy. Using a small-amplitude approximation for deviations from the zonal mean, their effect can be cast as a modification of the eddy diffusivity K, which accounts for the effect of standing meanders (e.g., Plumb and Ferrari 2005; Vallis 2006; Abernathey and Cessi 2014). Since this contribution is expected to enhance the effective eddy diffusivity, the result would be a weakening of the isopycnal slope compared to the prediction in (3) and thus a shallowing of the cell interface compared to the prediction in (4).

Ignoring potential changes in the effective eddy diffusivity, the depth of the cell interface according to (4) is controlled by the geometry of the domain and boundary conditions but not by the rate of surface buoyancy loss. However, we notice that (4) directly predicts the cell interface only at the basin channel boundary and may not generally be representative for the entire basin. Moreover, we will argue below that the “cell interface” alone may not always be the most relevant variable characterizing the vertical extent of the two overturning cells, as the two cells can become increasingly separated for large buoyancy loss rates around Antarctica. Finally, the effect of standing meanders can change in response to variations in the buoyancy loss rate.

The rate of buoyancy loss may also play an important role in setting the strength of the abyssal overturning circulation and stratification. Theoretical models for the abyssal circulation and stratification under prescribed buoyancy flux have been proposed by Shakespeare and Hogg (2012) and Stewart et al. (2014). The robust conclusion is that the stratification is expected to increase with increased buoyancy loss rate around Antarctica. The expected response of the overturning circulation to changes in Southern Ocean buoyancy loss instead remains less clear.

Assuming that the overturning circulation in the channel adiabatically connects the surface to the abyssal basin, the surface buoyancy loss rate around Antarctica can be related to the buoyancy transport into the basin:
e5
where is the (upward) surface buoyancy flux per unit area, and the integral extends over the region of buoyancy loss around Antarctica; is the zonally integrated residual overturning transport (throughout this paper we will use uppercase Ψ to denote the zonally integrated overturning transport and lowercase ψ for zonal averages), and Δb is the bulk buoyancy contrast across the overturning cell. Notice that is generally negative for the abyssal cell.
The buoyancy flux into the basin in turn has to be balanced by diffusion between the upper and abyssal cell, which suggests a scaling for the stratification near the cell interface as
e6
where L and W are the length and width of the basin, and κ is the diapycnal diffusivity at the cell interface. For a given diapycnal diffusivity, the stratification near the cell interface is therefore expected to increase approximately linearly with the integrated buoyancy loss rate around Antarctica. A similar result has been derived by Stewart et al. (2014) for the limit of vanishing stratification at the bottom of the abyssal cell (although their model becomes formally ill-defined in this limit). A linear increase in abyssal stratification with the buoyancy loss rate in the Southern Ocean is also predicted by the analytical model of Shakespeare and Hogg (2012). However, the mechanism in the model of Shakespeare and Hogg (2012) differs, as becomes clear by noting that their result was derived in the adiabatic limit (κ = 0), for which the scaling argument presented here predicts a diverging stratification.
A scaling relation for the overturning circulation can be obtained if we assume that the bulk buoyancy contrast across the overturning cell can be related to the stratification at the top of the cell as , where h is a characteristic depth scale of the abyssal cell. Combining (5) and (6) then yields a relation between the strength and vertical extent of the abyssal overturning circulation as
e7
Similar scaling arguments for the abyssal overturning cell have been derived repeatedly (e.g., Ito and Marshall 2008; Nikurashin and Vallis 2011; Stewart et al. 2014), though ambiguity remains as to what sets the relevant vertical scale h. The result in (7) suggests a relationship between the strength of the abyssal overturning circulation and its depth scale h, but an additional constraint is required to understand how both respond to changes in the buoyancy loss rate. Deviating from previous theories, which have focused on the dynamics in the channel, we will argue in section 3c that such an additional constraint is most readily derived by considering the dynamics of the overturning circulation in the basin.

3. Numerical simulations

a. Model setup

The numerical simulations use the Massachusetts Institute of Technology General Circulation Model (MITgcm; Marshall et al. 1997) in a hydrostatic Boussinesq configuration. The idealized domain extends from 70°S to 70°N, covers 60° in longitude, and is 4 km deep. The horizontal resolution is 1° × 1°, and the vertical resolution ranges from 50 m near the surface to 200 m in the deep ocean, with a total of 28 levels. A thin strip of land extends from the northern boundary to 48°S, leaving a periodic channel between 69° and 48°S. The channel extends to a depth of 3000 m, below which it is interrupted by a sill. Except for this sill (which helps to avoid unrealistically strong barotropic flows), the geometry of the domain is similar to that used by Nikurashin and Vallis (2012). The geometry of the model is highly idealized, but we crudely interpret the basin to represent the Atlantic, while the channel region is thought to represent the Southern Ocean. Consistently, and for easy readability, we will refer to the southern boundary of the domain as Antarctica.

All surface boundary conditions are zonally symmetric. The meridional structure of the wind stress is chosen to crudely reflect the zonal-mean wind stress experienced by the present-day ocean (Fig. 1). For simplicity, the model uses a linear equation of state, with a single buoyancy variable, which lumps together the effects of temperature and salinity on the density of seawater. Over most of the domain, the surface buoyancy flux is described as a restoring toward a fixed latitudinally dependent density profile,1 shown in Fig. 1. The surface restoring can be understood as an idealized representation primarily of heat exchange with the atmosphere, which restores the sea surface temperature to the atmospheric temperature and dominates the buoyancy flux over most of the ocean. The restoring time scale for the 50-m-deep top layer is 3 months, which corresponds to a piston velocity of about 55 cm day−1. The restoring profile is somewhat asymmetric between the hemispheres, with higher equilibrium densities in the Northern Hemisphere (Fig. 1). This asymmetry may be thought of as a crude representation of excess evaporation over the Atlantic basin, which contributes to the relatively high density of surface waters in the North Atlantic. From a practical perspective, the asymmetry of the restoring profile also ensures that the net buoyancy flux in the Southern Hemisphere channel is positive just north of the “sea ice” region, which is described below. Varying the meridional extent of the sea ice region thus allows us to directly control the latitude where the surface buoyancy flux changes sign.

Fig. 1.
Fig. 1.

(top) Surface wind stress and (bottom) “equilibrium” surface density used for restoring. The surface density in the figure corresponds to a case where sea ice extent is set to 2°. In simulations with larger sea ice extent, the meridional coordinate is contracted such that the equilibrium surface density at the sea ice edge remains unchanged.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

In regions of quasi-permanent sea ice cover, the annual-mean atmospheric temperature is well below the freezing point. Surface buoyancy fluxes are here likely dominated by brine rejection associated with sea ice formation and export (Ferrari et al. 2014). In addition, strong heat loss can occur in leads and polynyas (Smith et al. 1990). Both mechanisms lead to a buoyancy loss and cannot be described adequately by a restoring condition. In our idealized model we represent this transition near the sea ice line by a switch from a restoring boundary condition to a prescribed buoyancy loss rate near the southern end of the domain. The main goal of this study is to understand how the abyssal ocean circulation and stratification depends on the meridional extent and rate of this buoyancy loss. A similar boundary condition could be applied at high northern latitudes, but preliminary simulations showed that the effect of such a modification on the deep-ocean circulation is small, as the restoring condition already leads to a large buoyancy loss at high northern latitudes. Notice also that a change in the prescribed buoyancy loss rate around Antarctica unavoidably leads to compensating changes elsewhere. These changes tend to occur primarily in the channel just north of the sea ice region, where deep-water upwells to the surface. The dipole pattern of buoyancy flux changes around the sea ice edge is realistic if we are aiming to represent changes in the rate of sea ice export, which would lead to enhanced brine rejection (buoyancy loss) around Antarctica and enhanced melting (buoyancy gain) north of the ice line.

All simulations use a GM parameterization of mesoscale eddy transport, with an eddy transfer coefficient K = 700 m2 s−2, characteristic of the Southern Ocean (Farneti and Gent 2011; Tulloch et al. 2014). The reference simulations use a constant vertical diffusivity of κ = 6 × 10−5 m2 s−1 in rough agreement with characteristic deep-ocean values (Ledwell et al. 2011; Nikurashin and Ferrari 2013; Waterhouse et al. 2014). The effect of a realistic vertical structure in the diffusivity will also be discussed. Convection is parameterized using a diffusive adjustment with a convective diffusivity κconv = 10 m2 s−1 whenever the stratification is statically unstable. All simulations are integrated to equilibrium, which takes around 10 000 yr (depending on the exact set of parameters). Computational needs for these long simulations were reduced by the use of an accelerated tracer time stepping, following Bryan (1984). While this scheme distorts the physics of transients, the steady-state equilibrium solutions discussed here are unaffected.

b. Results

We start by discussing a reference simulation with a buoyancy forcing crudely representative of the present-day ocean: a buoyancy loss rate of 1.5 × 10−8 m2 s−3 is prescribed over 2° from the southern boundary (cf. to Ferrari et al. 2014). The net surface buoyancy flux resulting from the fixed-flux condition in this “sea ice region” around Antarctica and restoring elsewhere is shown in Fig. 2. Buoyancy loss in the channel region is largely limited to the sea ice region, with buoyancy gain dominating farther equatorward. A large region of buoyancy loss is found at high latitudes in the northern basin.

Fig. 2.
Fig. 2.

Surface buoyancy flux for the reference simulation with = 1.5 × 10−8 m2 s−3. Positive values indicate surface buoyancy gain by the ocean, while negative values indicate buoyancy loss.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

The resulting zonal-mean potential density and meridional overturning circulation are shown in Fig. 3. The density structure reproduces the general features found in observations, with isopycnals sloping down from the southern channel toward the basin, while remaining largely flat within most of the basin (e.g., Fig. 2 in Ferrari et al. 2014). The deep-ocean stratification in the basin is on the same order as observed in the Atlantic. The stratification near the southern boundary is unrealistically small, which is an expected problem in coarse-resolution models, which cannot represent bottom-water formation via shelf processes and entraining gravity currents.

Fig. 3.
Fig. 3.

Zonal-mean overturning streamfunction (color shading) and potential density (contours) for the reference simulation with = 1.5 × 10−8 m2 s−3. The different panels show (a) the Eulerian-mean overturning transport , (b) the sum of and the parameterized transient eddy transport , (c) the total isopycnal overturning transport , and (c) the residual transport computed by remapping the isopycnal overturning streamfunction back into physical space. Notice that the color scale is saturated in parts of the upper cell.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

Figure 3a shows the explicitly resolved Eulerian-mean overturning circulation:
e8
The circulation exhibits a strong Deacon cell in the southern channel, which results directly from the wind-driven Ekman transport. In the basin we find upper and abyssal overturning cells, crudely reproducing the observations in the Atlantic; although the abyssal overturning cell is likely weaker, while the upper cell is likely somewhat stronger than observed (e.g., Lumpkin and Speer 2007). This difference may be attributable to the lack of vertical structure in the eddy diffusivity—a topic that we will return to below. As expected, the Deacon cell is largely compensated by the eddy-driven overturning circulation generated by the GM parameterization (Fig. 3b). However, a significant cross-isopycnal overturning circulation remains in the channel region even after the parameterized transient eddy transport is included. This apparently “diabatic” overturning can be explained by deviations from zonal symmetry, which drive an additional “standing eddy” contribution to the overturning transport.
We can compute the true isopycnal overturning transport by integrating the thickness-weighted meridional transport zonally along isopycnals (Andrews 1983). Integrating in the vertical yields an isopycnal overturning streamfunction as
e9
where the zonal integral is taken at fixed potential density σ, and is the parameterized mesoscale eddy transport velocity. In isopycnal space, the overturning circulation shows two interhemispheric overturning cells, separated at σ ≈ 1027.9 kg m−3 (Fig. 3c).

It is instructive to interpolate the isopycnal circulation back into physical space by mapping onto the zonal-mean potential density. In the limit of small-amplitude perturbations, the resulting residual circulation is identical to the transformed Eulerian mean, but the present approach remains well defined and useful even for large perturbations to the zonal mean (Andrews and McIntyre 1976; Andrews 1983; Plumb and Ferrari 2005; Vallis 2006). The thus defined residual circulation shows the familiar picture with upwelling in the channel predominantly along isopycnals (Fig. 3d).

To analyze the effect of changes in the rate and extent of buoyancy loss in the sea ice region around Antarctica, we start by comparing the reference simulation discussed above to two additional simulations. In the “large ice extent” simulation, the same buoyancy loss rate per unit area (1.5 × 10−8 m2 s−3) is applied over 8° from the boundary, implying an approximately 4.5-fold increase in the integrated buoyancy loss rate around Antarctica. In the “large buoyancy loss” simulation, a buoyancy loss rate per unit area of 6.75 × 10−8 m2 s−3 is applied over 2° from the southern boundary, which yields approximately the same integrated buoyancy loss rate as for the large ice extent simulation but applied over the same small sea ice region as in the reference simulation.

The response of the stratification and residual overturning circulation to changes in sea ice area and the rate of buoyancy loss is shown in Fig. 4. An increase of the sea ice area (with constant buoyancy loss rate per unit area) leads to a strong increase in the abyssal stratification, with the density of AABW increasing by about 1.5 kg m−3. The increase in abyssal stratification is in broad agreement with proxy evidence for the LGM (Roberts et al. 2016). The simulations also suggest a significant rearrangement of the overturning circulation, with the upper cell contracting to reduce the penetration depth of NADW. The abyssal cell on the other hand does not appear to expand, with the bulk of the abyssal overturning instead being arguably confined more closely to the bottom of the ocean. As a result, a dead zone with very little circulation appears between about 1500- and 2500-m depth. Similar results are obtained if the buoyancy loss in the sea ice region is enhanced without a corresponding increase in the meridional sea ice extent (Fig. 4c), which indicates that stratification and circulation changes are affected primarily by the magnitude of the integrated buoyancy loss around Antarctica. Increasing the integrated buoyancy loss rate around Antarctica (with or without an increase in the area) also leads to a slight increase in the strength of the abyssal overturning circulation.

Fig. 4.
Fig. 4.

Zonal-mean residual overturning (shading) and potential density (contours) for three simulations with varying extent and rate of high-latitude surface buoyancy loss. (a) A buoyancy loss rate of 1.5 × 10−8 m2 s−3 is prescribed within 2° of the southern boundary. (b) The same buoyancy loss rate per surface area is prescribed within 8° of the southern boundary. (c) A buoyancy loss rate of 6.75 × 10−8 m2 s−3 is prescribed over 2°, yielding about the same integrated buoyancy loss as in (b). The dashed red and blue lines indicate the depth at which the upper and abyssal overturning cells decrease to 25% of their maximum value at the respective latitude, while the black dashed line indicates the cell interface where the streamfunction changes sign. Notice that in particular the cell interface becomes poorly defined at large buoyancy loss rates in the northern part of the domain, where a wide depth range with vanishingly weak circulation develops. Lines are discontinued where their definition becomes ambiguous due to multiple zero crossings.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

To better understand the effect of varying buoyancy loss in the sea ice region around Antarctica, we analyze a series of simulations with varying buoyancy loss rates, using a fixed meridional ice extent of 4°. Buoyancy loss rates range from = 0.5 × 10−8 to 3 × 10−8 m2 s−3 in steps of 0.5 × 10−8 m2 s−3. The resulting basin-averaged stratification and overturning streamfunction are shown in Fig. 5. The figure corroborates the results inferred above. Increasing the buoyancy loss rate leads to a marked and monotonic increase in the deep-ocean stratification below about 1500 m, a monotonic upward shift of the southward-flowing NADW (the positive slope in the overturning streamfunction around 1500 m) and a (less monotonic) contraction of the abyssal overturning cell. As a result of the contraction of both the upper and abyssal cell, a broad depth range of almost stagnant water appears around a depth of 2500 m.

Fig. 5.
Fig. 5.

Basin-averaged stratification (solid) and residual overturning (dashed), as a function of depth, for simulations with a varying rate of buoyancy loss around Antarctica. The color of the lines indicates the rate of buoyancy loss, ranging from = 0.5 × 10−8 m2 s−3 (blue) to = 3 × 10−8 m2 s−3 (orange). In all simulations buoyancy loss is applied over 4° of sea ice extent. The black line indicates an exponential stratification profile with an e-folding depth of 300 m.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

To quantify the changing structure of the deep-ocean circulation, we compute the 75% quantile levels of the upper and abyssal overturning cells, as well as the cell interface, from the basin-averaged circulation shown in Fig. 5. The 75% quantile level for each cell is defined as the level where the overturning streamfunction is reduced to 25% of its peak value; that is, 75% of the southward transport in the upper cell is above its 75% quantile level, while 75% of the southward transport in the abyssal cell is below its 75% quantile level. The cell interface is defined as the level where the overturning streamfunction changes sign. At small buoyancy loss rates, the 75% quantile levels of both cells are about 500 m apart, and both shift upward, together with the cell interface, as the buoyancy loss rate is increased (Fig. 6). As the upper cell contracts, the abyssal cell thus fills the void. However, once the integrated buoyancy loss rate in the sea ice region exceeds about 1.5 × 104 m4 s−3, a further increase in the buoyancy loss rate also leads to a contraction of the abyssal cell, which opens up an increasing gap between the two cells.

Fig. 6.
Fig. 6.

Separation depth between the upper and abyssal cells as a function of the integrated buoyancy loss over the sea ice region around Antarctica. The 75% quantile level of the upper cell (red) is defined such that 75% of the NADW flows southward above this level, while the 75% level of the abyssal cell (blue) is defined such that 75% of AABW returns southward below this level. Also shown is the level where the basin-averaged overturning streamfunction changes sign (black). Pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and squares denote the simulation with 8° sea ice extent. Blue diamonds show the 75% quantile level of the abyssal cell in simulations where the upper cell is suppressed (see text). The black line indicates the predicted dependence of the upper-cell depth on the integrated buoyancy loss rate, using (11) with he = 300 m.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

Figure 6 also includes the simulations with reduced and enhanced sea ice extent from Fig. 4. The 75% quantile levels for both overturning cells in these simulations are largely predicted by the integrated buoyancy loss in the sea ice region, with the meridional extent of the sea ice region only weakly affecting the extent of the abyssal cell. The depth of the cell interface on the other hand is more sensitive to the sea ice extent, shifting upward by about 500 m as the sea ice extent increases from 2° to 8°, qualitatively consistent with (4) and the argument in Ferrari et al. (2014) and Watson et al. (2015). The mean depth of the cell interface also shows some (nonmonotonic) sensitivity to the buoyancy loss rate, which is not predicted by (4). Notice, however, that the cell interface is somewhat poorly defined in the limit of large, integrated buoyancy loss, as the overturning circulation is very weak over a wide depth range.

The results in Fig. 6 represent basin averages, but significant differences exist between changes near the northern end of the basin and at the channel–basin boundary (see also Fig. 4). The upper cell contracts most strongly in the northern part of the basin, while its 75% quantile at the channel–basin boundary in fact slightly deepens. The cell interface deepens weakly but monotonically at the basin channel interface, while it tends to shoal and become poorly defined farther northward (following the contraction of the upper cell there). The abyssal cell contracts monotonically and most strongly near the basin channel boundary, with the nonmonotonic behavior in Fig. 6 explained by an initial expansion at higher northern latitudes (again following the contraction of the upper cell). We will return to these patterns below.

c. Interpretation and scaling relations

In this section, we want to rationalize the key results found above, building on the scaling arguments for the abyssal stratification and overturning circulation discussed in section 2.

1) Abyssal stratification

The increase in the abyssal stratification is readily understood by noting that the buoyancy loss around Antarctica has to be balanced by a diffusive buoyancy flux between the abyssal and upper cells. This balance yields the scaling relation in (6), which suggests that the stratification at the top of the cell interface is expected to increase linearly with the integrated buoyancy loss rate over the sea ice region. While (6) formally holds only for the stratification at the top of the abyssal cell, Fig. 5 shows that the stratification changes relatively little below, such that (6) is expected to provide a reasonable approximation for the bulk abyssal stratification.

Figure 7 shows the stratification averaged over the basin and below 2000-m depth as a function of the integrated buoyancy loss rate. The predicted linear relationship between the abyssal stratification and the integrated buoyancy loss rate holds to a good approximation.

Fig. 7.
Fig. 7.

Abyssal stratification, averaged over the basin and below 2000-m depth, as a function of the integrated buoyancy loss rate in the sea ice region. Pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and the square denotes the simulation with 8° sea ice extent. The black line indicates a linear relationship.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

2) Contraction of the upper cell

As discussed above (and seen in Fig. 4), the upper cell contracts most strongly in the Northern Hemisphere, indicating that the contraction is not directly driven by processes in the channel. Instead the upward shift of NADW is best understood in terms of the thermodynamics in the basin. Figure 5 indicates that the stratification near the maximum of the upper cell changes relatively little in response to changes in the buoyancy loss rate around Antarctica and approximately follows an exponential with an e-folding scale of he ≈ 300 m (we will return to the question of what sets this scale below). We can then estimate the bottom of the upper cell by matching this profile with the stratification at the cell interface predicted by (6), which effectively provides a bottom boundary condition for the upper cell. Notice that the cell interface per se becomes poorly defined for high buoyancy loss rates where a significant dead zone with approximately constant stratification develops below the upper cell. For diagnostic purposes, we here define the bottom of the upper cell again based on the 75% quantile level. Matching (6) with an exponential stratification above z75% yields
e10
where is the stratification at some fixed reference level in the near-exponential regime and is assumed to be approximately constant between simulations (in agreement with Fig. 5). If we are interested only in the change of z75% in response to variations in , the various constants drop out and we find
e11
Using the diagnosed e-folding scale he ≈ 300 m, (11) provides a reasonable fit to the variations in the basin-averaged depth of z75% (solid line in Fig. 6), although it slightly overestimates the contraction of the upper cell. The overestimate can be attributed to the lack of a contraction near the southern end of the basin, where the depth of the overturning cell is instead controlled by adiabatic dynamics in the channel.

Gnanadesikan (1999) and Nikurashin and Vallis (2012) derive scaling relations for the depth scale of the upper cell, which suggest a weak dependence on the buoyancy contrast across the cell and on the eddy diffusivity in the channel. [Although the dependency on the eddy diffusivity drops out in the limit deemed most relevant by Nikurashin and Vallis (2012).] Changes in the buoyancy contrast are small in our simulations and cannot explain the observed contraction of the upper cell. The effective eddy diffusivity in the channel needs to include the effect of standing meanders (see section 2), which appear to account for the slight deepening of the upper cell and cell interface at the channel basin boundary [see also (4)]. The dominant contraction of the upper cell over most of the basin instead is not readily explained by the scaling arguments of Gnanadesikan (1999) and Nikurashin and Vallis (2012). Our interpretation is that the depth scale predicted by the scaling relations of Gnanadesikan (1999) and Nikurashin and Vallis (2012) is best regarded as a predictor for the e-folding scale of the stratification in the upper-cell domain he, which indeed appears to change relatively little (see Fig. 5). However, the bulk of the return flow occurs at the depth where this profile gives way to the more constant stratification below, which in turn is predicted by (11). That is, while the scalings of Gnanadesikan (1999) and Nikurashin and Vallis (2012) provide the vertical scale of the stratification in the upper-cell regime, (6) provides the bottom boundary condition for the upper cell, which is crucial in determining the penetration depth of NADW.

3) Contraction and strengthening of the abyssal cell

In the limit of small buoyancy loss rates around Antarctica, the extent of the abyssal overturning cell appears to be limited largely by the presence of the upper cell. As the upper cell contracts, the abyssal cell fills the void. For larger buoyancy loss rates, however, the abyssal cell ceases to extend all the way to the overlying deep cell and instead starts to contract. This contraction goes together with a strengthening of the abyssal overturning circulation.

We can rationalize the strengthening and contraction of the abyssal cell by noting that the northward transport in the basin is dominated by a bottom boundary layer with downward-sloping isopycnals. Since the heat flux through the bottom boundary vanishes, the horizontal advection of buoyancy in this boundary layer has to be balanced by diffusion through the top of the boundary layer, which yields a scaling relation for the overturning transport as (see also Mashayek et al. 2015):
e12
where LBL is the scale of the meridional buoyancy gradient in the boundary layer, and hBL is the depth of the boundary layer.
The residual overturning circulation in the basin is generally dominated by the Eulerian-mean contribution, which in turn can be obtained by vertical integration of the thermal wind relation. This yields
e13
where ΔbBL is the buoyancy contrast across the boundary layer, Ω is the planetary rotation rate, and WBL is the scale of the zonal buoyancy gradient in the boundary layer. Assuming that WBL/LBL ~ O(1), which is supported by our numerical simulations (see Fig. 8), we can combine (12) and (13) to obtain
e14
Equation (14) resembles the classical scaling for the overturning in a diffusive thermocline (e.g., Vallis 2006), which has here been adapted for the abyssal boundary layer. The expression in (14) is not closed, as it still depends on ΔbBL and LBL, which are not external parameters. However, for the present purpose it suffices to note that ΔbBL increases with increasing buoyancy loss rate around Antarctica, while changes in LBL are comparatively small. The overturning circulation therefore strengthens as the buoyancy loss rate increases (albeit relatively weakly so). The scaling relation in (14) is tested in Fig. 9. Here, ΔbBL is diagnosed from the model results, and LBL is assumed constant. The scaling relation provides a reasonable approximation for the response of the abyssal overturning strength to changes in the buoyancy loss rate.
Fig. 8.
Fig. 8.

Abyssal density, averaged over the lowest 600 m, for two simulations with 4° of sea ice extent and differing buoyancy loss rates: = (left) 1.5 × 10−8 and (right) 3 × 10−8 m2 s−3 m2 s−3. Black arrows indicate the flow in the lowest model layer (i.e., lowest 200 m). Notice that zonal and meridional density gradients are of similar order, and both increase strongly as the buoyancy loss rate is increased (note different color bars in two panels). Notice also that zonal density gradients change sign in the Northern Hemisphere, as required to maintain an overturning circulation in thermal wind balance.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

Fig. 9.
Fig. 9.

Abyssal overturning transport [evaluated as the maximum of the (negative) isopycnal overturning streamfunction in the basin] against the scaling relation in (14) with LBL = W = 6 × 106 m. The term ΔbBL is computed as the buoyancy contrast between the northern end of the basin and the basin channel interface averaged zonally and vertically over the lowest 600 m. As before, pluses indicate simulations with 4° sea ice extent, circles denote simulations with 2° sea ice extent, and the square denotes the simulation with 8° sea ice extent. The black line indicates a linear relationship.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

The contraction of the abyssal cell follows directly from the strengthening of the overturning circulation, as can be seen by combining (7) and (14), which yields a scaling relation for the vertical extent of the abyssal cell as
e15
Remember that L is the length of the basin, which may differ from LBL.

Since ΔbBL increases monotonically with the buoyancy loss rate, (15) suggests a monotonic contraction of the abyssal cell with increasing buoyancy loss rate and thus cannot explain the nonmonotonic behavior shown in Fig. 7. We believe that the reason for this deviation is rooted in the fact that the presented arguments for the upper and abyssal cell extent effectively treat the two cells in isolation and do not consider the limited depth of the basin. In the limit of small buoyancy loss rates, both cells are predicted to keep expanding, implying that they must eventually be “competing” for the limited space in the basin. A closed theory that fully accounts for interactions between the two cells in this limit is beyond the scope of this study. However, we can test the assertion that the nonmonotonic contraction of the abyssal cell is in fact related to the presence of the upper cell. To do so, we repeat three of our simulations with modified surface boundary conditions to suppress the upper cell. In both hemispheres, zero surface buoyancy fluxes are prescribed poleward of 45°, except in the 4° strip around Antarctica, where the buoyancy loss rate is set to = 0.5 × 10−8, 1.5 × 10−8, and 3 × 10−8 m2 s−3, respectively. As expected, the abyssal cell in these simulations contracts monotonically with increasing buoyancy loss rates (blue diamonds in Fig. 6). In the simulation with the largest buoyancy loss rate, the 75% quantile level of the abyssal cell is almost unchanged from the simulation with the upper cell, consistent with the notion that the two cells are well separated and independent in this limit. For the weakest buoyancy loss rate, the abyssal cell instead expands if the upper cell is suppressed, consistent with the notion that the extent of the abyssal cell is limited by the presence of the upper cell in this limit. Curiously, the 75% quantile at intermediate buoyancy loss rate suggests a slight contraction of the abyssal cell if the upper cell is suppressed, which is likely due to other aspects of the rather drastic modification in the surface boundary conditions.

The scenario with the suppressed upper cell may be regarded as a crude model for the Pacific. The numerical results and scaling arguments presented above then predict that increased buoyancy loss rates around Antarctica would lead to a monotonic contraction of the abyssal cell in the Pacific. Whether this prediction holds up in a multibasin configuration remains to be tested.

Previous scaling arguments (e.g., Ito and Marshall 2008; Nikurashin and Vallis 2011) have focused on the dynamics in the channel, while simply assuming a vertical advective–diffusive closure in the basin. From the channel perspective, the contraction of the abyssal cell for large buoyancy loss rates appears to be associated with a weakening of the effect of standing meanders, which results in a steepening of isopycnal slopes. Since the buoyancy flux boundary condition prescribes the meridional extent of the abyssal cell at the surface in the channel, a steepening of the isopycnals is consistent with an increasing confinement of the abyssal cell toward the bottom of the ocean. Notice that this differs from the situation discussed by Ito and Marshall (2008) and Nikurashin and Vallis (2011), where a fixed-surface buoyancy boundary condition is assumed in the channel. A steepening of the isopycnals is then argued to be associated with an increasing vertical scale of the stratification in the basin—a relationship that does not hold in our simulations.

d. The effect of vertically varying mixing

The simulations discussed above use vertically constant diapycnal diffusivity. While this representation simplifies the interpretation of the results, it is not a realistic description of small-scale turbulent mixing in the ocean. Instead diapycnal mixing is generally strongly enhanced near rough bottom topography, while being much smaller in the thermocline (e.g., Waterhouse et al. 2014). To test the robustness of our results with regards to the vertical structure of diapycnal mixing, we repeat the three example simulations shown in Fig. 4 but using vertically varying diapycnal diffusivity. Nikurashin and Ferrari (2013) estimate rates of diapycnal mixing driven by internal wave breaking over the global ocean. A diapycnal mixing profile is generated based on the horizontally averaged diffusivity estimates of Nikurashin and Ferrari (2013), augmented by a small background diffusivity of 10−5 m2 s−1. The resulting profile is shown in Fig. 10. Notice that the diapycnal diffusivity decreases by more than one order of magnitude between the abyssal ocean and the thermocline.

Fig. 10.
Fig. 10.

Vertical structure of the diapycnal diffusivity κ used in simulations with vertically varying mixing.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

Figure 11 shows the results of the reference, large ice extent, and large buoyancy loss simulations with vertically varying diapycnal diffusivities (cf. to Fig. 4 for the corresponding simulations with constant diapycnal diffusivity). Focusing first on the reference case (Fig. 11a), the most notable differences compared to the simulation with constant diapycnal diffusivity are 1) a strongly enhanced stratification in the lower thermocline (~500 m), 2) a somewhat reduced stratification in the abyss, 3) a reduced overturning transport in the upper cell, 4) an enhanced overturning transport in the abyssal cell, 5) a contracted upper cell (particularly in the northern part of the basin), and 6) a somewhat expanded abyssal cell. All results can directly be attributed to the reduced diapycnal mixing in the depth range of the upper cell and increased diapycnal mixing in the depth range of the abyssal cell. Increased diapycnal mixing acts to reduce the stratification and strengthen the diapycnal upwelling (and thus overturning transport) and vice versa. The contraction of the upper cell with reduced diapycnal mixing and expansion of the abyssal cell with enhanced diapycnal mixing are also in qualitative agreement with previous results (Gnanadesikan 1999; Ito and Marshall 2008; Nikurashin and Vallis 2011, 2012).

Fig. 11.
Fig. 11.

As in Fig. 4, but using the vertically varying diapycnal diffusivity shown in Fig. 10.

Citation: Journal of Physical Oceanography 46, 11; 10.1175/JPO-D-16-0084.1

The response of the stratification and circulation to an increase in the sea ice cover or buoyancy loss rate yields qualitatively similar results to those obtained with constant diapycnal mixing (cf. Fig. 11 to Fig. 4). An increase in the integrated buoyancy loss rate around Antarctica (whether or not associated with an expansion of the sea ice region) leads to a strongly increased stratification in the deep ocean, a contraction of the upper cell, as well as a contraction and strengthening of the abyssal cell. As a result of these rearrangements, a significant dead zone again appears between the two overturning cells, with very little transport but relatively strong stratification. As required from a vertical advective–diffusive balance, the stratification in the dead zone is approximately constant in the simulations with vertically constant diapycnal diffusivity but increases upward in the presence of a vertically decreasing diffusivity.

4. Discussion and conclusions

The results of this study highlight the important role played by the integrated buoyancy loss rate around Antarctica in regulating the deep-ocean circulation and stratification. Enhanced buoyancy loss around Antarctica (as has likely occurred during glacial climates) leads to a strong increase in the abyssal stratification. Enhanced buoyancy loss also leads to a contraction of the upper overturning cell and thus upward shift of NADW. The abyssal overturning cell initially expands to fill the void. However, if the buoyancy loss rate further increases, the abyssal cell starts to contract as well, leaving a dead zone with vanishing meridional flow at middepth.

In the real ocean, most of the AABW makes its way into the Pacific and Indian Ocean basins where it upwells and returns as Pacific Deep Water (PDW) and Indian Ocean Deep Water (IDW; e.g., Lumpkin and Speer 2007; Talley 2013). Much of the PDW and IDW returns southward at lower densities and depths than NADW. From the perspective of the global overturning circulation, the upper and abyssal cells therefore overlap, and the resulting circulation arguably more resembles a figure eight than two separated overturning cells (Talley 2013; Ferrari et al. 2014). In the single-basin setup analyzed in this study, the upper and abyssal cells by definition cannot overlap. Nevertheless, the mechanisms discussed here suggest that the contraction of both the abyssal and upper cell in response to enhanced surface buoyancy loss rates is likely to be robust. This leads us to speculate that enhanced buoyancy loss rates around Antarctica would generate an upward shift of NADW and a downward shift of PDW and IDW. As a result we may expect the two overturning cells to become increasingly separated as the buoyancy loss rate increases. The rearrangement would be similar to that sketched in Ferrari et al. (2014) for the difference in the circulation between the present and LGM, although the proposed mechanism is somewhat different.2 However, the question of how exactly the change in the overturning circulation would play out with multiple basins remains an open question, which we plan to address in a follow-up study.

The changes in stratification and overturning circulation found here in response to enhanced buoyancy loss around Antarctica resemble proxy observations for the LGM. Roberts et al. (2016) estimate that the density contrast between intermediate and abyssal waters in the South Atlantic increased by about 3 kg m−3 between the present and LGM, suggesting that the stratification in the deep Atlantic during the LGM was about as large as in our simulations with the largest integrated buoyancy loss rates. The circulation changes predicted here are also in qualitative agreement with the presence of a middepth water mass age maximum inferred for the LGM (e.g., Burke et al. 2015 and references therein). This middepth age maximum is expected as a result of the upward shift of relatively young NADW, which is replaced either by returning AABW (for moderate buoyancy loss rates) or by a dead zone with very weak meridional flow (for large buoyancy loss rates). Either reconfiguration is expected to lead to significantly older water masses at middepth.

The numerical model used here does not consider potential changes in the mesoscale transient eddy diffusivity in response to changes in the buoyancy loss rate, which could potentially lead to additional feedbacks. The increased buoyancy gradient in the channel region found for higher buoyancy loss rates would likely lead to an increase in the mesoscale eddy diffusivity (Green 1970; Stone 1972; Held and Larichev 1996; Jansen et al. 2015). An increased mesoscale eddy diffusivity in turn is expected to lead to a further contraction of the upper cell (Nikurashin and Vallis 2012), thus enhancing the discussed response of the deep-ocean circulation to changes in the buoyancy loss rate around Antarctica.

Acknowledgments

We thank Raffaele Ferrari for providing the eddy diffusivity data from Nikurashin and Ferrari (2013) as well as for interesting discussions and comments. We also thank Jess Adkins and two anonymous reviewers for their stimulating comments. The MITgcm configuration files used for this study are available upon request from the corresponding author. Computational resources for this project were generously provided by the University of Chicago Research Computing Center. M. F. J. acknowledges support from NSF Award OCE-1536450. L. P. N. acknowledges support from FQRNT (Grant 2017-NC-197086) and NSERC (Grant 06712-2015).

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1

The model dynamics only depend on the buoyancy b = g(ρρref)/ρref. For easy comparison to ocean observations, buoyancy fields have been translated to density fields by choosing a reference density characteristic of the present-day ocean. Notice, however, that the absolute value of the density is dynamically meaningless.

2

In Ferrari et al. (2014), the rearrangement is attributed to a geometric effect associated with the increased sea ice extent, while the present study highlights the role of the magnitude of the integrated buoyancy loss around Antarctica. In practice, the two effects may work together, which strengthens the notion that increased sea ice extent and buoyancy loss around Antarctica during the LGM could have led to a separation between the upper and abyssal overturning cells.

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