a. Volume and salt budgets

The volume $\mathbb{V}$ and salt content $\mathbb{S}$ of the region of all seawater fresher than S* and south of ϕ (illustrated in Fig. 1) are given by

$\mathbb{V}\left(\varphi ,S^{*},t\right)={\displaystyle \underset{S\left(x,y,z,t\right)\le S^{*}}{\iiint }H\left(\varphi -y\right)\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}\hspace{0.17em}\text{and}$(1a)

$\mathbb{S}\left(\varphi ,S^{*},t\right)={\displaystyle \underset{S\left(x,y,z,t\right)\le S^{*}}{\iiint }H\left(\varphi -y\right){\rho }_{0}S\hspace{0.17em}dx\hspace{0.17em}dy\hspace{0.17em}dz}.$(1b)

In Eq. (1), H() denotes the Heaviside step function, y is latitude, S(x, y, z, t) is the three-dimensional salinity field, and the integral bounds refer to the region of seawater fresher than S* (commonly used to define the integral domain in the water mass transformation literature; Groeskamp et al. 2019). The volumetric distribution in latitude–salinity space, described by Eq. (1a), is shown in Fig. 2c.

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Schematic of the processes that contribute to the volume and salt content of the region of seawater bounded by the S(x, y, z, t) = S* isohaline and the y = ϕ latitude. Straight arrows correspond to volume fluxes. Wavy arrows correspond to salt fluxes. The volume evolves through diahaline volume fluxes $\mathcal{G}$, atmospheric volume fluxes ${\mathcal{J}}_F$, and volume fluxes across the y = ϕ boundary, denoted Ψ. The salt content evolves through salt transport across the S = S* isohaline from diffusion D and advection ${\rho }_0{S}^{*}\mathcal{G}$, and meridional salt fluxes across the boundary at y = ϕ are represented by $\mathcal{A}$, which includes both advective (${\mathcal{A}}_{\text{adv}}$) and diffusive (${\mathcal{A}}_{\text{diff}}$) components. A small surface salt flux ${\mathcal{J}}_S$ may occur in polar regions and near continents.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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Spatial pattern of (a) surface freshwater fluxes and (b) surface salinity. Surface fluxes and salinity are strongly correlated, with regions of net evaporation in the subtropics corresponding to more saline regions and regions of high precipitation in the tropics and high latitudes being fresher. (c) Volumetric salinity distribution of surface salinity in latitude–salinity space. The dashed curve show the maximum salinity at each latitude of the global ocean (the high-salinity values of the Mediterranean Sea, the Red Sea, and the Persian Gulf have been omitted from these curves). The dotted curve shows the mean salinity at each latitude.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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The salt budget of the volume $\mathbb{V}$ is given by

${\displaystyle \frac{\partial \mathbb{S}}{\partial t}}=-\underset{{\rho }_0{S}^{*}\mathcal{G}}{\underbrace{{\displaystyle \underset{S=S^{*}}{\iint }H}\left(\varphi -y\right){\rho }_0{S}^{*}\left(\mathbf{v}-{\mathbf{v}}_S\right)\cdot {\widehat{\mathbf{n}}}_S\hspace{0.17em}d{A}_S}}-\underset{\mathcal{D}}{\underbrace{{\displaystyle \underset{S=S^{*}}{\iint }H\left(\varphi -y\right)}{\mathbf{D}}_S\cdot {\widehat{\mathbf{n}}}_S\hspace{0.17em}d{A}_S}}-\underset{{\mathcal{A}}_{\text{adv}}}{\underbrace{{\displaystyle \underset{S\le S^{*},y=\varphi }{\iint }{\rho }_{0}S\mathbf{v}}\cdot \widehat{\mathbf{y}}\hspace{0.17em}dx\hspace{0.17em}dz}}-\underset{{\mathcal{A}}_{\text{diff}}}{\underbrace{{\displaystyle \underset{S\le S^{*},y=\varphi }{\iint }{\mathbf{D}}_{\varphi }}\cdot \widehat{\mathbf{y}}\hspace{0.17em}dx\hspace{0.17em}dz}}-\underset{{\mathcal{J}}_S}{\underbrace{{\displaystyle \underset{S\le S^{*},y\le \varphi }{\iint }{\mathbf{Q}}_S}\hspace{0.17em}dx\hspace{0.17em}dy}}.$(3)

The first integral on the right-hand side of Eq. (3), denoted ${\rho }_0{S}^{*}\mathcal{G}$, is the diahaline salt transport associated with the diahaline volume transport $\mathcal{G}$. The second integral, $\mathcal{D}$, is the diahaline diffusive salt transport. The third and fourth integrals, ${\mathcal{A}}_{\text{adv}}$ and ${\mathcal{A}}_{\text{diff}}$, are the meridional salt transport across y = ϕ from advection and along-isopycnal (neutral) diffusion, respectively. The total meridional salt transport across y = ϕ is given by $\mathcal{A}={\mathcal{A}}_{\text{adv}}+{\mathcal{A}}_{\text{diff}}$. The accumulated surface salt transport is denoted ${\mathcal{J}}_S$. While little salt is exchanged between the ocean and atmosphere, there are salt inputs from runoff and sea ice formation, denoted here by Q_S; Q_S also includes nonphysical salt fluxes that are often introduced in the upper grid cells of ocean models to restore the salinity to a climatology. The processes contributing to the salt budget Eq. (3) are illustrated by the wavy arrows in Fig. 1. The processes contributing to the volume and salt budgets are summarized in Table 1.

Table 1.

Table of symbols.

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The relationship between surface freshwater fluxes and sea surface salinity is shown in Figs. 2a and 2b. Notably, despite this relationship, the surface freshwater flux ${\mathcal{J}}_F$ does not contribute to the salt budget. This means that, in isolation, Eq. (3) is not useful for understanding pathways of freshwater in the ocean and cannot be used to quantify ocean salinity.

b. Internal salt content

Here, we combine the budgets for volume [Eq. (2)] and salt [Eq. (3)] to define the “internal salt content” of the region of seawater fresher than the isohaline S* and south of the latitude ϕ. The internal salt content of this region, which is adapted from the internal heat content that was introduced by Holmes et al. (2019a,b), measures the salt content associated with the deviation in salinity between the mean salinity of the region and its bounding isohaline.

c. Internal salt transport

The approach taken above to derive the internal salt content of the region can be applied to the meridional salt transport to separate it into internal and external components. The internal component corresponds to a “salt function” that quantifies the transport of internal salt achieved by branches of circulation that link precipitative and evaporative regions.

d. Internal salt budget

e. Equivalent surface freshwater transport

Both internal salt and internal freshwater can be used to quantify the processes that determine ocean salinity. As an approach to quantify the global oceanic water cycle, the internal saltwater/freshwater budget framework offers the following benefits:

1. Internal salt content is defined relative to the salinity of the bounding isohaline and therefore does not require the definition of an arbitrary reference salinity. This offers a significant improvement over other approaches that quantify the meridional transport of freshwater (e.g., Wijffels 2001; Tsubouchi et al. 2012).

2. The internal saltwater/freshwater transport of specific components of the circulation can be unambiguously quantified. Furthermore, a vector field can be defined describing the pathways through which internal freshwater is redistributed in the ocean between precipitative sources and evaporative sinks.

3. The use of water mass coordinates and the use of a numerical model’s salinity budget tendency terms allows us to unambiguously isolate the roles that surface freshwater forcing, mixing, and meridional exchanges can play in setting the distribution of salinity in the ocean.

a. Diahaline and meridional processes

Analysis of the time-averaged global internal salt budget as a function of salinity S* (Fig. 3a) and the vertically and zonally integrated budget as a function of latitude ϕ (Fig. 3b) allows us to examine the processes involved in diahaline and meridional internal salt transport in isolation. The global internal salt budget reveals the balance between surface forcing (green curve in Fig. 3a) and mixing (blue, orange, and purple curves in Fig. 3a). The tendency term (red line in Fig. 3a) is relatively small indicating that the model is near equilibrium. Surface fluxes transfer freshwater across the global mean salinity of 34.6 g kg⁻¹ from high-salinity water in the subtropics to low salinity in the subpolar and tropical regions. By concentrating salinity in more saline regions through net evaporation and diluting salinity in fresher regions through net precipitation, forcing stretches the global distribution of salinity (Zika et al. 2015). Approximately 2.3 Sv of freshwater is transferred between evaporative and precipitative regions by the atmosphere (shown in the units of the right-hand axis in Figs. 3a and 3b). This is equivalent to 8 × 10⁷ kg s⁻¹ of salt, which is comparable to the budgets presented by Hieronymus et al. (2014), Zika et al. (2015), and Grist et al. (2016).

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The time-averaged (a) globally integrated internal salt budget [Eq. (10)] as a function of salinity S^* shows the global contributions of surface forcing $\mathcal{F}\left(S^{*}\right)$ (green curve), which moves freshwater from high-salinity water to low-salinity water (shown as equivalent salt), and mixing, which moves salt from high-salinity water to low-salinity water through vertical mixing $\mathcal{M}\left(S^{*}\right)$ (blue curve), neutral (along isopycnal) mixing $\mathcal{N}\left(S^{*}\right)$ (orange curve), and numerical mixing $\mathcal{I}\left(S^{*}\right)$ (purple curve). (b) The vertically integrated internal salt budget as a function of latitude ϕ shows the balance between surface forcing $\mathcal{F}\left(\varphi ,S^{\max }\right)$ (green curve) and internal salt transport ${\mathcal{A}}_I\left(\varphi ,S^{\max }\right)$. Numerical mixing should not contribute to (b), because it fluxes salt or freshwater only across isohalines and not across latitude lines. However, numerical mixing is calculated here by residual and also includes a small error associated with missing the meridional volume flux associated with a sea surface height smoother included to suppress a computational mode in MOM’s B-grid barotropic equations. In (b) this term is thus denoted η-smoother.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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The stretching of the global salinity distribution through surface forcing is balanced by interior mixing, which transfers salt downgradient from high-salinity to low-salinity water (Hieronymus et al. 2014; Zika et al. 2015). Given the near equilibrium state of the model, mixing balances surface forcing almost exactly. Mixing includes contributions from several processes. Vertical mixing $\mathcal{M}$, which includes parameterized boundary layer mixing processes, transports approximately 2.8 × 10⁷ kg s⁻¹ of salt across the mean salinity (blue curve in Fig. 3a). Vertical mixing is largest above and below the mean salinity, reflecting the dominant role of boundary layer mixing processes in regions of strong precipitation or strong evaporation. The contribution of parameterized neutral diffusion $\mathcal{N}$ is larger at the global mean salinity, transferring approximately 3.5 × 10⁷ kg s⁻¹ of salt to water fresher than 34.4 g kg⁻¹ (orange curve in Fig. 3a). Numerical mixing $\mathcal{I}$ is smaller than the parameterized mixing terms but still provides a significant contribution to the total mixing [purple curve in Fig. 3a; a more detailed discussion of numerical mixing is presented in Holmes et al. (2019a)].

In the steady state, meridional salt transport is negligible. Therefore, the vertically integrated internal salt budget effectively reduces to the vertically integrated mass budget. The meridional convergence of mass within the ocean must balance the surface freshwater transport, shown in Fig. 3b. Here, we see that the surface internal salt flux and meridional transports are separated into distinct regions of convergence, whose boundaries are given by the zeros of the two curves at 22°S and 16°N. These boundaries separate the evaporative regions in both hemispheres and constrain the pathways of internal salt transport, which is discussed in section 4b. Note that there is a small residual in the vertically integrated internal salt budget associated with the sea surface height smoother included to suppress a checkerboard null mode in the B-grid barotropic equations (purple curve in Fig. 3b).

b. Internal salt transport in latitude–salinity space

Contours of time-averaged meridional volume transport Ψ describe the pathways of the circulation of seawater in latitude–salinity space. The latitude–salinity coordinate streamfunctions shown in Figs. 4a–c are qualitatively similar to the streamfunctions of the idealized simulations by Ferreira and Marshall (2015), which suggests that they are an emergent consequence of the geometry of the ocean basins and surface freshwater fluxes.

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Time-averaged (top) salinity streamfunction Ψ and (bottom) salt function ${\mathcal{A}}_I$ for the (a),(d) global ocean; (b),(e) Indo-Pacific Ocean; and (c),(f) Atlantic Ocean. Positive values of the streamfunction correspond to counterclockwise circulation. Contours describe the pathway of internal salt between sources in the evaporation-dominated subtropics and sinks in the precipitation-dominated tropics and poles. The dashed and dotted curves show the maximum salinity and mean salinity, respectively, at each latitude of the global ocean and each of the ocean basins as in Fig. 2c. Vertical dashed lines show the meridional boundaries of the Indo-Pacific and Atlantic–Arctic basins.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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The salinity along closed contours of Ψ evolves through the diahaline exchange of salt and freshwater by surface forcing and mixing. Figure 4a shows that the closed cells of Ψ are bounded within each of the meridional convergence regions identified in Fig. 3b. The Southern Hemisphere contains a counterclockwise cell that circulates fresher water from the Southern Ocean northward into the high-salinity midlatitudes of the Southern Hemisphere before returning saltier water to the Southern Ocean, with a maximum volume transport of approximately 30 Sv. The tropical and Northern Hemisphere regions of convergence each contain a large clockwise circulation cell, which transport a maximum volume of around 20 Sv. The maximum salinity range between the northward and southward branches of each of these major cells is approximately 2–3 g kg⁻¹.

The salt function ${\mathcal{A}}_I$ quantifies the meridional internal salt transport across a given latitude ϕ, including both advective internal salt transport and neutral diffusion. In steady state, the contours of ${\mathcal{A}}_I$ can be interpreted as the pathways of internal salt transport that connect the high-salinity regions of net evaporation and the low-salinity regions of net precipitation. Figures 4d–f show that contours of ${\mathcal{A}}_I$ are steepest near regions with strong surface freshwater fluxes, reflecting the dominance of diahaline processes in these regions. Between these regions, the contours of ${\mathcal{A}}_I$ become flatter, which indicates that ocean circulation plays an important role in maintaining the ocean’s salinity distribution by moving fresher seawater from regions of net precipitation to the midlatitudes and carrying high-salinity seawater back to the adjacent precipitative regions.

The contributions to the global internal salt transport from the individual Indo-Pacific and Atlantic–Arctic basins are shown in Figs. 4b and 4c, respectively. The salinity in the North Pacific is maintained by northward internal salt transport from the region of net evaporation north of 20°N and by a southward internal salt transport of approximately 1.2 × 10⁶ kg s⁻¹ through the Bering Strait from the Arctic Ocean. Internal salt transport from the Arctic Ocean into the Pacific is fed by a northward transport of approximately 1 × 10⁷ kg s⁻¹ in the North Atlantic. The Atlantic Ocean contains a large, clockwise circulation cell that extends over the entire basin, which is shown in 4c. The Northward branch shows significant variations in salinity associated with evaporation over the subtropics, precipitation in the tropics and high latitudes, and mixing, indicating transport in the mixed layer associated with the northward branch of the Atlantic is dominated by a combination of the Atlantic meridional overturning circulation (AMOC) and the wind-driven subtropical gyres. The fresher water advected southward experiences little variation in salinity, which indicates that mixing is weak and suggests that it is transported at depth by the deep southward flowing branch of the AMOC. This large circulation cell drives a net northward transport of internal salt throughout the entire basin (Fig. 4f).

The circulation cell across 34°S associated with the AMOC occupies a relatively small salinity range. Two weaker counterclockwise cells circulate across 34°S between the Atlantic and the Southern Ocean, one fresher and another more saline than the AMOC circulation cell (Fig. 4c). The fresher of these cells, associated with Antarctic Bottom Waters, circulates in a narrow salinity range, moving freshwater northward across the equator. The more saline cell also carries freshwater into the Atlantic and is associated with shallow water transport along the continental boundaries (not shown).

In comparison with the Indo-Pacific, there is only a very small internal salt transport southward across 34°S in the Atlantic Ocean. The overturning in salinity–latitude coordinates indicates that there are two reasons for the smallness of this transport: 1) within the dominant clockwise circulation, which transports internal salt northward, the northward moving water is not substantially saltier than the southward moving water (~0.2 g kg⁻¹) and 2) there are two anticlockwise circulations, one at high and another at low salinities, whose combined southward internal salt transport is larger than the clockwise cell leading to a net southward internal salt transport. The clockwise cell manifests as a southward oriented vector while the two anticlockwise cells manifest as northward vectors in Fig. 6c. The incoming higher-salinity water (northward flow between approximately 35 and 35.5 g kg⁻¹) is likely associated with Agulhas leakage. If the salinity of this incoming water were increased, this could easily alter the internal salt transport from net southward to net northward.

c. Regional contributions from forcing and mixing

While the internal salt transport discussed in section 4b depends on the meridional exchange of seawater of differing salinities between evaporative and precipitative regions of the ocean, it also requires the exchange of salt and freshwater across isohalines by surface forcing and mixing. Here we examine the regional importance of forcing and mixing for internal salt transport using the salinity–latitude structure of the diahaline fluxes (given by the meridional derivative of the accumulated diahaline fluxes $\mathcal{F}$, $\mathcal{N}$, $\mathcal{M}$, and $\mathcal{I}$; Holmes et al. 2019b).

The surface forcing term $\partial \mathcal{F}/\partial \varphi$ reveals the regional pattern of surface freshwater fluxes (shown in Figs. 5a–c for the global ocean and individual basins). Net evaporation occurs in the midlatitudes of both Hemispheres over water more saline than the local mean salinity (red regions in Figs. 5a–c). These evaporative fluxes provide the atmospheric moisture for the net precipitation in water fresher than the local mean salinity in the high latitudes and tropics. As discussed in section 4a ocean circulation is arranged to balance the surface fluxes from adjacent evaporative and precipitative regions. This means that the effect of surface freshwater fluxes is a local diahaline stretching of the salinity distribution.

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Diahaline processes in latitude–salinity space. The contribution to diahaline transport per unit latitude from the surface forcing $\partial \mathcal{F}/\partial \varphi$ is shown in (a) global, (b) Indo-Pacific, and (c) Atlantic Oceans, showing the pattern of evaporation over the subtropics and precipitation over the tropics and high latitudes. (d)–(f) The contribution to diahaline transport per unit latitude from vertical mixing $\partial \mathcal{M}/\partial \varphi$, showing the close relationship of boundary layer mixing and surface forcing. (g)–(i) The contribution to diahaline salt transport per unit latitude from neutral mixing $\partial \mathcal{N}/\partial \varphi$. (j)–(l) The per-latitude residual diahaline transport $\partial \mathcal{I}/\partial \varphi$. The dashed and dotted curves show the maximum salinity and mean salinity, respectively, at each latitude of the global ocean and each of the ocean basins as in Fig. 2c.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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The strong region of net precipitation in the tropics of the Northern Hemisphere of the global ocean (Fig. 5a) occurs predominately in the Indo-Pacific Ocean basin (Fig. 5b). This large input of freshwater is provided by atmospheric transport from the adjacent evaporative regions in the Indo-Pacific, as well as transport of freshwater evaporated over the North Atlantic Ocean (Wijffels et al. 1992; Schmitt 2008). The Atlantic Ocean is dominated by evaporation, which is reflected in its relatively high salinity in comparison with the Indo-Pacific (cf. the salinity ranges in Figs. 5b,c). The major surface freshwater input occurs through river runoff near the equator from the Amazon river, which dilutes the salinity of the shallow northward branch of the AMOC (Fig. 4c). This freshwater input provides a relatively minor contribution to ${\mathcal{A}}_I$; however, it influences the flow of internal salt in latitude–salinity space.

The steep sections along contours of ${\mathcal{A}}_I$ that occur near regions of strong evaporation and precipitation (Figs. 4d–f) reflect the dominance of diahaline processes. In these regions, mixing fluxes salt downgradient from high-salinity to low-salinity water, balancing the large salinity gradients in the upper ocean that are introduced by surface freshwater fluxes. The action of mixing to smooth salinity gradients in the boundary layer is reflected by the downgradient (blue in Fig. 5) salt flux across the local mean salinity due to vertical mixing, $\partial \mathcal{M}/\partial \varphi$ (Figs. 5d–f). The total salt flux from all mixing processes is significantly larger in the tropics than the high-latitude regions, with 3.5 × 10⁷ kg s⁻¹ of internal salt transported across the global mean salinity in the tropics, as compared with 2 × 10⁷ kg s⁻¹ of internal salt in the high latitudes.

Vertical mixing is the largest mixing process in the tropics and is dominated by boundary layer mixing. Vertical mixing is strong in the tropics in both the Indo-Pacific Ocean and the Atlantic Ocean, with the large diffusive diahaline salt flux in the equatorial Atlantic Ocean corresponding to the large freshwater input from river runoff that is mixed into saltier ocean waters (Figs. 5e,f). In contrast to the tropics, parameterized neutral diffusion, which occurs predominately in the interior ocean, is the largest contributor to mixing in the high latitudes.

Unlike vertical mixing, neutral diffusion can drive meridional fluxes of salt and freshwater that can result in net convergences or divergences at any given latitude (i.e., $\partial \mathcal{N}/\partial \varphi$ in Figs. 5g–i can be both negative and positive). Neutral diffusion is highly localized, providing large divergences and convergences of salt in the Southern Ocean, near the equator and in the high latitudes of the Atlantic. Numerical mixing provides a relatively small contribution to regional mixing (Figs. 5j–5l, where the small regions of positive values arise from the neglect of the volume transport due to the sea surface height smoother in the internal salt budget).

d. The global freshwater balance

The vector field defined by F_S and F_ϕ defined in Eq. (12) describe the oceanic processes responsible for internal freshwater transport within the ocean. The pathways of internal freshwater transport are similar to the contours of the salt function (Fig. 4) except that here we separate out only those components arising from oceanic transport (i.e., we exclude the contribution from surface forcing). The vector field therefore describes the redistribution of internal freshwater from sources in the high latitudes and tropics to the subtropical sinks. They also allow us to describe the pathways of net freshwater transport between ocean basins, which balance asymmetries in freshwater forcing.

The time-averaged vector fields for the global ocean and the individual basins are shown in Figs. 6a–c. The transport vectors diverge away from regions of net precipitation (blue in Figs. 6a–c)and converge in regions of net evaporation (red in Figs. 6a–c). The strongly diahaline (vertical) vectors reflect the regional importance of mixing. Mixing is particularly strong in the precipitative regions in the tropics and Southern Ocean. In the Northern Hemisphere freshwater is mixed over larger salinity and latitude ranges, which reflects the different salinity profiles of North Pacific and North Atlantic Ocean basins.

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Pathways of internal freshwater transport between sources and sinks in latitude–salinity space [Eq. (12)] for the (a) global, (b) Indo-Pacific, and (c) Atlantic Oceans. Black arrows correspond to the pathways through which oceanic processes redistribute freshwater added in regions of net precipitation. The thick black arrows at the boundaries of (b) and (c) show the internal freshwater transport between basins. The background contours show the pattern of surface freshwater fluxes, with precipitative fluxes in the tropics and high latitudes (blue) and evaporative fluxes in the midlatitudes (red). The gray dashed lines represent the boundary of the Southern Ocean at 34°S and Bering Strait at 64°N. The small dashed line in (c) shows the boundary between the Atlantic Ocean and Arctic Ocean. The dashed curves and dotted curves show the maximum and mean salinity at each latitude, respectively, as in Fig. 2c.

Citation: Journal of Physical Oceanography 51, 7; 10.1175/JPO-D-20-0212.1

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Figures 6b and 6c show the vector fields in the Indo-Pacific and Atlantic–Arctic Ocean basins. Almost all of the northward internal freshwater transport out of the Southern Ocean enters the Indo-Pacific. Approximately 0.6 Sv is transported equatorward, which balances the evaporative fluxes in the subtropics of the Indo-Pacific to about 20°S. A southward pathway of internal freshwater transport from approximately 8°N provides the remaining internal freshwater transport required to balance the evaporative region in the Southern Hemisphere north of 22°S. The majority of the internal freshwater that is added in the high latitudes of the Pacific through precipitation is transported southward into the subtropics of the North Pacific. Only a relatively small internal freshwater transport of 0.04 Sv passes through the Bering Strait into the Arctic Ocean, which is similar in magnitude and direction to estimates of net freshwater transport reported in other studies (e.g., Talley 2008).

Internal freshwater transport in the Atlantic is predominately southward (vectors in Fig. 6c). The Arctic Ocean provides approximately 0.26 Sv of internal freshwater that is transported southward, freshening the North Atlantic Ocean. The freshened water is transported at depth by the southward branch of the AMOC, which extends along the entire Atlantic Ocean basin, but is also redistributed into the midlatitudes through diahaline processes (Fig. 4c). The large freshwater input at low latitudes provides the other major source of internal freshwater within the Atlantic Ocean. However, this predominately freshens the northward branch of the AMOC (shown in the strong diahaline pathway leading upward from low-salinity water in Fig. 6c). The Atlantic Ocean receives only a small internal freshwater transport of 0.01 Sv across 34°S from the Southern Ocean. This indicates that the salinity of the Atlantic Ocean basin does not receive a significant contribution from the Southern Ocean, and is therefore not a major pathway to balance asymmetries in surface freshwater fluxes between the various ocean basins in ACCESS-OM2.