Internal Salt Content: A Useful Framework for Understanding the Oceanic Branch of the Water Cycle

Christopher Bladwell; Ryan M. Holmes; Jan D. Zika

doi:10.1175/JPO-D-20-0212.1

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Journal of Physical Oceanography

Abstract
Significance Statement
1. Introduction
2. Internal salt framework
3. Model
4. Results and discussion
5. Conclusions
Acknowledgments
Data availability statement
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Fig. 1.

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 $G$ , atmospheric volume fluxes $J_{F}$ , 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 $ρ_{0} S^{*} G$ , and meridional salt fluxes across the boundary at y = ϕ are represented by $A$ , which includes both advective ( $A_{adv}$ ) and diffusive ( $A_{diff}$ ) components. A small surface salt flux $J_{S}$ may occur in polar regions and near continents.

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Fig. 2.

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.

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Fig. 3.

The time-averaged (a) globally integrated internal salt budget [Eq. (10)] as a function of salinity S^* shows the global contributions of surface forcing $F (S^{*})$ (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 $M (S^{*})$ (blue curve), neutral (along isopycnal) mixing $N (S^{*})$ (orange curve), and numerical mixing $I (S^{*})$ (purple curve). (b) The vertically integrated internal salt budget as a function of latitude ϕ shows the balance between surface forcing $F (ϕ, S^{\max})$ (green curve) and internal salt transport $A_{I} (ϕ, S^{\max})$ . 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.

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Fig. 4.

Time-averaged (top) salinity streamfunction Ψ and (bottom) salt function $A_{I}$ 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.

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Fig. 5.

Diahaline processes in latitude–salinity space. The contribution to diahaline transport per unit latitude from the surface forcing $\partial F / \partial ϕ$ 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 $\partial M / \partial ϕ$ , 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 $\partial N / \partial ϕ$ . (j)–(l) The per-latitude residual diahaline transport $\partial I / \partial ϕ$ . 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.

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Fig. 6.

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.

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Fig. 7.

Schematic of the major processes contributing to the internal freshwater budget. To balance atmospheric freshwater fluxes, internal freshwater is transported within the ocean from the precipitative, low-salinity bowls in the high latitudes and tropics (blue regions) to the evaporative, high-salinity bowls in the midlatitudes (red regions). Transport of internal freshwater across isohalines requires vertical mixing (blue arrows), neutral (along-isopycnal) mixing (orange arrows), or numerical mixing (purple arrows). Meridional internal freshwater transport between low-salinity and high-salinity regions is shown with the black arrows, crossing the approximate boundaries between evaporative and precipitative latitudes. Meridional internal freshwater transport is constrained by nodes where the transport is zero (corresponding to where the latitudinally accumulated surface freshwater flux is zero) at 22°S and 16°N, depicted by the thick dashed lines.

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Editorial Type:: Article

Article Type:: Research Article

Internal Salt Content: A Useful Framework for Understanding the Oceanic Branch of the Water Cycle

Christopher Bladwell

Christopher Bladwell^aSchool of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

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Ryan M. Holmes

Ryan M. Holmes^bClimate Change Research Centre, ARC Centre of Excellence for Climate Extremes, Sydney, New South Wales, Australia
^aSchool of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

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Jan D. Zika

Jan D. Zika^aSchool of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

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Online Publication:: 10 Jun 2021

Print Publication:: 01 Jul 2021

DOI:: https://doi.org/10.1175/JPO-D-20-0212.1

Page(s):: 2167–2179

Received:: 28 Aug 2020

Accepted:: 17 Feb 2021

Published Online:: 10 Jun 2021

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

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Abstract

The global water cycle is dominated by an atmospheric branch that transfers freshwater away from subtropical regions and an oceanic branch that returns that freshwater from subpolar and tropical regions. Salt content is commonly used to understand the oceanic branch because surface freshwater fluxes leave an imprint on ocean salinity. However, freshwater fluxes do not actually change the amount of salt in the ocean and—in the mean—no salt is transported meridionally by ocean circulation. To study the processes that determine ocean salinity, we introduce a new variable “internal salt” along with its counterpart “internal fresh water.” Precise budgets for internal salt in salinity coordinates relate meridional and diahaline transport to surface freshwater forcing, ocean circulation, and mixing and reveal the pathway of freshwater in the ocean. We apply this framework to a 1° global ocean model. We find that for freshwater to be exported from the ocean’s tropical and subpolar regions to the subtropics, salt must be mixed across the salinity surfaces that bound those regions. In the tropics, this mixing is achieved by parameterized vertical mixing, along-isopycnal mixing, and numerical mixing associated with truncation errors in the model’s advection scheme, whereas along-isopycnal mixing dominates at high latitudes. We analyze the internal freshwater budgets of the Indo-Pacific and Atlantic Ocean basins and identify the transport pathways between them that redistribute freshwater added through precipitation, balancing asymmetries in freshwater forcing between the basins.

Significance Statement

Recent efforts to measure changing rainfall patterns have focused on sea surface salinity. This presents a number of challenges because salinity is determined by surface freshwater fluxes as well as circulation and mixing within the ocean, which depend on salinity gradients. We introduce the concepts of “internal salt” and “internal fresh water,” which measure the salt and freshwater content associated with variations in salinity within water masses in the ocean. We present precise budgets of internal salt and freshwater that we use to identify the oceanic pathways through which precipitation added in the subpolar and tropical regions is redistributed to balance evaporation in the subtropics. Future studies will investigate the response of circulation and mixing to long-term water cycle change.

Corresponding author: Christopher Bladwell, c.bladwell@unsw.edu.au

Abstract

Significance Statement

Corresponding author: Christopher Bladwell, c.bladwell@unsw.edu.au

Keywords: Ocean; Mixing; Hydrologic cycle; Ocean models

1. Introduction

The atmospheric branch of the water cycle can be characterized as an extraction of freshwater from the sea surface at subtropical latitudes via net evaporation and a deposition of freshwater via precipitation outside of the subtropics. This deposition is manifest as an intense rainband in the tropics associated with the intertropical convergence zone and broad net precipitation zones toward the poles. In steady state, freshwater transported away from the midlatitudes by the atmosphere and rivers must be balanced by an equal and opposite convergence of freshwater into the midlatitudes within the ocean (Wijffels 2001; Schmitt 2008).

Freshwater fluxes at the ocean’s surface play a central role in the distribution of salinity in the upper ocean: net evaporation over the midlatitudes concentrates the salinity, while in the tropics and toward the poles net precipitation dilutes salinity (Wüst 1936). The consequent salinity gradients created in the upper ocean are essential for driving ocean circulation (Zika et al. 2012).

Recent efforts to study water cycle change have focused on the relationship between the spatial pattern of oceanic precipitation and evaporation, and the distribution of ocean salinity. An intensification in the pattern of upper-ocean salinity has been observed in response to the changing atmospheric water cycle (Durack and Wijffels 2010; Helm et al. 2010; Skliris et al. 2014; Zika et al. 2018). However, using ocean salinity to better quantify this change necessitates a deeper understanding of the complex balance between atmospheric freshwater transport, large-scale circulation and mixing within the ocean.

Global salt and freshwater transports were estimated by Wijffels et al. (1992). Such studies have been valuable in broadly characterizing the redistribution of freshwater from net precipitation to net evaporation zones by ocean circulation. However, accurately quantifying the precise pathways of freshwater using these methods has been hampered by the fact that mass exchanges by the large-scale ocean circulation are far larger than the small net meridional freshwater transport. That is, from tens to hundreds of Sverdrups (1 Sv ≡ 10⁶ m³ s⁻¹) of seawater can be exchanged meridionally by large-scale ocean currents, flowing northward and southward with very similar salinities, while the net meridional transport of freshwater is typically less than 1 Sv (Craig et al. 2017).

Methods to study the relationship between ocean circulation and atmospheric freshwater transport have focused on quantifying the convergences of salt and freshwater in the ocean that balance atmospheric freshwater fluxes [see Craig et al. (2017) for a recent summary]. This approach, which allows the mass and salt budgets to be combined into a single expression, have been used to quantify both global salt (Tréguier et al. 2014) and freshwater transport (Wijffels 2001; Talley 2008). However, one of the challenges presented by these methods is that conventional definitions of “salt transport” only have a useful meaning in terms of freshwater transport when the total mass transport across a section is zero (otherwise salt transport can be dominated by the net mass transport multiplied by the chosen reference salinity). When such methods are used to attribute salt or freshwater transport to the flow across sections with nonzero mass transport or even to individual currents, these transports are calculated using the deviation between the local salinity and an arbitrary reference salinity, which means that global budgets may not close and transports can vary in sign depending on the choice of reference salinity (Schauer and Losch 2019; Tsubouchi et al. 2012).

A number of studies have used the water mass transformation framework (Walin 1977; Groeskamp et al. 2019) applied in salinity coordinates to study the role that forcing and mixing play in the distribution of ocean salinity. A global budget of diahaline transport processes in salinity coordinates was formally derived by Hieronymus et al. (2014). Zika et al. (2015) introduced a method that combined atmospheric forcing and diffusive salt fluxes into a single budget, demonstrating that changes to the volumetric distribution of salinity could be used to infer changes to atmospheric forcing. This approach was subsequently applied to reanalysis products and perturbation experiments to estimate water cycle change (Skliris et al. 2016; Zika et al. 2018). However, while these methods quantify the response of the volumetric salinity distribution to global changes in mixing and forcing, they do not describe regional variations in these processes. One notable exception is Grist et al. (2016), who mapped evaporation and precipitation rates into both salinity and temperature coordinates.

In this study we introduce the concept of “internal salt,” adapted from the internal heat content introduced by Holmes et al. (2019a,b), to study links between the atmospheric water cycle and diahaline and meridional processes within the ocean. Internal salt quantifies the salt content associated with variations in salinity within a volume of seawater. The use of both spatial latitude and water mass transformation salinity coordinates allows us to relate both the meridional and diffusive transport to atmospheric forcing, unifying methods based on the divergence of freshwater (e.g., Wijffels 2001) with methods based on the balance of diffusion and forcing (e.g., Zika et al. 2015).

As a component of the internal salt budget, we introduce a salt function that describes the pathway of internal salt between the evaporative and precipitative regions (Ferrari and Ferreira 2011; Holmes et al. 2019b). A similar concept was used by Ferreira and Marshall (2015) to relate variations in salinity along branches of meridional circulation to the atmospheric water cycle.

We demonstrate that the internal salt content can be expressed as a related quantity we call “internal fresh water.” Using the internal freshwater budget, we derive an expression for the pathway taken by freshwater between regions of net precipitation and regions of net evaporation. The freshwater function, which describes the internal freshwater transport, is similar to methods used to study the meridional convergence of freshwater (e.g., Wijffels 2001; Talley 2008) but does not depend on a reference salinity. Our freshwater function also differs from the freshwater function introduced by Liu et al. (2017), which defined freshwater transport using the salinity anomaly of the meridional overturning circulation, in that ours includes the contributions of both eddy advection and along-isopycnal diffusion. As a component process of the internal freshwater budget, our freshwater function explicitly quantifies the role that mixing plays in the pathways taken by freshwater within the ocean.

The remainder of this paper is structured as follows: in section 2 we define internal salt and internal freshwater and derive their budgets in latitude–salinity coordinates; in section 3 we describe an application of these budgets to the 1° ACCESS-OM2 global ocean model; in section 4 we discuss the results, and in section 5 we offer conclusions for this study and motivate future work on water cycle change.

2. Internal salt framework

In this section we introduce the volume, salt, and internal salt budgets of the region of seawater bounded by an isohaline with salinity value S* and to the north by some latitude ϕ (Walin 1977; Holmes et al. 2019a,b). We derive an equivalent expression for internal freshwater and demonstrate that the two budgets are interchangeable for studying the oceanic water cycle. The framework is derived for a Boussinesq fluid with constant density ρ₀, so we consider volume rather than mass conservation.

a. Volume and salt budgets

The volume

V

and salt content

S

of the region of all seawater fresher than S* and south of ϕ (illustrated in Fig. 1) are given by

V (ϕ, S^{*}, t) = \underset{S (x, y, z, t) \leq S^{*}}{∭} H (ϕ - y) d x d y d z and

(1a)

S (ϕ, S^{*}, t) = \underset{S (x, y, z, t) \leq S^{*}}{∭} H (ϕ - y) ρ_{0} S d x d y d z .

(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.

The volume budget of the layer bounded by the S* isohaline and the latitude ϕ is given by

\frac{\partial V}{\partial t} = - \underset{G}{\underset{︸}{\iint_{S = S^{*}} H (ϕ - y) (v - v_{S}) \cdot {\hat{n}}_{S} d A_{S}}} - \underset{J_{F}}{\underset{︸}{\iint_{S \leq S^{*}} H (ϕ - y) (v - v_{η}) \cdot {\hat{n}}_{η} d A_{η}}} - \underset{Ψ}{\underset{︸}{\iint_{S \leq S^{*}, y = ϕ} v \cdot \hat{y} d x d z}} .

(2)

The first integral on the right-hand side of Eq. (2), denoted

G

, is the diahaline volume transport toward saltier water (the definitions of

G

and other terms in the budget do not include the signs outside the integrals). This is given by the difference between the fluid velocity (including eddy-driven circulation), denoted v, and the velocity v_s of the surface S(x, y, z, t) = S*, where

\hat{n}

is the outward normal from this surface and dA_S is an area element on the isohaline surface (Groeskamp et al. 2019). The second integral,

J_{F}

, is the freshwater transport due to evaporation, precipitation, runoff, and ice formation across the ocean–atmosphere boundary η( x, y, t). The unit normal

{\hat{n}}_{η}

is oriented such that

J_{F} > 0

where the net freshwater flux is out of the ocean. The velocity of the ocean surface η(x, y, t) is denoted v_η. The third integral, Ψ, is the volume flux across the fixed latitude boundary at y = ϕ, where

\hat{y}

is the outward unit normal at this boundary (see Fig. 1); Ψ is equivalent to the latitude–salinity streamfunction [discussed by, e.g., Zika et al. (2013) and Ferreira and Marshall (2015)]. The processes contributing to the latitude–salinity volume budget are illustrated by straight arrows in Fig. 1.

The salt budget of the volume

V

is given by

\frac{\partial S}{\partial t} = - \underset{ρ_{0} S^{*} G}{\underset{︸}{\iint_{S = S^{*}} H (ϕ - y) ρ_{0} S^{*} (v - v_{S}) \cdot {\hat{n}}_{S} d A_{S}}} - \underset{D}{\underset{︸}{\iint_{S = S^{*}} H (ϕ - y) D_{S} \cdot {\hat{n}}_{S} d A_{S}}} - \underset{A_{adv}}{\underset{︸}{\iint_{S \leq S^{*}, y = ϕ} ρ_{0} S v \cdot \hat{y} d x d z}} - \underset{A_{diff}}{\underset{︸}{\iint_{S \leq S^{*}, y = ϕ} D_{ϕ} \cdot \hat{y} d x d z}} - \underset{J_{S}}{\underset{︸}{\iint_{S \leq S^{*}, y \leq ϕ} Q_{S} d x d y}} .

(3)

The first integral on the right-hand side of Eq. (3), denoted

ρ_{0} S^{*} G

, is the diahaline salt transport associated with the diahaline volume transport

G

. The second integral,

D

, is the diahaline diffusive salt transport. The third and fourth integrals,

A_{adv}

and

A_{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

A = A_{adv} + A_{diff}

. The accumulated surface salt transport is denoted

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.

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 $J_{F}$ 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.

To define the internal salt content, we first write Eq. (1b) in terms of the salt content of the volume within a given salinity interval

S (ϕ, S^{*}, t) = \int_{0}^{S^{*}} H (ϕ - y) ρ_{0} S \frac{\partial V}{\partial S} d S,

(4)

where (∂

V

/∂S)dS is the volume contained in a salinity interval dS. Applying integration by parts to Eq. (4), we obtain

S (ϕ, S^{*}, t) = ρ_{0} S^{*} V - \underset{S_{I}}{\underset{︸}{\int_{0}^{S^{*}} H (ϕ - y) ρ_{0} V d S}} .

(5)

The first term on the right-hand side is the salt content the layer would have if the entire layer had the same salinity as its bounding isohaline S*. We call this term the “external salt content” as it merely depends on the mass of the layer and the bounding salinity. The second term on the right-hand side depends only on variations in salinity within the water mass (anomalies with respect to the bounding salinity S*). We thus call this term the “internal salt content” S_I. This terminology parallels the definitions of internal and external heat content put forward by Holmes et al. (2019a). We do not draw a connection between internal salt/heat and the term internal energy in thermodynamics.

Rearranging Eq. (5), we can write the internal salt content in terms of the salt content associated with the difference between the mean salinity of the region and the bounding isohaline, given by

S_{I} (ϕ, S^{*}, t) = ρ_{0} V (\bar{S} - S^{*}),

(6)

where

\bar{S} = {(ρ_{0} V)}^{- 1} S

is the mean salinity of the region.

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.

To define the internal salt transport we first write the meridional salt transport

A

in terms of the mass transport per salinity interval and apply integration by parts, which gives

\begin{array}{l} A (ϕ, S^{*}, t) = \int_{0}^{S^{*}} ρ_{0} S \frac{\partial Ψ}{\partial S} d S + A_{diff} \\ = ρ_{0} S^{*} Ψ - \int_{0}^{S^{*}} ρ_{0} Ψ d S + A_{diff} . \end{array}

(7)

The first term on the final line of Eq. (7) describes the external salt transport. The last two terms define the internal salt transport or salt function,

A_{I} (ϕ, S^{*}, t) : = - \int_{0}^{S^{*}} ρ_{0} Ψ d S + A_{diff} .

(8)

The first term in Eq. (8) quantifies the salt transport associated with differences in salinity between branches of the streamfunction Ψ, while the second term quantifies the contribution to internal salt transport from along-isopycnal diffusion.

A_{I}

therefore describes the internal salt transport across the latitude ϕ at salinities less than S*. The total internal salt transport across the latitude ϕ is obtained by evaluating

A_{I} (ϕ, S^{\max}, t)

, where S^max(ϕ, t) is the maximum salinity at the latitude ϕ.

Rearranging Eq. (7), we can express Eq. (8) in terms of the transport across a latitude multiplied by the deviation between the local salinity and the bounding isohaline, given by

A_{I} (ϕ, S^{*}, t) = \iint_{S \leq S^{*}} ρ_{0} υ (x, ϕ, z, t) (S - S^{*}) d x d z .

(9)

This form closely resembles the net salt transport by Tréguier et al. (2014) and the convergence of freshwater by Wijffels (2001) and Talley (2008), which are calculated using the difference between the local salinity and a reference salinity. Our formulation specifies that the advective component of the internal salt transport will always oppose the meridional mass transport (as S ≤ S*).

d. Internal salt budget

We now develop a budget for the evolution of

S_{I}

by combining Eqs. (3), (2), (5), and (8):

\frac{\partial S_{I}}{\partial t} = - F - D - A_{I},

(10)

where

F \equiv ρ_{0} S^{*} J_{F} - J_{S}

is the surface internal salt forcing, which can be interpreted as sources of internal salt in the net evaporative subtropics and sinks of internal salt in the net precipitative tropics and high latitudes. Equation (10) shows that

S_{I}

evolves through surface forcing, and through mixing and meridional internal salt transport within the ocean. The conventional salt budget [Eq. (3)] is not influenced by the net input of freshwater

(J_{F})

since this does not alter the amount of salt in seawater, and therefore it cannot be used to understand

J_{F}

directly. Here, through our definition of an internal salt budget [Eq. (10)], we have defined a salinity variable that is directly related to net freshwater input via the source term

F

e. Equivalent surface freshwater transport

Equation (10), the budget for internal salt, can equivalently be expressed as a budget for internal freshwater by multiplying by (ρ₀S*)⁻¹, given by

P = - \frac{1}{ρ_{0} S *} [D + A_{I}] - \frac{\partial}{\partial t} V (\frac{\bar{S} - S *}{S *}) .

(11)

Here

P = J_{F} - {(ρ_{0} S^{*})}^{- 1} J_{S}

is the surface volume transport through the ocean–atmosphere boundary, which includes the contributions from both surface freshwater fluxes and the equivalent volume transport associated with the surface salt flux. The diffusive contribution,

- D / (ρ_{0} S^{*})

, can be interpreted as the diffusive freshwater flux from low-salinity to high-salinity water, while

- A_{I} / ρ_{0} S^{*}

can be interpreted as a freshwater function that quantifies internal freshwater transport. The final term is the tendency of internal freshwater, which can be interpreted as the change in the freshwater content associated with the difference between the mean and bounding salinity [similar to the interpretation of the tendency of internal salt in Eq. (10)].

Equation (11) relates surface freshwater fluxes to oceanic processes. Taking the time average and ignoring the tendency term in Eq. (11), we can derive an expression for the isohaline and meridional derivative of the surface freshwater flux per latitude and salinity, given by

\frac{\partial^{2} \bar{P}}{\partial ϕ \partial S} = - \frac{1}{ρ_{0} S *} \frac{\partial}{\partial S} \underset{F_{S}}{\underset{︸}{(\frac{\partial \bar{D}}{\partial ϕ})}} - \frac{1}{ρ_{0} S *} \frac{\partial}{\partial ϕ} \underset{F_{ϕ}}{\underset{︸}{(\frac{\partial \bar{A_{I}}}{\partial S})}} .

(12)

Here the fluxes F_S and F_ϕ define a vector field in latitude–salinity coordinates that describe the diahaline and meridional, respectively, pathways of freshwater in the ocean. We remark that over most of the ocean and, in particular, away from the polar and continental regions,

J_{S} \approx 0

. This means that

P \approx J_{F}

, such that the surface forcing is dominated by freshwater fluxes from evaporation and precipitation. Under this approximation, Eq. (12) can be thought of as the pathway taken by freshwater between its addition to the ocean through precipitation and its removal through evaporation.

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:

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).
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.
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.

3. Model

We analyze the internal salt budget of the last 10 years of a 500-yr run of the 1° ACCESS-OM2 global ocean sea ice model (Kiss et al. 2020). The model consists of the Modular Ocean Model 5.1 (MOM5) (Griffies 2012) coupled to the sea ice model CICE 5.1.2, forced with repeat year 1990–91 forcing from the JRA55-do atmospheric reanalysis, implemented as a surface freshwater flux (Tsujino et al. 2018; Stewart et al. 2020). Simulations were run with a Boussinesq approximation, using a constant reference density ρ₀ = 1035 kg m⁻³. The surface volume flux contains contributions from evaporation, precipitation, river runoff, and sea ice. Volume exchanges between the ocean and sea ice have salinity 5 g kg⁻¹, while terrestrial runoff is exchanged with 0 g kg⁻¹. Evaporative fluxes are calculated dynamically by the model.

To prevent drift in the model, surface salinity is restored to the World Ocean Atlas 2013 v2 monthly climatology as a salt flux in the surface grid cells with a restoring period of 21.3 days. This is normalized so that the global salt content remains unchanged by surface restoring. There is also a nonphysical lateral salt flux associated with a sea surface height smoother included to suppress a checkerboard null mode present in the B-grid barotropic equations (Griffies 2004). The surface salt flux that is associated with sea ice formation, salinity restoring, and the surface smoother in the model is included in $J_{S}$ and in the surface forcing $F$ in Eq. (10).

The diffusive contribution

D

consists of several explicitly parameterized processes as well as numerical mixing associated with truncation errors in the model’s tracer advection scheme (Holmes et al. 2019a). Vertical mixing including boundary layer mixing is parameterized using the K-profile parameterization (Large et al. 1994), a background vertical diffusivity with latitudinal structure following Jochum (2009) and a bottom-intensified tidal mixing scheme (Simmons et al. 2004). The diahaline salt flux associated with vertical mixing is denoted

M

. The contribution to the cross isohaline (diahaline) internal salt flux from along-isopycnal diffusion is explicitly parameterized in the model (Redi 1982). We denote this neutral diahaline flux

N

. As discussed in Holmes et al. (2019a), the residual of Eq. (10),

I = - \frac{\partial S_{I}}{\partial t} - F - M - N - A_{I},

(13)

contains the contribution to diahaline salt transport associated with truncation errors in the model’s numerical advection scheme, which we refer to as “numerical mixing.” Residual

I

also contains a small error associated with the fact that the meridional volume transport Ψ does not include the transport arising from a sea surface height smoother applied in order to suppress a checkerboard numerical mode in MOM’s B-grid equations. The total diahaline diffusive flux is given by

D = M + N + I

The salt function $A_{I}$ includes contributions to the meridional internal salt transport from the parameterizations for mesoscale (Gent and McWilliams 1990; Griffies 1998) and mixed layer submesoscale (Fox-Kemper et al. 2008) eddy transports as well as the meridional component of along-isopycnal diffusion, denoted separately by $A_{diff}$ . Component $A_{diff}$ only concerns the meridional transport of internal salt (i.e., across latitudes) and is distinct from $N$ , which concerns the diffusive transport of internal salt across salinity surfaces. More information on the model configuration is contained in Kiss et al. (2020).

The numerical implementation of transport in tracer coordinates follows the approach taken by Holmes et al. (2019a). Diagnostics from parameterized mixing and boundary fluxes are accumulated within salinity intervals between S* and S* + dS at each time step. In this study we used a constant bin size of dS = 0.25 over the salinity range 0–40 g kg⁻¹. Binning of all model diagnostics was done online. The tendencies of volume and salt were computed from snapshots taken at the beginning and end of each month (Holmes et al. 2019a).

4. Results and discussion

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).

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 $M$ , 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 $N$ 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 $I$ 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.

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 $A_{I}$ 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 $A_{I}$ 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 $A_{I}$ are steepest near regions with strong surface freshwater fluxes, reflecting the dominance of diahaline processes in these regions. Between these regions, the contours of $A_{I}$ 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 $F$ , $N$ , $M$ , and $I$ ; Holmes et al. 2019b).

The surface forcing term $\partial F / \partial ϕ$ 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.

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 $A_{I}$ ; however, it influences the flow of internal salt in latitude–salinity space.

The steep sections along contours of $A_{I}$ 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, $\partial M / \partial ϕ$ (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., $\partial N / \partial ϕ$ 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.

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.

5. Conclusions

In this study we have introduced the internal salt budget framework (section 2, based on the internal heat framework of Holmes et al. 2019a) to connect atmospheric forcing, ocean circulation and turbulent mixing to the meridional distribution of ocean surface salinity. We have introduced a salt function that quantifies the transport of internal salt, based on the heat function of Ferrari and Ferreira (2011). The internal salt content can equivalently be interpreted as internal freshwater. Using the time-averaged internal freshwater budget, we have derived a vector field of internal freshwater transport in latitude–salinity space. This vector field defines the pathways that redistribute freshwater within the ocean between the precipitative regions in the midlatitudes and the evaporative regions in the tropics and high latitudes.

Analysis of the time-averaged internal salt budget of the 1° ACCESS-OM2 ocean model reveals that the pathways of internal freshwater transport that connect precipitative and evaporative regions are separated into three distinct regions, with boundaries at 22°S and 12°N, which are shown in Fig. 7 by the heavy dotted lines. These boundaries mean that the convergence of freshwater in the evaporative region north of 22°S is supplied by cross-equatorial pathway of internal freshwater from the tropical Northern Hemisphere. The internal freshwater transport away from each of the precipitative regions is summarized in Fig. 7 (shown at the global mean salinity by the horizontal arrows crossing the boundaries of the precipitative regions).

The salinity of the Atlantic Ocean is predominately maintained by a southward internal freshwater transport from the Arctic Ocean, while the salinity of the Indo-Pacific Ocean basin is maintained by a northward internal freshwater transport from the Southern Ocean (see Figs. 6a–c). Approximately 0.6 Sv of internal freshwater gained through net precipitation in the Southern Ocean is transferred into the Indo-Pacific Ocean. This accounts for almost all of the northward transport across 34°S globally, with only 0.01 Sv of internal freshwater entering the Atlantic Ocean. In the steady state, the salinity of the North Atlantic is maintained by 0.26 Sv of internal freshwater that is transferred from the Arctic Ocean to the North Atlantic. This input is likely involved in the formation of NADW carried southward at depth by the AMOC (Wunsch and Heimbach 2013). The Indo-Pacific exports internal freshwater through the Bering Strait. However, only around 15% of the internal freshwater that is transferred into the Atlantic from the Arctic can be attributed to a transfer from the North Pacific Ocean to the Arctic through the Bering Strait. The rest is provided by net precipitation and run off directly into the Arctic Ocean.

The fact that the Atlantic Ocean imports internal freshwater through the northern and southern boundaries supports the theory that the higher salinity of the Atlantic Ocean is driven by asymmetries in surface forcing (Ferreira et al. 2010; Wills and Schneider 2015). The response of internal freshwater transport across the northern and southern borders of the Atlantic basin under an intensifying water cycle will be an important area of future research (see, e.g., Ferreira et al. 2018), with potential implications for the stability of the AMOC (Sijp et al. 2012), NADW formation, and North Pacific Intermediate Water formation (see, e.g., Talley 2008).

The convergence of freshwater in the midlatitudes and the associated meridional freshwater fluxes from fresh, precipitative regions to salty, evaporative regions can only occur if freshwater crosses isohalines. These diahaline freshwater fluxes are achieved by diffusive mixing (summarized in Fig. 7). Globally, freshwater forcing stretches the distribution of salinity away from the mean salinity, while mixing contracts the distribution. Here, the use of latitude–salinity coordinates allows us to quantify the regional contribution that mixing makes to the internal salt budget. Large diahaline fluxes occur in regions where forcing creates strong salinity gradients in the upper ocean, which are reflected by steep contours of the salt function in Figs. 4d–f. A number of diffusive processes contribute to this diahaline transport in the coarse-grid model. Vertical mixing in the boundary layer is strongest in the tropics, contributing approximately 1.5 × 10⁷ kg s⁻¹ of the total downgradient salt flux across the 34.4 g kg⁻¹ isohaline. Neutral mixing, which occurs predominately in the interior ocean, is highly localized but significantly more important than vertical mixing at higher latitudes. The regional contribution from each of these diffusive processes to the internal freshwater budget are summarized in Fig. 7.

Internal freshwater transport within the ocean must be organized to balance the atmospheric freshwater fluxes that drive salinity gradients in the upper ocean. As atmospheric circulation connects adjacent evaporative and precipitative regions, the effect of an intensifying atmospheric water cycle is to stretch the local salinity distribution. The convergence of freshwater that maintains the regional salinity distribution can only occur through the diahaline exchange of salt and freshwater that occurs through ocean mixing. This means that understanding the response of diffusive processes to increased surface forcing is essential to understanding atmospheric water cycle change. While quantifying this response is central to understanding water cycle change, the sensitivity of the internal freshwater transport pathways to atmospheric changes is also of particular interest given the importance of salinity for ocean circulation.

Acknowledgments

We acknowledge technical support and advice provided by A. Heerdegen, M. Ward, and S. Griffies. Modeling and analysis were undertaken using facilities at the National Computational Infrastructure (NCI), which is supported by the Australian government. The authors are supported by the ARC’s Centre of Excellence for Climate Extremes, Australian Government Research Training Program Scholarship, and Grant DP190101173.

Data availability statement

The data used for this study and model configuration files are available upon reasonable request to the authors.

REFERENCES

Craig, P. M., D. Ferreira, and J. Methven, 2017: The contrast between Atlantic and Pacific surface water fluxes. Tellus A, 69, 1330454, https://doi.org/10.1080/16000870.2017.1330454.
- Search Google Scholar
- Export Citation
Durack, P. J., and S. E. Wijffels, 2010: Fifty-year trends in global ocean salinities and their relationship to broad-scale warming. J. Climate, 23, 4342–4362, https://doi.org/10.1175/2010JCLI3377.1.
- Search Google Scholar
- Export Citation
Ferrari, R., and D. Ferreira, 2011: What processes drive the ocean heat transport? Ocean Modell., 38, 171–186, https://doi.org/10.1016/j.ocemod.2011.02.013.
- Search Google Scholar
- Export Citation
Ferreira, D., and J. Marshall, 2015: Freshwater transport in the coupled ocean-atmosphere system: A passive ocean. Ocean Dyn., 65, 1029–1036, https://doi.org/10.1007/s10236-015-0846-6.
- Search Google Scholar
- Export Citation
Ferreira, D., J. Marshall, and J.-M. Campin, 2010: Localization of deep water formation: Role of atmospheric moisture transport and geometrical constraints on ocean circulation. J. Climate, 23, 1456–1476, https://doi.org/10.1175/2009JCLI3197.1.
- Search Google Scholar
- Export Citation
Ferreira, D., and Coauthors, 2018: Atlantic-Pacific asymmetry in deep water formation. Annu. Rev. Earth Planet. Sci., 46, 327–352, https://doi.org/10.1146/annurev-earth-082517-010045.
- Search Google Scholar
- Export Citation
Fox-Kemper, B., R. Ferrari, and R. Hallberg, 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. J. Phys. Oceanogr., 38, 1145–1165, https://doi.org/10.1175/2007JPO3792.1.
- Search Google Scholar
- Export Citation
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.
- Search Google Scholar
- Export Citation
Griffies, S. M., 1998: The Gent–McWilliams skew flux. J. Phys. Oceanogr., 28, 831–841, https://doi.org/10.1175/1520-0485(1998)028<0831:TGMSF>2.0.CO;2.
- Search Google Scholar
- Export Citation
Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton University Press, 518 pp.
Griffies, S. M., 2012: Elements of the Modular Ocean Model (MOM). GFDL Ocean Group Tech. Rep. 7, 645 pp., https://mom-ocean.github.io/assets/pdfs/MOM5_manual.pdf.
Grist, J. P., S. A. Josey, J. D. Zika, D. G. Evans, and N. Skliris, 2016: Assessing recent air-sea freshwater flux changes using a surface temperature-salinity space framework. J. Geophys. Res. Oceans, 121, 8787–8806, https://doi.org/10.1002/2016JC012091.
- Search Google Scholar
- Export Citation
Groeskamp, S., S. M. Griffies, D. Iudicone, R. Marsh, A. G. Nurser, and J. D. Zika, 2019: The water mass transformation framework for ocean physics and biogeochemistry. Annu. Rev. Mar. Sci., 11, 271–305, https://doi.org/10.1146/annurev-marine-010318-095421.
- Search Google Scholar
- Export Citation
Helm, K. P., N. L. Bindoff, and J. A. Church, 2010: Changes in the global hydrological-cycle inferred from ocean salinity. Geophys. Res. Lett., 37, L18701, https://doi.org/10.1029/2010GL044222.
- Search Google Scholar
- Export Citation
Hieronymus, M., J. Nilsson, and J. Nycander, 2014: Water mass transformation in salinity–temperature space. J. Phys. Oceanogr., 44, 2547–2568, https://doi.org/10.1175/JPO-D-13-0257.1.
- Search Google Scholar
- Export Citation
Holmes, R. M., J. D. Zika, and M. H. England, 2019a: Diathermal heat transport in a global ocean model. J. Phys. Oceanogr., 49, 141–161, https://doi.org/10.1175/JPO-D-18-0098.1.
- Search Google Scholar
- Export Citation
Holmes, R. M., J. D. Zika, R. Ferrari, A. F. Thompson, E. R. Newsom, and M. H. England, 2019b: Atlantic Ocean heat transport enabled by Indo-Pacific heat uptake and mixing. Geophys. Res. Lett., 46, 13 939–13 949, https://doi.org/10.1029/2019GL085160.
- Search Google Scholar
- Export Citation
Jochum, M., 2009: Impact of latitudinal variations in vertical diffusivity on climate simulations. J. Geophys. Res., 114, C01010, https://doi.org/10.1029/2008JC005030.
- Search Google Scholar
- Export Citation
Kiss, A. E., and Coauthors, 2020: ACCESS-OM2 v1. 0: A global ocean-sea ice model at three resolutions. Geosci. Model Dev., 13, 401–442, https://doi.org/10.5194/gmd-13-401-2020.
- Search Google Scholar
- Export Citation
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32, 363–403, https://doi.org/10.1029/94RG01872.
- Search Google Scholar
- Export Citation
Liu, X., A. Köhl, and D. Stammer, 2017: Dynamical ocean response to projected changes of the global water cycle. J. Geophys. Res. Oceans, 122, 6512–6532, https://doi.org/10.1002/2017JC013061.
- Search Google Scholar
- Export Citation
Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12, 1154–1158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.
- Search Google Scholar
- Export Citation
Schauer, U., and M. Losch, 2019: “Freshwater” in the ocean is not a useful parameter in climate research. J. Phys. Oceanogr., 49, 2309–2321, https://doi.org/10.1175/JPO-D-19-0102.1.
- Search Google Scholar
- Export Citation
Schmitt, R. W., 2008: Salinity and the global water cycle. Oceanography, 21, 12–19, https://doi.org/10.5670/oceanog.2008.63.
- Search Google Scholar
- Export Citation
Sijp, W. P., M. H. England, and J. M. Gregory, 2012: Precise calculations of the existence of multiple AMOC equilibria in coupled climate models. Part I: Equilibrium states. J. Climate, 25, 282–298, https://doi.org/10.1175/2011JCLI4245.1.
- Search Google Scholar
- Export Citation
Simmons, H. L., S. R. Jayne, L. C. S. Laurent, and A. J. Weaver, 2004: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell., 6, 245–263, https://doi.org/10.1016/S1463-5003(03)00011-8.
- Search Google Scholar
- Export Citation
Skliris, N., R. Marsh, S. A. Josey, S. A. Good, C. Liu, and R. P. Allan, 2014: Salinity changes in the world ocean since 1950 in relation to changing surface freshwater fluxes. Climate Dyn., 43, 709–736, https://doi.org/10.1007/s00382-014-2131-7.
- Search Google Scholar
- Export Citation
Skliris, N., J. D. Zika, G. Nurser, S. A. Josey, and R. Marsh, 2016: Global water cycle amplifying at less than the Clausius-Clapeyron rate. Sci. Rep., 6, 38752, https://doi.org/10.1038/srep38752.
- Search Google Scholar
- Export Citation
Stewart, K., and Coauthors, 2020: JRA55-do-based repeat year forcing datasets for driving ocean–sea-ice models. Ocean Modell., 147, 101557, https://doi.org/10.1016/J.OCEMOD.2019.101557.
- Search Google Scholar
- Export Citation
Talley, L. D., 2008: Freshwater transport estimates and the global overturning circulation: Shallow, deep and throughflow components. Prog. Oceanogr., 78, 257–303, https://doi.org/10.1016/j.pocean.2008.05.001.
- Search Google Scholar
- Export Citation
Tréguier, A.-M., and Coauthors, 2014: Meridional transport of salt in the global ocean from an eddy-resolving model. Ocean Sci., 10, 243–255, https://doi.org/10.5194/os-10-243-2014.
- Search Google Scholar
- Export Citation
Tsubouchi, T., and Coauthors, 2012: The Arctic Ocean in summer: A quasi-synoptic inverse estimate of boundary fluxes and water mass transformation. J. Geophys. Res., 117, C01024, https://doi.org/10.1029/2011JC007174.
- Search Google Scholar
- Export Citation
Tsujino, H., and Coauthors, 2018: JRA-55 based surface dataset for driving ocean–sea-ice models (JRA55-do). Ocean Modell., 130, 79–139, https://doi.org/10.1016/j.ocemod.2018.07.002.
- Search Google Scholar
- Export Citation
Walin, G., 1977: A theoretical framework for the description of estuaries. Tellus, 29, 128–136, https://doi.org/10.3402/tellusa.v29i2.11337.
- Search Google Scholar
- Export Citation
Wijffels, S. E., 2001: Ocean transport of fresh water. Ocean Circulation and Climate, International Geophysics, Vol. 77, Elsevier, 475–488.
Wijffels, S. E., R. W. Schmitt, H. L. Bryden, and A. Stigebrandt, 1992: Transport of freshwater by the oceans. J. Phys. Oceanogr., 22, 155–162, https://doi.org/10.1175/1520-0485(1992)022<0155:TOFBTO>2.0.CO;2.
- Search Google Scholar
- Export Citation
Wills, R. C., and T. Schneider, 2015: Stationary eddies and the zonal asymmetry of net precipitation and ocean freshwater forcing. J. Climate, 28, 5115–5133, https://doi.org/10.1175/JCLI-D-14-00573.1.
- Search Google Scholar
- Export Citation
Wunsch, C., and P. Heimbach, 2013: Two decades of the Atlantic meridional overturning circulation: Anatomy, variations, extremes, prediction, and overcoming its limitations. J. Climate, 26, 7167–7186, https://doi.org/10.1175/JCLI-D-12-00478.1.
- Search Google Scholar
- Export Citation
Wüst, G., 1936: Surface salinity, evaporation and precipitation in the oceans. Länderkundliche Forschung, Festschrift Norbert Krebs zur Vollendung des 60. Lebensjahres dargebracht, Engelhorn, 347–359.
Zika, J. D., M. H. England, and W. P. Sijp, 2012: The ocean circulation in thermohaline coordinates. J. Phys. Oceanogr., 42, 708–724, https://doi.org/10.1175/JPO-D-11-0139.1.
- Search Google Scholar
- Export Citation
Zika, J. D., W. P. Sijp, and M. H. England, 2013: Vertical heat transport by ocean circulation and the role of mechanical and haline forcing. J. Phys. Oceanogr., 43, 2095–2112, https://doi.org/10.1175/JPO-D-12-0179.1.
- Search Google Scholar
- Export Citation
Zika, J. D., N. Skliris, A. G. Nurser, S. A. Josey, L. Mudryk, F. Laliberté, and R. Marsh, 2015: Maintenance and broadening of the ocean’s salinity distribution by the water cycle. J. Climate, 28, 9550–9560, https://doi.org/10.1175/JCLI-D-15-0273.1.
- Search Google Scholar
- Export Citation
Zika, J. D., N. Skliris, A. T. Blaker, R. Marsh, A. G. Nurser, and S. A. Josey, 2018: Improved estimates of water cycle change from ocean salinity: The key role of ocean warming. Environ. Res. Lett., 13, 074036, https://doi.org/10.1088/1748-9326/AACE42.
- Search Google Scholar
- Export Citation

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Internal Salt Content: A Useful Framework for Understanding the Oceanic Branch of the Water Cycle

Abstract

Significance Statement

Abstract

Significance Statement

1. Introduction

2. Internal salt framework

a. Volume and salt budgets

b. Internal salt content

c. Internal salt transport

d. Internal salt budget

e. Equivalent surface freshwater transport

3. Model

4. Results and discussion

a. Diahaline and meridional processes

b. Internal salt transport in latitude–salinity space

c. Regional contributions from forcing and mixing

d. The global freshwater balance

5. Conclusions

Acknowledgments

Data availability statement

REFERENCES

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GENERAL CONDITIONS

No. III

BAROMETRIC PRESSURE

VERIFICATIONS

MISCELLANEOUS PHENOMENA

Internal Salt Content: A Useful Framework for Understanding the Oceanic Branch of the Water Cycle

Abstract

Significance Statement

Abstract

Significance Statement

1. Introduction

2. Internal salt framework

a. Volume and salt budgets

b. Internal salt content

c. Internal salt transport

d. Internal salt budget

e. Equivalent surface freshwater transport

3. Model

4. Results and discussion

a. Diahaline and meridional processes

b. Internal salt transport in latitude–salinity space

c. Regional contributions from forcing and mixing

d. The global freshwater balance

5. Conclusions

Acknowledgments

Data availability statement

REFERENCES

Share Link

AMS Publications

Get Involved with AMS

Affiliate Sites

Follow Us

Contact Us