1. Introduction
The terrestrial freshwater cycle and its behavior in a changing climate is a study area of utmost importance to humanity, specifically from a socioeconomic viewpoint (Durack 2015). Because of the interconnection of various branches of the water cycle and the vastly larger size of the ocean reservoir relative to the land surface (Durack 2015; Schmitt 2008), understanding the oceanic branch might be key in improving our understanding of how a changing climate will influence the terrestrial water cycle.
Studying the freshwater flux over the ocean is very challenging because of the complicated and spatially sparse measurements and the reliance on bulk formulas for various flux products, resulting in large uncertainties between datasets (Schanze et al. 2010). Because of these difficulties, the idea of using sea surface salinity (SSS) as a proxy of the integrated freshwater forcing has emerged (Schmitt 2008; Gordon and Giulivi 2008). By removing (adding) freshwater through evaporation E (precipitation P) at the surface, the SSS is raised (lowered). The general alignment between the areas of positive net evaporation (E − P) and local salinity maxima in the subtropical gyre of the North Atlantic (NA) was pointed out as early as Wüst (1936). The complication with this approach, often called “salinity as an ocean rain gauge” (Schmitt 2008), is the influence of ocean dynamics (Vinogradova and Ponte 2013; Ponte and Vinogradova 2016; Gordon 2016).
The SSS distribution is influenced by advection and mixing both horizontally and vertically, and all processes need to be quantified in order to relate changes in the SSS field to changes in the water cycle. To achieve this goal, the Salinity Processes in the Upper Ocean Study (SPURS) field experiment was carried out in the SSS maximum (SSS-max) of the subtropical North Atlantic, with the goal to observe all relevant processes in one of the global salinity maxima and then apply these findings to the other subtropical regions in the global ocean. An overview of the program and many relevant publications is given by Lindstrom et al. (2015).
Besides being relevant for the study of the surface salinity expression of a change in the global water cycle, the SSS maxima are source regions for subtropical underwater (STUW; O’Connor et al. 2005) that feed into the shallow overturning circulation (e.g., Schott et al. 2004). These subducted water-mass characteristics are important for the global climate since they contribute significantly to global tracer transports (e.g., Boccaletti et al. 2005). This results from the strong circulation paired with strong near-surface gradients, compared to the deep ocean. Hence, changes in mean gradients of temperature and salinity might modify meridional heat and freshwater transports of the upper ocean. Additionally the subducted water masses are a potential pathway for subtropical surface anomalies to the tropical thermocline and subsequently the upwelling regions of the globe. Changes in surface salinity on isopycnals are by definition associated with temperature (spice) anomalies that have the potential to alter sea surface temperature once upwelled in the tropics. This emphasizes the need to study the mechanisms responsible for the variability of the SSS.
Observations during SPURS show strong lateral salinity gradients associated with mesoscale filaments. These gradients are most intense near the surface, and the salinity variability is strongly reduced along the subduction path of the SSS-max (Busecke et al. 2014). Motivated by these findings, this study focuses on the process of lateral eddy mixing within the mixed layer. The importance of eddy mixing to the mean salinity and volume budgets in the North Atlantic has been covered in various studies (Gordon et al. 2015; Busecke et al. 2014; Bryan and Bachman 2014; Schmitt and Blair 2015; Johnson et al. 2016; Amores et al. 2016) using different methods and data sources. When the destruction of the saltiest water masses is compared to the creation by positive net evaporation, the studies infer different mean values and temporal variability.
We introduce a novel approach to estimate the eddy mixing contribution in all subtropical basins with a coherent methodology. A suite of observation-driven experiments is conducted where the mechanism of water-mass destruction via eddy mixing is isolated. Using a salinity coordinate system, as in the pioneering study of Walin (1977), we investigate all major ocean basins. Together with the comparison of the mean effect of eddy mixing for the SSS-max, we examine the variability induced by the observed surface velocity field and test the sensitivity to seasonal and interannual variations in SSS fields. These sensitivity experiments enable us to identify the dominant processes for the variability in eddy mixing—the surface velocities or the SSS fields.
The manuscript is structured as follows: In the remainder of the introduction, we address the discrepancies within the existing estimates with a brief overview of the existing studies estimating the relevance of eddy mixing to the North Atlantic SSS-max and discuss potential sources for disagreement. Then we introduce the methodology, model setup, and data used for this study in section 2. We present and discuss the results in section 3 and conclude in section 4, including possible future work.
a. Budgets and the choice of a control volume
To evaluate the importance of any process to a large-scale feature like the SSS-max, it is useful to investigate the salinity budget over a control volume that encompasses the feature of interest.
Two general choices of volumes are used in the literature:
The Eulerian control box: Most studies use some variation of a box fixed in space. Either a local grid box (Busecke et al. 2014) or point measurement from a mooring (Farrar et al. 2015), zonally elongated boxes within the SSS-max (Gordon and Giulivi 2014), or a larger box around the SSS-max (Qu et al. 2011; Amores et al. 2016).
- The water-mass boundary: The studies of Bryan and Bachman (2014), Schmitt and Blair (2015), Johnson et al. (2016), and this study utilize a control volume V(S0, t) bounded by a surface of constant salinity S0. It can be shown that this eliminates the advection term from the salinity budget, leaving only diffusion (both lateral and vertical) as a possible compensation for the surface forcing (Walin 1977; Marshall et al. 1999). The budget becomesNote that in this case the surface forcing is also evaluated on the same isohaline control surface. The salinity budget in V can be related to the time change in volume bounded by the same isohaline [transformation rate (TFR); see Bryan and Bachman (2014) for full derivation]:
The SSS-max exhibits variability from seasonal (Gordon and Giulivi 2014; Gordon et al. 2015) to interannual (Bingham et al. 2014) to decadal (Gordon and Giulivi 2008; Durack and Wijffels 2010) time scales. Furthermore, there is evidence for strong spatial variability of lateral diffusivities and SSS gradients (Abernathey and Marshall 2013; Gordon et al. 2015), implying strong spatial variability of the resulting diffusive fluxes. This could explain some of the spread of results between the studies using fixed control volumes. In the presence of strong inhomogeneity, even small differences in the position of the control volume will lead to very different results for each of the terms in the salinity–volume budget. Besides the choice of the control volume, a second major factor is the actual quantification of each of the terms in the budget. We focus our study on a particular process—lateral eddy mixing in the near-surface layer—and proceed by reviewing common methods to quantify this process.
b. Quantifying eddy mixing
In this section, we outline the exact processes we aim to study in detail with respect to the SSS-max.
Unsteady motions in the ocean play a large role for the general circulation, tracer transports, and thereby global climate. Fox-Kemper et al. (2013) provides a review of mesoscale eddy transport in the ocean. Following their terminology, all fluctuations from the mean circulation with time scales of weeks and length scales of several hundred kilometers (i.e., mesoscale) will be referred to as “eddies.”
Tracer fluxes caused by eddies are commonly expressed as a covariance term 
To circumvent these issues, we choose to simulate the evolution of surface tracer fields using observed surface velocities and diagnose the diffusive flux within a coordinate system defined by a water mass (here salinity). As illustrated in Figs. 1a and 1b in a tracer coordinate system, advective stirring by eddies stretches and filaments tracer contours, leading to irreversible mixing (also known as water-mass transformation) at small scales and a net diffusive flux across tracer contours (Fig. 1c). In this context, and throughout our study, eddy mixing refers to the enhancement of small-scale mixing by mesoscale stirring.
Schematic illustrating the investigated processes. Orange surfaces symbolize lines of constant surface salinity scaled by the mean mixed layer depth (MLD). The (a) smooth initial condition in each experiment gets stirred by mesoscale velocities (blue arrows), which (b) enhances the diffusive flux (black arrows) across the contour. (c) The integrated flux across a closed contour (indicated by wavy gray arrows) leads to the destruction of salty water masses within the contour—the TFR [indicated by dashed arrows in (c)].
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
To further separate the effects of the large-scale tracer gradients and velocity, we employ the concept of effective diffusivity (Nakamura 1996). This diffusivity is appropriate for our analysis since it does not correspond to an Eulerian diffusivity but rather represents the averaged enhancement of small-scale diffusivity along a tracer contour. Thus, it is directly relevant to the net diffusive flux across isohalines and into the SSS-max.
2. Methods and data
As stated above, when evaluating a volume bounded by a tracer surface, the flux across this boundary can only be achieved by diffusion and the flux through the sea surface [Eqs. (5) and (6)]. The sum of these fluxes is directly related to the volume bounded by the isohaline.
Our approach is only focused on the near-surface layer for several reasons. First, the availability of velocity data for over 20 years through altimetry enables us to conduct a data-driven study on eddy mixing, which is not possible with subsurface data at this point. Second, the strong lateral gradients observed within the mixed layer of the North Atlantic SSS-max (Busecke et al. 2014) point to the importance of the near-surface lateral eddy mixing versus the interior. Global inverse mixing estimates (Groeskamp et al. 2017) support the idea of lateral near-surface eddy mixing being much stronger than along-isopycnal mixing in the interior.
With this setup we purposely neglect all other processes that influence the SSS in the real ocean like the surface forcing and all vertical processes, for example, subduction, entrainment, and diapycnal mixing. The robust nature of this diagnostic, which relies just on the area within a contour and isolation of the mixing effect of the observed velocities, enables the study of temporal variability in eddy mixing. The downside of this approach clearly is the integral character of the results. It is not possible to diagnose local extrema in fluxes. It is well suited for the purpose of this study, since the main interest lies in the role of lateral eddy mixing to the formation and maintenance of the large-scale SSS maxima.
a. Surface forcing compensation
b. Effective diffusivities
It is worth dissecting variability of the TFR into contributions from variability in the stirring (velocity fluctuations) and variability in the background salinity field, which includes changes in local gradients as well as a changing position of the reference isohaline. To isolate the effect of the velocity fluctuations, we calculate the effective diffusivity. This method uses the same water-mass frame of reference as the TFR and is thus directly comparable to the other results.
Even though this diagnostic has been mostly used in scenarios with a high degree of uniformity in the zonal direction like the Southern Ocean (Abernathey et al. 2010) and the central part of the Pacific (Abernathey and Marshall 2013), it can be applied to any tracer field. An example of this application can be found in Lee et al. (2009), who studied the effective diffusivity of a tracer patch released in the subtropical gyre. In the case of the SSS-max, the salinity contour values map geographically to the distance from the center of the maximum.
The effective diffusivity is not defined for a vanishing background gradient. To avoid the occurrence of weak tracer gradients, our initial conditions are reset in regular intervals as described below.
c. Data
We use absolute geostrophic velocities from the AVISO Data Unification and Altimeter Combination System (DUACS) 2014 (1993–2014) altimetry product, produced by SSALTO/DUACS and distributed by AVISO, with support from CNES (http://www.aviso.altimetry.fr/duacs/). The data are subset in weekly fields and have a native spatial resolution of ¼°. We assume that the velocity fluctuation of the largest, most energetic eddies are captured by this data. The long-standing AVISO record represents our current best estimate of the surface eddy field. Since there is no similarly long, global observational record of higher resolution, we are not able to investigate how unresolved velocity structures influence the results. Such a comparison will be left to future studies. The geostrophic velocities do not include the Ekman velocities at the surface, but as Rypina et al. (2012) show, these have little influence on the mixing characteristics at the surface. Climatological SSS fields as well as mixed layer depth are taken from the Monthly Isopycnal/Mixed-Layer Ocean Climatology (MIMOC) (Schmidtko et al. 2013). The data are given as climatological months with a spatial resolution of ½°. Additionally, annual SSS fields are used from ECCO–Massachusetts Institute of Technology (MIT) version 4 (V4) release 2 (R2) ocean state estimate (Forget et al. 2015) and the Asia-Pacific Data Research Center (ADPRC) gridded Argo product (http://apdrc.soest.hawaii.edu/projects/Argo/data/gridded/).
The E data are taken from the OAFlux (Yu et al. 2008) monthly mean product and P are from the Global Precipitation Climatology Project (GPCP; Huffman et al. 1997), both of which have a spatial resolution of 1°. The fields are averaged into climatological monthly means and interpolated on the MIMOC grid for analysis.
d. Model setup
We conduct a suite of experiments by stirring initial SSS fields with observed velocities. From these experiments, we diagnose the transformation rate by eddy mixing and surface forcing as well as the effective diffusivity.
The bases for this study are numerical experiments run in the MITgcm (Marshall et al. 1997) following the setup of Abernathey and Marshall (2013). The model output is calculated in 900-s intervals, and tracer snapshots are output every 7 days. Initial SSS fields are passively advected by 7-day snapshots of two-dimensional AVISO absolute geostrophic velocities after both have been interpolated onto the ⅞° model grid. The velocities need to be slightly corrected in order to be nondivergent, using the procedure described in Abernathey and Marshall (2013; see their appendix A). The only difference from that study is that here we used the newer DUACS 2014 product from AVISO. Tracer transport across isolines can only be achieved via the model’s prescribed grid-scale diffusivity κ (the schematic in Fig. 1 illustrates the process). However, as discussed in detail in Abernathey and Marshall (2013) and references therein, the width of tracer filaments (and thereby 
In addition to calculating long-term averages of TFREddy and Keff, we expanded the method with the explicit goal of resolving temporal fluctuations in eddy mixing. Because of the lack of a restoring mechanism for the tracer, over long time scales the tracer field will increasingly homogenize, and large-scale features might be deformed and shifted. In a homogenized tracer field, no mesoscale velocity can produce a tracer fluctuation, and the diagnostics presented here become meaningless. The advection and deformation of large-scale features will impact a useful remapping of the results to the initial conditions. This prompts us to reset the tracer fields in regular intervals, or results could not be interpreted anymore using the initial position of the SSS maxima. This methodology is well suited to examine the SSS maxima in the subtropical gyres, since mean advection is relatively low, and the main features are not advected out of their original position quickly. Two tracers are simulated in parallel and reset at different phase, and the results are averaged to eliminate any residual drift in the diagnostics and maintain the background field as quasi constant. We obtained an uncertainty associated with the reset period by comparing certain ranges. All results that are discussed as significant exceed this uncertainty and are as such assumed to be robust features of the input fields derived from observations. For further details, see the appendix.
e. Initial conditions
Each setup as described above will result in time series of TFR and Keff for each basin, describing the influence of a changing velocity field, which evolves with time but is the same in each experiment. The results might depend on the initial condition, which determines the position and hence exposure of the reference isohaline to possibly different features of the velocity field. To investigate the eddy mixing sensitivity to changes in the initial conditions, we evaluate a suite of experiments with varying tracer initial conditions, all of which are averaged SSS fields. These are reset in an identical manner as described above, keeping each of the different initial conditions quasi constant. Nothing but the initial condition is changed between the various experiments. In the following, each experiment is denoted by a suffix indicating the initial conditions used as outlined in Table 1.
List of initial conditions and corresponding suffixes used in the text. Data sources are given in parentheses in the last column. See section 2 for details.
Comparison between the different initial condition experiments then gives an indication of the sensitivity of the results to the variable background fields. None of these experiments will give a realistic representation of the actual variations in eddy mixing that are likely to depend on both variable velocities and SSS fields.
Consider a strong stirring anomaly that only occurs during a time X. One of the SSS-max features could move into that particular region during time Y. This would result in a strong variation of the diffusivity and TFR in the experiments with the initial conditions close to time Y. This, however, could be irrelevant for the “actual” SSS-max when time X is not equal to time Y, or it could even emphasize the variability when they are equal. To get a crude estimate of such a combined variability, we introduce the “combined” experiments. These are not separate experiments but instead combine the results of the existing experiments according to the matching initial conditions. This still does not provide a fully resolved time series for each basin, but it provides a guide for interpreting the importance of variability in diffusivity and transformation rate and exclude completely improbable scenarios that can arise due to the combination of the full variable velocity record with averaged and nonevolving initial conditions. Using these estimates, we can investigate situations where the spread between experiments is large and whether any detected variability could be significant for the real-world SSS-max.
The procedure is explained in detail in the appendix and shown schematically in Fig. A2. To summarize the main diagnostics used in this paper before, we discuss the results:
Effective diffusivity: The cross-isohaline eddy diffusivity, relevant for water-mass transformation. A measure of the stirring strength of the velocity field on the boundary of the volume, not dependent on the background gradient.
TFR: A measure of the integrated diffusive flux into the volume bounded by an isohaline. Compared to the effective diffusivity TFR incorporates both the velocity statistics and the background gradient.
SFC: The comparison of the lateral diffusive flux into the volume versus the surface forcing integrated over the corresponding sea surface. This gives an indication of how important surface eddy mixing is for the volume budget.
3. Results
The mean salinity differs significantly between the global ocean basins. To compare the saltiest regions, we use the reference salinities Sref from Gordon et al. (2015). Each basin is then analyzed in regional boxes to ensure the values represent only the SSS-max region and not other areas with identical salinities. See Fig. 2 for the position of the reference salinities as well as the regional boxes used.
(top) Mean SSS from MIMOC and (bottom) surface diffusivities reproduced from Abernathey and Marshall (2013) in color. In the upper plot, the black contour represents the Sref contour for each basin based on Gordon et al. (2015) for the MIMOCmean initial condition. In the lower box, the same salinity is shown for all used initial conditions (see Table 1 for reference). Black boxes indicate regional domains used in this study.
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
a. Mean
The results for the mean SSS fields can be seen in Fig. 3, with each of the diagnostics plotted against the bounding salinity contour with the regional reference salinity subtracted. The purpose of showing the full salinity domain is to demonstrate that, within the highest salinities of each basin, the results are relatively constant and not strongly dependent on the choice of the reference salinity. Hence, for all further analysis we show the values on the basin-specific reference isohaline Sref only (indicated by the horizontal line in Fig. 3).
Time-averaged diagnostics in salinity space computed from MIMOCmean experiment. (a) TFR by eddy mixing. (b) Surface forcing compensation. (c) Effective diffusivities Keff. (d) Mean transformation rates by surface forcing. Colors indicate ocean basin. The y axis represents the difference from the Sref value (Fig. 2) in each basin, with positive values representing isohalines toward the center of the SSS-max. When the area within an isohaline is smaller than 100 grid boxes, the line is dashed.
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
Note that the lower values represent isohalines farther outward from the SSS-max. Thus, they might not be contained within the regional boxes. This will violate the previously outlined equations by introducing a nonzero lateral boundary flux. As discussed later in the appendix, the low lateral gradient in the southern Indian Ocean (SI) presents a problem with regard to this constraint. Outer salinities in the SI should be regarded as unreliable. We confirmed that for all experiments the actual reference isohaline is well contained in the regional domains (see appendix).
Figure 3 shows the TFREddy,mean is highest in the SI and North Pacific (NP) with mean values of about 3.4/3.5 Sv (1 Sv ≡ 106 m3 s−1). The other basins show lower TFR with the NA at about 2 Sv, followed by the South Atlantic (SA) with about 1.5 Sv, and the South Pacific (SP) with 1.2 Sv. The difference between the NP/SI and NA/SA/SP might reflect the larger area within salinity contours due to the weaker lateral salinity gradient and do not necessarily indicate a higher relative contribution to the budget by eddy mixing. The SFC (Fig. 3b) illustrates this by showing what percentage of the TFREP is compensated by TFREddy,mean. Here, the SI still has the highest value (25%), while the NP is found well in the spread of the other basins. The standout basin in terms of TFR and SFC seems to be the SP, which shows the lowest SFC at <10% for salinities < Sref throughout most of the salinity space. The NA, which in terms of salinity processes has received the majority of the attention in the science community during recent years, has a SFC of around 20%.
Regional differences also emerge in the diffusivities (Fig. 3c). The SP again shows the lowest values compared to the other regions. But the basin ranking in SFC is not mirrored in all the Keff values. Most notably, the SI has weak diffusivity values, while the transformation rate is highest. Alignment of high local diffusivities with high gradients that dominate the overall TFR, and in turn the SFC, is necessary to explain this behavior. This illustrates that localized structures can be decisive for the total diffusive flux out of the SSS-max. The effects of these structures for the mean quantities are captured with the methods used here, but it is not possible to locate these “hot spots” in space with our method.
Any localized covariance between gradient and diffusivity is important for understanding temporal variability in eddy mixing. Our observation-driven model studies are therefore well posed to investigate temporal variability in eddy mixing by representing the interrelated variability of the SSS and eddy fields in both time and space.
b. Comparison to existing studies
To our knowledge, the closest studies using a comparable control volume (isohaline coordinates) are Bryan and Bachman (2014; North Atlantic only) and Johnson et al. (2016; global). Both studies use the same methodology and model setup. Another study by Schmitt and Blair (2015) applies diffusivity estimates to a climatology in a similar framework and finds similar results as Bryan and Bachman (2014). They investigate the full volume bounded by the isohaline, including the subsurface below the mixed layer. There are some caveats to the comparison as outlined below, but, as we conclude, the most striking regional characteristics seem robust when compared to our results.
The comparison between the three studies above might be complicated by several issues. The model studies show large biases in their surface salinity fields, which changes the mean position of the outcrop area. Hence, even when we present our results in the exact reference salinities of their study, the bounded area can vary significantly. This could not only affect the water-mass transformation by eddy mixing but also the appropriate surface forcing term. Bryan and Bachman (2014) show a comparison of the forcing term and the water-mass transformation rate due to surface fluxes, where the model term deviates significantly from estimates using climatological datasets (their Fig. 11).
To compare our results with these previous studies, most of which evaluate the salinity budget, we additionally calculated the SFC for the salinity budget. By integrating the right-hand side of Eqs. (9) and (11) in salinity space and dividing them similar to Eq. (12).
Results are shown in Table 2 as SFCS. Furthermore, we evaluated all results on the reference salinities from Johnson et al. (2016; Table 2; second columns). For each basin, except the SI, the difference in the various SFC values is 5% or smaller, a minor difference considering the spread in regional results from previous studies (e.g., 10%–50% SFC in the NA). We will discuss the possible reason for the wide range of results below.
Mean results. The columns show the results from the MIMOC mean experiment. In each column (basin), the values are calculated according to the reference salinities from Gordon et al. (2015; bold) and Johnson et al. (2016). The rank for each basin is given in parentheses after the value. From top to bottom: TFR, the SFC from the volume budget, the SFC from the salinity budget (SFCS), the SFC estimate from the salinity budget over the full depth from Johnson et al. (2016; SFCS,FullDepth) and a comparison between SFCS and SFCS,FullDepth (mixed layer vs interior). Note that for the last row the results are derived for both reference salinities by dividing both values for SFCS by the single results from Johnson et al. (2016). Please note the bold values in the last row are comparing values where the reference salinities are not equal. For details see text.
Some similarities emerge: The SP SSS-max has the weakest eddy mixing contribution both for the mixed layer and the full isohaline volume. Our results using the SFC based on the volume budget as well as the full-depth results from Johnson et al. (2016) suggest that the largest contribution by eddy mixing is found in the SI. Results for alternative reference salinities might be biased since the area within the isohaline could be leaving the regional boundary in our study (see appendix).
The remaining basins differ in their ranking depending on the metric used. It should not come as a surprise that not all basins compare well in both studies, as the comparison is between eddy mixing estimates for the mixed layer only versus the full-depth isohaline volume. Assuming the results are indeed comparable, despite the aforementioned reasons, one can estimate a crude ratio of SFC between the mixed layer and the interior by comparing the SFC values to each other (Table 2; last row). The ratio varies from 22% up to 37%. Given the small surface area of the lateral mixed layer boundary compared to the surface of the subsurface isohaline volume, this might indicate a significant depth dependency of the lateral eddy mixing—strong in the mixed layer and comparably weak in the interior. Further research has to show to what degree these studies are actually comparable and if these findings can be confirmed from independent estimates.
Besides the choice of control volume, the actual quantification method for FEddy could matter for the resulting SFC. Gordon and Giulivi (2014) proposed the idea of eddy fluxes as a significant contribution to the salinity–freshwater budget in the North Atlantic SSS-max region. They estimate the covariance term from SODA reanalysis data by defining the prime terms as the deviation from the zonal average over a box that is approximately 25° wide. This is about 50 times the range of the first Rossby radius in this area (about 50 km; Chelton et al. 1998), possibly including large-scale circulation features in the prime terms. This potentially biases the contribution of eddy mixing by adding some of the long-term advective variability. That would explain why this study concludes the highest SFC in the mixed layer of the North Atlantic at around 50%. Our results agree reasonably well with Busecke et al. (2014), who estimated 10%–30% SFC in the NA mixed layer based on the distribution of local divergence of eddy diffusion by using a constant scalar eddy diffusivity and a typical SSS curvature found in a similar box as Gordon and Giulivi (2014). The choice of a typical SSS curvature might effectively mitigate some of the variability caused by the moving SSS-max combined with a fixed control volume.
c. Seasonal variability
We find that temporal variability exists in the TFR as well as Keff on various time scales. We focus on the seasonal and interannual signal. In agreement with Bryan and Bachman (2014) and Johnson et al. (2016), this variability is small compared to the other terms in the volume budget (not shown), namely, surface forcing and vertical diffusion. Since these two effects are largely compensating, the eddy mixing can still play an important role for the tendency term in the volume budget of the SSS maxima. Indeed variations in interannual TFREddy,mean are of comparable magnitude as the TFR calculated from the actual change in area from observations (using the same fixed MLD, not shown).
Before we present the results, we begin with a discussion of mechanisms that can cause a temporal variability in the TFR. We will assume that the diffusive flux across the contour is expressed as the product of a mean cross-contour diffusivity Keff and the salinity gradient on the contour ∇lS (by definition perpendicular to the contour). As outlined above, Keff itself is independent of the background gradient, since it only measures the enhancement of a spatial gradient (which has to be nonzero) by the stirring action of a given velocity field. The resulting flux will scale with both the cross-contour diffusivity as well as the cross-contour gradient. Since Keff is the result of the velocities acting on the background fields, and the velocities can vary both in space and time, there are three principal mechanisms that could cause temporal variability in TFR. In each basin there is likely a contribution by each of these mechanisms, but in the following list we lay out how each mechanism would affect the results in isolation in order to facilitate the identification of the dominant process within the results that follow:
Change of Keff due to temporal variability in the velocity field. Assume the velocity field would have spatially homogeneous stirring characteristics that vary with time. All experiments would show coherent variability in both TFR and Keff, since for each experiment the position of the cross-contour gradient is constrained by the reset procedure; hence, the diffusivity would control the time evolution of the TFR.
Change of Keff due to changes in the position of the contour in a field of spatially variable stirring. Opposite to the above, now assume a temporally constant stirring action of the velocity field, which varies in space instead. All experiments would show constant TFR and Keff, since for a constrained contour in a single experiment the stirring action resulting in Keff as well as the cross-contour gradient would remain quasi constant. The position of the reference contour varies between each experiment, potentially exposed to other parts of the velocity field. This would cause a spread between experiments in both TFR and Keff.
Change in salinity gradient ∇lS on the contour. As explained above, single experiments would show no variability in either TFR or Keff, since the gradient is constrained by the reset. Experiments would show constant TFR and Keff, as in 2; however, the spread between experiments only affects TFR. Contrary to 2, the Keff would remain constant between experiments, since the stirring characteristics and the contour position are identical, and Keff is independent from the background gradient (see section 2).
The left column in Fig. 4 shows the seasonal cycle for each experiment, separated into ocean basins. The seasonal cycle extracted from the experiments with monthly (gray lines), mean (blue), initial conditions and the combined (black) experiment are shown. Regional differences in the seasonal cycle are evident. The combined seasonal cycle in the SI and SP is very small or not truly an annual harmonic. In the NA, SA, and NP, the combined seasonal cycle is of significant size compared to the mean and is shaped close to an annual harmonic with the highest values during the spring of the respective hemisphere. The SI and SP show relatively weak seasonal cycles in Keff,mean (red) that cannot be related to the TFRmean in a straightforward manner, suggesting increased importance of the local interplay of diffusivities and gradients or simply a nonsignificant seasonal signal.
(left) Seasonal cycle and (right) interannual variability of transformation rate (Sv) on Sref. The sign is reversed, with positive values indicating destruction of salty water masses. Colors indicate different experiments (see Table 1). Blue indicates TFRmean, black is TFRcombined, and gray lines are all TFRmonthly experiments. The interannual record is derived by preaveraging every 4 months and smoothing with a 1.5-yr Gaussian window. Colors as before with gray indicating all experiments with annual initial conditions (Table 1). Thick black and dashed black lines indicates TFRcombined derived from experiments with annually averaged initial conditions from ECCO and Argo, respectively; for more details see text. Keff (red) is displayed in all plots normalized by the mean and std dev of TFRmean for comparison.
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
We want to focus on the NP and NA in particular, as they seem to display two regionally different origins of the combined seasonality related to the idealized scenarios from above. In the NA, every experiment with monthly initial condition is exhibiting a very similar seasonal cycle in terms of timing and amplitude. When comparing the Keff values for the NA (Fig. 5a), the variability is very coherent and larger than the offset between the single experiments. This suggests a local change in diffusivities (mechanism 1 from above) as the leading cause of variability in the NA. The time lag of about a month between Keff,mean and TFRmean in the NA (Fig. 4a) is an interesting result in itself, which is robust for all experiments (not shown). We interpret the lag as the time between the fast creation of lateral tracer gradient variance (stirring, reflected in Keff, which is then slowly digested by small-scale diffusion acting on this gradient variance). This, yet again, illustrates the complex nature of the eddy mixing and the problems that may arise when eddy mixing is diagnosed from methods involving matching of vastly different datasets. Because of the less coherent signals in other basins, it is unclear if the length of this lag is the same in every basin.
Effective diffusivities for Sref; Keff,mean (thick lines) and the std dev (thin lines) of the (left) monthly and (right) annual experiments. Ocean basins are indicated by colors. Signals shown are processed identical to the TFR (see Fig. 4).
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
In the NP, the TFR of each experiment seems to be rather constant with a larger offset in between experiments. The Keff values in Fig. 5a show a similar offset between experiments as the NA, but in the case of the NP, it is not small compared to the annual cycle. Hence, it seems likely that a change in diffusivity due to the changing position is responsible for the variability in TFR. This is plausible if we consider the variable position of the NP Sref contour and its vicinity to strong gradients in surface diffusivities (Fig. 2). We cannot rule out a change in local gradient on the contour as a contribution. It is clear, however, that in the NP the initial fields of SSS are more important for the variability in eddy mixing than the velocity field, contrary to the NA.
The SA exhibits the largest spread in Keff between experiments. We suggest that this is caused by its unique position in the western boundary current. The SA SSS-max is exposed to strong advection, possibly moving in and out of areas of spatially heterogeneous diffusivities. This does not result in a clear seasonal cycle as in the NA and NP, and it is left for further studies to determine whether this large variability remains robust when other processes (as mentioned in the method section) are invoked. We will now apply the same analysis to the interannual signals to investigate if we find evidence for local changes of diffusivities on time scales longer than a year.
d. Interannual variability
Figure 4 (right column) and Fig. 5 (right) show interannual variability of Keff and TFR.
Similar to the seasonal plots, the gray lines in Fig. 4 (right column) mark each experiment with annual-averaged initial conditions, while the TFRannual,combined is shown in black. The combined experiment should be viewed as a check whether various initial conditions can change or compensate the variability imposed by the velocity field.
The character of the longer-term variations is quite different between basins. The NA TFR increases until circa 2006 and then decreases in a similar fashion. This is consistent with the combined ECCO experiment, but the combined Argo experiment shows an offset, which suggests the TFR stays high in the later part of the record. The SA shows several shorter fluctuations, while the longer term seems to be quite steady.
The NP shows an increase in Keff and TFR around 1998 in several experiments. For the SSS-max, this seems to be rather irrelevant, since the combined experiment does not capture it. Toward the end of the record, the TFR seems to decrease slightly. Similar to the seasonal cycle, the NP shows the largest spread between experiments compared to all other basins, again indicating the possible larger sensitivity to changes in SSS fields compared to the other basins. The SP shows a strong maximum in TFRannual/Keff,annual in 1998. When the combined experiment is considered, the amplitude is lessened somewhat, but the peak remains the largest interannual anomaly in all ocean basins. The SI again shows very little variability, similar to the seasonal cycle. The comparison between the combined experiments from Argo and ECCO suggests that results in the NA and to a lesser degree in the SP are sensitive to the source of initial conditions. In the SA, NP, and SI the records diverge only slightly. Especially for the earlier years of the Argo record the mismatch might be caused by limited float coverage.
It is worth noting that in the SP (and in many experiments for the NP) the variability in eddy mixing seems to be roughly coincident with the strong El Niño of 1997–98. This indicates that large-scale environmental processes might be linked to time-variable mixing relevant for the subtropical SSS maxima. The tight distribution of Keff,annual values for the NA and SP suggest that these changes are mainly caused by local changes in diffusivity, which appear very coherent in space, affecting most experiments. Even in the NP, the high number of experiments showing a peak around 1998 contributes to this idea. The SSS-max might not be impacted by the anomalous velocities, because of an anomalous contour position, but it indicates that diffusivity changes might be happening adjacent to the SSS-max.
These results suggest a link between large-scale climate forcing and the eddy mixing in the NA and SP SSS-max via locally changing diffusivities (mechanism 1 from above).The SA and NP show considerable spread between the Keff values. Similar to the seasonal interpretation, we conclude that the changing position of the reference isohaline is the dominant driver for the variability in the NP and SA. Both of these basins show larger lateral gradients in surface diffusivities (Abernathey and Marshall 2013), qualitatively confirming the potential for high variability in diffusivities by changing the position of the reference isohaline.
The SI shows little spread in Keff and little variability in the single experiments. The variability in TFR is also low compared to the other basins. This is particularly interesting since it has arguably the largest contribution of eddy mixing to the budget, while having both a small mean diffusivity and by far the least variability. Local hot spots for the eddy mixing (locations where diffusivity and gradient line up locally to dominate the overall TFR) could explain the discrepancy between the high integrated diffusive flux and the low-averaged diffusivity.
The following list summarizes the regional character [lending from Gordon et al. (2015)] of each basin with respect to the eddy mixing in the surface layer:
The SP has by far the lowest SFC of all the basins. This is likely due to its unique separation from the western boundary current. The southern intertropical convergence zone shifts the SSS-max far into the eastern part of the basin, prohibiting access to the energetic western region of the basin. The seasonal cycle is very irregular, although the amplitude is relatively higher than in the SI in agreement with Gordon et al. (2015, their Fig. 3). The interannual record shows the strongest signal of all basins with a strong pulse of elevated TFR and Keff around 1998, which is proposed to be related to larger-scale climate variability modulating local diffusivities with time.
The SI is the strongest basin in terms of SFC and TFR but interestingly has very low Keff and low temporal variability in eddy mixing, possibly influenced by its unique poleward position in a predominantly zonal mean flow, stabilizing seasonal gradients, and possibly suppressing the eddy diffusivities in a region relatively high in EKE (e.g., Klocker and Abernathey 2014).
The SA has a similar SFC to the NP and NA and shows a less coherent seasonal cycle in TFR that is similar in magnitude and timing (with a 6-month shift accounting for the hemispheric difference) to the NP and NA. It seems that it represents somewhat of a mixed case in terms of the responsible mechanism (local diffusivity changes vs monthly position of SSS fields).
The NA seems to be largely dominated by local changes in diffusivities both for the seasonal and interannual variability. What exactly renders this mechanism so dominant in the NA is subject to speculation. It might be related to the high lateral salinity gradient (inhibiting strong lateral movement of the reference isohaline) or the relatively low lateral gradient in surface diffusivities, which further reduce the influence of a changing isohaline position to the effective diffusivity.
The NP variability in eddy mixing is strongly dependent on the SSS fields. Both the seasonal cycle as well as interannual variability are shown to be strongly influenced by the position of the reference isohaline, supported by conditions of low lateral SSS gradient and high surface diffusivity gradient. The interannual record shows some indications of a long-term change, which might be caused by local changes in the diffusivities similar to the SP and NA.
4. Conclusions
a. Relevance for the SSS maxima in the global ocean
Using diagnostics for eddy diffusivity and integrated diffusive flux in a water-mass framework, we documented marked regional differences in the strength, variability, and the responsible mechanisms for eddy mixing in the SSS maxima.
The temporal variability is a result of regionally differing mechanisms, dominated by variability in either the velocity field or the surface salinity field: on the one hand, local changes of the eddy field resulting in local diffusivity changes, and on the other hand, changes in the position of the SSS maximum in a spatially varying field of surface diffusivities.
The results presented here support the notion of each of the SSS maxima having its own unique character in eddy mixing, in agreement with the results from Gordon et al. (2015) for the mean position and strength of the seasonal cycle.
We argue that temporal variability of eddy mixing and diffusivities has to be taken into account when constructing salinity budgets in the SSS-max regions. Furthermore, the application of results from one SSS-max region (e.g., the well-studied NA) to other basins might not be possible. Especially when considering a changing climate, which might influence the mechanisms responsible for temporal variability differently.
b. Implications for the global water cycle
Regional differences in eddy mixing could have implications for the diagnosis of water cycle changes using the SSS on long time scales. If the common conception of an intensifying water cycle in the future—“saltier regions get saltier and fresh regions become fresher” (Held and Soden 2006)—holds true, these changes might influence the eddy mixing in each basin differently. For instance, the NP shows the highest sensitivity to changes in the surface salinity. Presumably higher eddy mixing would ensue following the intensification of the lateral salinity gradient by an intensified hydrological cycle, and one could imagine a negative feedback. Of course, this would only be valid if the eddy diffusivities remain constant, an assumption that cannot be validated for the relevant time scales (more than 50 yr; Durack and Wijffels 2010) at this point. It seems that the observed decadal pattern intensification in SSS are especially weak/inconsistent in the NP, both for strongly forced model runs as well as historic observations (Durack 2015, their Fig. 7 A/D). This would be in line with the argument presented above. Further research is needed to investigate this mechanism and its potential importance for the imprint of a changing hydrological cycle on the SSS.
c. Beyond the surface salinity
This study suggests basin-scale changes of the local surface diffusivities, potentially affecting areas much broader than the SSS-max. In the case of the South and North Pacific, these changes seem connected to large-scale climate fluctuations related to ENSO, possibly forming an important climate feedback. To our knowledge such a connection has not been documented using an observationally driven method and could be of relevance to the larger oceanographic and climate science community. A dataset of monthly surface diffusivities combining methods from Abernathey and Marshall (2013) and this study will be helpful in identifying locations where eddy diffusivities respond coherently to the large-scale environment. Such a dataset is in preparation and will be published in a separate manuscript.
Acknowledgments
We are grateful for the detailed comments from two anonymous reviewers, which greatly improved the manuscript. We also thank Sjoerd Groeskamp, Sloan Coats, Claudia Giulivi, and Søren Thomsen for comments on the initial draft. Julius Busecke’s research was supported by NASA Award NNX14AP29H. Ryan P. Abernathey acknowledges support from NASA Award NNX14AI46G. Arnold L. Gordon’s research is supported by NASA Grant NNX14AI90G to Columbia University.
APPENDIX
Method Details
a. Reset procedure
Because of the nature of the presented experiments, which do not simulate key processes like surface forcing and all vertical processes, a steady state will never be reached in the TFR/Keff. The mixing will eventually just destroy all local maxima and completely homogenize the surface fields. To maintain a realistic quasi-constant background SSS field, the tracer fields have to be reset in regular intervals. Each reset to the smooth initial conditions causes a distinct spike in both TFR and Keff, which represents the adjustment phase in which increased variance is created by stirring the smooth initial conditions until the small-scale diffusion limits the variance and the change in TFR and Keff represents the temporal changes in eddy stirring. The aforementioned adjustment phase is unrealistic and has to be removed (we cut the first 2 months in our experiments, leaving a gap in the data record). We compute two different tracer outputs that are reset at shifted intervals and then averaged to create a continuous time series of TFR and Keff for each salinity S0. Shifting them exactly half of the reset period also ensures that any residual drift from the reset would be averaged out. Several considerations are influencing the choice of reset period:
The missing data might still slightly bias the results at the time of reset. It is vital to choose an odd number of months as the interval length to ensure that the possible effect of the reset is occurring at different months of the year each time, which should be averaged out when analyzing the seasonal cycle.
The mean position and area of the SSS-max features have to remain within a realistic range, which limits the maximal length of the reset interval to 9–11 months. After that, for instance, the NA SSS-max get slowly advected into the equatorial current system, and the velocity fluctuations acting on the reference isohaline are not representative of the subtropics anymore.
The reset interval has to be chosen so that the reference salinity does not get eroded too far, which specifically in the SI is a problem in reset periods over 9 months
Since the adjustment phase removes 2 months from the record, the reset period is chosen as long as possibly allowed by the above criteria to ensure a maximum of data points are derived from both tracer records.
b. Error due to reset procedure
Root-mean-square error due to reset procedure. Values are shown for the respective basins and the various time frames considered (see legend). For details see text.
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
c. Combined experiment
To evaluate the effect of the interplay between temporally evolving velocities and SSS fields, we created several combined experiments. As stated above they are not separate model experiments, but instead combinations of the single experiments, aiming to give the most realistic representation of the TFR for a climatological season or interannual variability. We split the existing experiments into chunks and stitch them together in order of their initial conditions. For the annual combined from January 2000 until December 2000, the values are taken from the ECCO 2000 experiment (see Table 1), and from January 2001 until December 2001 the values from the ECCO 2001 experiment (see Table 1) are inserted. This is repeated for all annual experiments. We present two annual combined records to cover the whole time frame of the altimetry record. From 1993–2011, we use annually averaged surface fields from ECCO as initial conditions, and from 2006 to 2014, we use Argo data (details in Table 1).
The monthly combined experiment is created by substituting each month in the record with data from the experiment with corresponding climatological initial conditions (see Fig. A2). Note that these are climatological monthly initial conditions, meaning the initial conditions are the same for each, for example, January. The velocities, however, vary interannually as in all other experiments.
Schematic for the construction of the combined monthly experiment. Each colored row is an experiment with quasi-constant initial conditions (see Table 1 and text for details). Each box represents a month in the full time record (extended for multiple years indicated by the dots on the right). The combined experiment is constructed by concatenating the time series from the respective experiment for each month (dark boxes).
Citation: Journal of Physical Oceanography 47, 4; 10.1175/JPO-D-16-0215.1
d. Boundary violation
The water-mass framework is well suited for the study of SSS maxima due to their appearance as local maxima in the SSS fields. One, however, has to define regional domains in order to not lump all maxima together globally, making the interpretation of local differences impossible. Depending on the basin, the definition of this local domain can be complicated, as one has to take good care that the isolines of interest neither leave the box at any time nor other features enter the domain. Our domains are chosen to guarantee both of these aspects for the reference salinity. Because of the regional setup, this can mean that even isolines as little away as 0.2 psu violate this criterion. This is especially critical in basins with low lateral SSS gradients and secondary local maxima in SSS like the SI and NP. In fact, in the SI we were not able to completely keep the reference isohaline in the box without making the box unreasonably large, reaching into the SA and SP. Hence, we decided to allow a possible but likely small leakage of the reference isohaline on the southern coast of Australia. Values at isohalines larger than the reference salinity are not affected by the boundary violation but might be biased because the highest salinity values will simply disappear over the reset time, as they diffuse outwards. Thus, we urge the reader to interpret the values only on the reference salinity, for which extensive testing has excluded above issues.
REFERENCES
Abernathey, R. P., and J. Marshall, 2013: Global surface eddy diffusivities derived from satellite altimetry. J. Geophys. Res. Oceans, 118, 901–916, doi:10.1002/jgrc.20066.
Abernathey, R. P., J. Marshall, M. Mazloff, and E. Shuckburgh, 2010: Enhancement of mesoscale eddy stirring at steering levels in the Southern Ocean. J. Phys. Oceanogr., 40, 170–184, doi:10.1175/2009JPO4201.1.
Amores, A., O. Melnichenko, and N. Maximenko, 2016: Coherent mesoscale eddies in the North Atlantic subtropical gyre: 3-D structure and transport with application to the salinity maximum. J. Geophys. Res. Oceans, 122, 23–41, doi:10.1002/2016JC012256.
Bingham, F. M., J. Busecke, A. L. Gordon, C. F. Giulivi, and Z. Li, 2014: The North Atlantic subtropical surface salinity maximum as observed by Aquarius. J. Geophys. Res. Oceans, 119, 7741–7755, doi:10.1002/2014JC009825.
Boccaletti, G., R. Ferrari, A. Adcroft, D. Ferreira, and J. Marshall, 2005: The vertical structure of ocean heat transport. Geophys. Res. Lett., 32, L10603, doi:10.1029/2005GL022474.
Bryan, F., and S. Bachman, 2014: Isohaline salinity budget of the North Atlantic salinity maximum. J. Phys. Oceanogr., 45, 724–736, doi:10.1175/JPO-D-14-0172.1.
Busecke, J., A. L. Gordon, Z. Li, F. M. Bingham, and J. Font, 2014: Subtropical surface layer salinity budget and the role of mesoscale turbulence. J. Geophys. Res. Oceans, 119, 4124–4140, doi:10.1002/2013JC009715.
Chelton, D. B., R. A. DeSzoeke, M. G. Schlax, K. El Naggar, and N. Siwertz, 1998: Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr., 28, 433–460, doi:10.1175/1520-0485(1998)028<0433:GVOTFB>2.0.CO;2.
Durack, P. J., 2015: Ocean salinity and the global water cycle. Oceanography, 28, 20–31, doi:10.5670/oceanog.2015.03.
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, doi:10.1175/2010JCLI3377.1.
Farrar, J. T., and Coauthors, 2015: Salinity and temperature balances at the SPURS central mooring during fall and winter. Oceanography, 28, 56–65, doi:10.5670/oceanog.2015.06.
Forget, G., J. M. Campin, P. Heimbach, C. N. Hill, and R. M. Ponte, 2015: ECCO version 4: An integrated framework for non-linear inverse modeling and global ocean state estimation. Geosci. Model Dev. Discuss., 8, 3653–3743, doi:10.5194/gmdd-8-3653-2015.
Fox-Kemper, B., R. Lumpkin, and F. O. Bryan, 2013: Lateral transport in the ocean interior. Ocean Circulation and Climate: A 21st Century Perspective, G. Siedler et al., Eds., International Geophysics Series, Vol. 103, Academic Press, 185–209.
Gordon, A. L., 2016: The marine hydrological cycle: The ocean’s floods and droughts. Geophys. Res. Lett., 43, 7649–7652, doi:10.1002/2016GL070279.
Gordon, A. L., and C. Giulivi, 2008: Sea surface salinity trends over fifty years within the subtropical North Atlantic. Oceanography, 21, 20–29, doi:10.5670/oceanog.2008.64.
Gordon, A. L., and C. Giulivi, 2014: Ocean eddy freshwater flux convergence into the North Atlantic subtropics. J. Geophys. Res. Oceans, 119, 3327–3335, doi:10.1002/2013JC009596.
Gordon, A. L., C. Giulivi, J. Busecke, and F. M. Bingham, 2015: Differences among subtropical surface salinity patterns. Oceanography, 28, 32–39, doi:10.5670/oceanog.2015.02.
Groeskamp, S., B. M. Sloyan, J. D. Zika, and T. J. McDougall, 2017: Mixing inferred from an ocean climatology and surface fluxes. J. Phys. Oceanogr., doi:10.1175/JPO-D-16-0125.1, in press.
Held, I. M., and B. J. Soden, 2006: Robust responses of the hydrological cycle to global warming. J. Climate, 19, 5686–5699, doi:10.1175/JCLI3990.1.
Huffman, G. J., and Coauthors, 1997: The Global Precipitation Climatology Project (GPCP) Combined Precipitation Dataset. Bull. Amer. Meteor. Soc., 78, 5–20, doi:10.1175/1520-0477(1997)078<0005:TGPCPG>2.0.CO;2.
Johnson, B. K., F. O. Bryan, S. A. Grodsky, and J. A. Carton, 2016: Climatological annual cycle of the salinity budgets of the subtropical maxima. J. Phys. Oceanogr., 46, 2981–2994, doi:10.1175/JPO-D-15-0202.1.
Klocker, A., and R. Abernathey, 2014: Global patterns of mesoscale eddy properties and diffusivities. J. Phys. Oceanogr., 44, 1030–1046, doi:10.1175/JPO-D-13-0159.1.
Lee, M.-M., A. J. G. Nurser, A. C. Coward, and B. A. De Cuevas, 2009: Effective eddy diffusivities inferred from a point release tracer in an eddy-resolving ocean model. J. Phys. Oceanogr., 39, 894–914, doi:10.1175/2008JPO3902.1.
Lindstrom, E., F. Bryan, and R. Schmitt, 2015: SPURS: Salinity Processes in the Upper-Ocean Regional Study—The North Atlantic Experiment. Oceanography, 28, 14–19, doi:10.5670/oceanog.2015.01.
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 5753–5766, doi:10.1029/96JC02775.
Marshall, J., D. Jamous, and J. Nilsson, 1999: Reconciling thermodynamic and dynamic methods of computation of water-mass transformation rates. Deep-Sea Res. I, 46, 545–572, doi:10.1016/S0967-0637(98)00082-X.
Marshall, J., E. Shuckburgh, H. Jones, and C. Hill, 2006: Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport. J. Phys. Oceanogr., 36, 1806–1821, doi:10.1175/JPO2949.1.
Nakamura, N., 1996: Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate. J. Atmos. Sci., 53, 1524–1537, doi:10.1175/1520-0469(1996)053<1524:TDMEFA>2.0.CO;2.
O’Connor, B. M., R. A. Fine, and D. B. Olson, 2005: A global comparison of subtropical underwater formation rates. Deep-Sea Res. I, 52, 1569–1590, doi:10.1016/j.dsr.2005.01.011.
Ponte, R. M., and N. T. Vinogradova, 2016: An assessment of basic processes controlling mean surface salinity over the global ocean. Geophys. Res. Lett., 43, 7052–7058, doi:10.1002/2016GL069857.
Qu, T., S. Gao, and I. Fukumori, 2011: What governs the North Atlantic salinity maximum in a global GCM? Geophys. Res. Lett., 38, L07602, doi:10.1029/2011GL046757.
Rypina, I. I., I. Kamenkovich, P. S. Berloff, and L. J. Pratt, 2012: Eddy-induced particle dispersion in the near-surface North Atlantic. J. Phys. Oceanogr., 42, 2206–2228, doi:10.1175/JPO-D-11-0191.1.
Schanze, J. J., R. W. Schmitt, and L. L. Yu, 2010: The global oceanic freshwater cycle: A state-of-the-art quantification. J. Mar. Res., 68, 569–595, doi:10.1357/002224010794657164.
Schmidtko, S., G. C. Johnson, and J. M. Lyman, 2013: MIMOC: A global monthly isopycnal upper-ocean climatology with mixed layers. J. Geophys. Res. Oceans, 118, 1658–1672, doi:10.1002/jgrc.20122.
Schmitt, R. W., 2008: Salinity and the global water cycle. Oceanography, 21, 12–19, doi:10.5670/oceanog.2008.63.
Schmitt, R. W., and A. Blair, 2015: A river of salt. Oceanography, 28, 40–45, doi:10.5670/oceanog.2015.04.
Schott, F. A., J. P. Mccreary, and G. C. Johnson, 2004: Shallow overturning circulations of the tropical-subtropical oceans. Earth’s Climate, Geophys. Monogr., Vol. 147, Amer. Geophys. Union, 261–304.
Vinogradova, N. T., and R. M. Ponte, 2013: Clarifying the link between surface salinity and freshwater fluxes on monthly to interannual time scales. J. Geophys. Res. Oceans, 118, 3190–3201, doi:10.1002/jgrc.20200.
Walin, G., 1977: A theoretical framework for the description of estuaries. Tellus, 29, 128–136, doi:10.3402/tellusa.v29i2.11337.
Wüst, G., 1936: Oberflächensalzgehalt, verdunstung und niederschlag auf dem weltmeere nebst bemerkungen zum wasserhaushalt der Erde. Länderkd. Forsch., 1936, 347–359.
Yu, L., X. Jin, and R. A. Weller, 2008: Multidecade global flux datasets from the Objectively Analyzed Air-Sea Fluxes (OAFlux) project: Latent and sensible heat fluxes, ocean evaporation, and related surface meteorological variables. OAFlux Project Tech. Rep. OA-2008-01, 64 pp.
