Introduction

An essential challenge in physical oceanography and climate dynamics concerns the influence of polar lowsalinity seawater on the global ocean circulation. At low latitudes the ocean loses water to the atmosphere because evapouration exceeds precipitation. The atmosphere for 2000-2010relative to 1980-2000. And Proshutinsky et al. [2019] estimate an extra 6,400km 3 of liquid freshwater between 2003 and 2018 in the Beaufort Gyre, which is the largest Arctic freshwater reservoir. This buildup of liquid freshwater is seen in Fig. 1 (Liquid Storage panel), which shows observations of liquid freshwater volume increasing (red line; see Haine 2020 andHaine et al. [2015] for full discussion and details on the data sources; and see Wang et al. 2023 for a recent update). Fig. 1 reveals the sources of the extra liquid freshwater too: they are reduced sea ice (Solid Storage panel), increased runoff, and increased inflow through Bering Strait (left hand panels). The observed outflows (right hand panels) are unchanged or increasing in magnitude (Liquid Fram Strait panel; recent observations of Fram Strait liquid freshwater flux show no overall increase Karpouzoglou et al. 2022). They do not match the increased inflows, however, causing the freshwater accumulation in the Arctic Ocean.

Fig. 1 also shows results from the Community Earth System Model (CESM) version 1.1 based on Jahn and Laiho [2020]. The CESM is a fully coupled, state-of-the-art global Earth system model [Hurrell et al., 2013]. The model results comprise an ensemble of historical control simulations (gray) and two ensembles of 21st century projections (the large ensemble in purple and low warming scenario in green; see Jahn and Laiho 2020, Kay et al. 2015, and Sanderson et al. 2017 for details). Using the amplitude of the control ensemble variability (horizontal lines) allows to determine when the anthropogenic-forced signals emerge (vertical purple and green lines; see Jahn and Laiho 2020 for details). The anthropogenic decline in Arctic sea ice emerged first, in the 2000s (Solid Storage panel;IPCC 2021, Notz andMarotzke 2012). The anthropogenic increase in Arctic liquid freshwater emerged next, in the 2010s (Liquid Storage panel). None of the inflow or outflow fluxes in Fig. 1 show emergence of an anthropogenic signal yet. The CESM results suggest that anthropogenic effects will increase the freshwater flux through Davis Strait, however, with a signal emerging in the 2020s. The Fram Strait fluxes are projected to change too, with less solid (sea ice) flux, more liquid flux (and more total flux), but the anthropogenic-forced signal is not expected to emerge for 15-40 years.

The CESM results match the observations in Fig. 1 reasonably well, although the CESM liquid Fram Strait freshwater flux is too small. In recent follow-up studies, Zanowski et al. [2021] and Weijer et al. [2022] show that other Coupled Model Intercomparison Project 6th phase (CMIP6) coupled climate models do not have this bias. Still, more work is needed to characterize the fingerprint of anthropogenic perturbation to the Arctic freshwater cycle in the coming decades. The projected increase in atmospheric moisture flux convergence is moderately well established [Ford and Frauenfeld, 2022, McCrystall et al., 2021, Stadnyk et al., 2021, Vihma et al., 2016], but the anticipated changes to the marine outflows are poorly known. Moreover, well-known, stubborn biases exist in the Arctic Oceans of CMIP6 models [Heuzé et al., 2023, Khosravi et al., 2022, Muilwijk et al., 2023, Shu et al., 2023, Wang et al., 2023].

This evidence focuses on the kinematic inflows and outflows of freshwater to the Arctic (meaning they do not involve circulation changes). But dynamical mechanisms (involving circulation changes) are also important, especially for the Beaufort Gyre. Proshutinsky et al. [2019] summarize three main factors controlling the freshwater buildup in the Beaufort Gyre:

(i) Ekman pumping from anticyclonic winds, which accumulates freshwater from around the gyre, including runoff from the shelves, and deepens the halocline [Johnson et al., 2018, Manucharyan et al., 2016, Proshutinsky et al., 2002, Stewart and Haine, 2013].

(ii) Ice melt and growth, which limits the gyre spin-up. This "Ice-Ocean Governor" feedback mechanism emphasizes the role of sea ice in controlling geostrophic currents [Meneghello et al., 2018]. Specifically, the surface ocean stress depends on the difference between the sea ice velocity and the surface ocean velocity. Therefore, stress on the ocean can change, hence changing Ekman pumping and freshwater accumulation, by changing sea ice conditions with fixed winds (see also Giles et al. 2012 andMartin et al. 2014). (iii) Stratification and mixing changes along continental slopes, which deepens the halocline and lengthens the gyre spin-up time [Manucharyan andIsachsen, 2019, Manucharyan andSpall, 2016].

In particular, the Beaufort Gyre circulation has strengthened (become more anticyclonic) and expanded as the liquid freshwater has accumulated over the last 30 years [Fukumori et al., 2021a]. This strengthening is associated with stronger sea level air pressure (SLP) over the western Arctic [Proshutinsky and Johnson, 1997]. Weak Beaufort Gyre circulation events (and weak sea SLP) have also occurred, however, for example in 1989 [Haine et al., 2015]. Modulating the Beaufort Gyre strength by varying the western Arctic wind field (i.e., SLP) triggers large flushing of Arctic freshwater to the SPNA both east and west of Greenland, at least in model experiments [Stewart andHaine, 2013, Zhang et al., 2021]. Therefore, concern exists that the Arctic Ocean is primed to release freshwater to the SPNA, either in flushing events or as a steadily freshening stream. In summary: Observations show freshwater accumulating in the Arctic Ocean in the last few decades. Coupled climate models attribute this freshwater accumulation to anthropogenic forcing. Although understanding of the mechanisms responsible for the accumulation is incomplete, evidence suggests that a shift in Arctic Ocean winds could trigger a flushing of this freshwater into the North Atlantic.

Sub-polar North Atlantic freshwater variations and mechanisms

Observations show large-scale freshening events in the SPNA on decadal time scales. For example, Fig. 2 shows the liquid freshwater content for the SPNA since 1950 from hydrographic climatologies and the ECCOv4r3 dynamically-consistent state estimate (see Methods section (a)). The liquid freshwater content estimates broadly agree and show decade-long freshening events starting around 1965, 1980, and 2010. These events have been called "Great Salinity Anomalies" (GSAs) [Belkin, 2004, Belkin et al., 1998, Biló et al., 2022, Dickson et al., 1988]. They involve changes in liquid freshwater content of around 10,000km 3 , which is similar to the changes seen in the Arctic freshwater reservoirs in Fig. 1. GSAs appear to be a natural mode of Arctic/Atlantic Ocean variability that have occurred for at least the last century [Dooley et al., 1984, Sundby and Drinkwater, 2007, Zhang and Vallis, 2006] Fig. 2 also shows the average salinity in the upper 200m in the eastern SPNA over the last 30 years (see the purple boxes in Fig. 3 for the definition of the region). The data come from the EN4 observational climatology (Methods section (b)) and the ECCOv4r4 state estimate. Again, the data and state estimate broadly agree at interannual periods. The increase in liquid freshwater content for the whole SPNA centered on 2012 appears in the upper 200m eastern SPNA as a shift from a salty anomaly in 2008 to a fresh anomaly in 2016 with a salinity change of around 0.2g/kg. Indeed, Holliday et al. [2020] call 2014-2017 the largest freshening event in the eastern SPNA in the last 120 years.

The cause(s) of the 2016 fresh event (and of the 2008 saline event) are elucidated by the salinity and sea level observations in Fig. 3. The red sea level contours show the North Atlantic Current (NAC) path in the SPNA for the two years prior to the salinity anomalies (i.e., 2006-2007 and 2014-2015). Specifically, compare the red contours in the purple boxes in Fig. 3 for each period. In the two years prior to the 2008 saline anomaly the NAC extended further to the west, shrinking the sub-polar gyre and allowing saline subtropical water to enter the eastern SPNA. In the two years prior to the 2016 fresh anomaly the NAC extended further to the east, expanding the subpolar gyre and allowing fresh sub-polar water to enter the eastern SPNA. In other words, the upstream routing of saline subtropical or fresh sub-polar water determines the eastern SPNA salinity anomalies. The processes controlling eastern SPNA temperature anomalies are consistent: 2008 was a warm event, whereas 2016 was a cool event [Piecuch et al., 2017, Tesdal andHaine, 2020]. This argument is an example of a proximate mechanism to modulate the salinity in the eastern SPNA. Several ultimate causes for the salinity anomalies have been proposed in the literature. They include:

(i) The export of freshwater from the Arctic as sea ice and liquid freshwater via the Fram and Davis Straits to the western SPNA [Sundby andDrinkwater, 2007, Zhang et al., 2021]. The fresh anomalies then propagate to the eastern SPNA in the NAC. For example, Holliday et al. [2020] explain the 2016 fresh event as the rerouting of the Arctic-sourced Labrador Current water in the upper 200m into the northern branch of the NAC. (ii) Relatedly, saline events are attributed to anomalous salt transport from the subtropical gyre via the NAC [Holliday, 2003, Häkkinen et al., 2011, Tesdal and Haine, 2020, Thierry et al., 2008, Yeager et al., 2012, Zhang and Vallis, 2006]. (iii) Air/sea interaction in the SPNA. For example, Josey and Marsh [2005] argue that the freshening from 1960-2000 can be largely explained by changes in the air-sea freshwater exchange, mainly increased precipitation.

A natural and revealing complement to the Eulerian analyses in Figs. There are 17% more particles from the SPNA in the 2016 event (meaning an increase from 27.0% of all particles to 31.5% of all particles, see Fig. 4, which is a 17% increase). There are 7% fewer from the subtropics, and 27% more from the Arctic (9% more come from the Arctic, CAA, and Nordic Seas combined).

In other words, before the 2016 fresh event: water resided longer in the SPNA being freshened by air/sea interaction, less saline water came from the subtropics, and more freshwater came from the Arctic. These results are consistent with all of the mechanisms identified above.

Some potential mechanisms are considered to be less important. One example is anthropogenic loss of the Greenland Ice Sheet (GIS), which has not yet led to detectable SPNA freshening [ Böning et al., 2016, Stolzenberger et al., 2022]. Nevertheless, uncertainty exists on the fate of GIS meltwater because it depends on circulation model resolution and how the GIS discharge is parametrized [Marson et al., 2021, Schulz et al., 2022, Stolzenberger et al., 2022]. These processes are not accurately represented in the ECCOv4r4 state estimate.

Finally, other studies emphasize dynamical mechanisms controlling eastern SPNA salinity. Wind and buoyancy fluctuations influence the circulation, especially on interannual and decadal timescales, respectively [Biastoch et al., 2008, Jackson et al., 2022, Kostov et al., 2021, Yeager and Danabasoglu, 2014]. For example, when the North Atlantic Oscillation (NAO) is positive, anomalous mid-latitude westerly winds drive an expanded sub-polar gyre and fresh anomalies in the eastern SPNA, as in 2016 (Fig. 3; Weijer et al. 2022). Conversely, when the NAO is negative, the sub-polar gyre contracts and saline anomalies occupy the eastern SPNA, as in 2008.

In summary: Observations show decadal, upper-ocean, propagating salinity variations in the SPNA since 1950. The salinity variations involve shifts in the NAC and expansion/contraction of the sub-polar gyre in the eastern SPNA. Understanding of the ultimate causes of the salinity variations is incomplete. Nevertheless, the leading candidate mechanisms are: changes in salt transport from the subtropics and the Arctic, changes in the AMOC, and changes in SPNA precipitation. These mechanisms are typically associated with changes in SPNA winds, especially the NAO.

Sub-polar North Atlantic AMOC variations

The AMOC has also been implicated in SPNA salinity anomalies. Observations show the SPNA AMOC fluctuates on interannual to decadal periods. For example, it strengthened between 1980 and the mid 1990s, then weakened to the 2010s, and is now possibly strengthening again [Desbruyères et al., 2019, Jackson et al., 2022]. These variations are attributed to atmospheric forcing, especially the winter NAO [Biastoch et al., 2008, Yeager andDanabasoglu, 2014]. The variations broadly coincide with the fluctuations seen in Figs. 2 and3. Indeed, Bryden et al. [2020] estimate that the eastern SPNA freshening from 2008-2016 is consistent with the weakening of the 26 o N AMOC freshwater flux to the SPNA from 2009-2016. Robson et al. [2016] found support for this idea in a coupled climate model.

Other studies emphasize the importance of the horizontal gyre circulation, instead of the AMOC, in controlling interannual to decadal SPNA variations. For example, Piecuch et al. [2017] find in ECCOv4r3 that horizontal gyre circulation anomalies across the southern boundary of the SPNA mainly determine 1992-2015 SPNA heat content anomalies. Tesdal and Haine [2020] reach the same conclusion for SPNA LFC anomalies. Both these studies consider anomalies for the entire, full-depth SPNA, however, integrating from the sea-surface to the sea-floor. How this picture depends on different choices of control volume is unclear, however. For example, the salinity changes in the upper 200m of the eastern SPNA seen in Fig. 2 may depend less on anomalies inherited from the subtropics (either from horizontal gyre circulation or AMOC changes). Moreover, Holliday et al. [2018] use transbasin SPNA hydrographic sections to show that high heat flux associates with high AMOC strength, whereas high freshwater flux associates with high gyre circulation. Reconciling these divergent viewpoints is an important challenge.

Looking ahead to 2100, the AMOC is projected to decline in almost all coupled climate models as a result of anthropogenic forcing [Cheng et al., 2013, Weijer et al., 2020].foot_0 Moreover, the AMOC may weaken irreversibly, meaning that the circulation system crosses a threshold (or tipping point) that leads to a non-linear, abrupt slowdown [Weijer et al., 2019]. This possibility is deemed to have low likelihood [IPCC, 2021, Lohmann andDitlevsen, 2021], but the impacts on humankind would be large [Armstrong McKay et al., 2022, Lenton et al., 2019]. Despite the possibility of such forced signals, the observed AMOC variations mentioned above are probably natural [Fu et al., 2020, Latif et al., 2022]. In other words, the anthropogenic forced AMOC signal has not yet emerged from the noise of natural variability. In summary: Variations in both the AMOC and the horizontal gyre circulation have been implicated in SPNA salinity variations, based on evidence from both observations and models. Yet, inconsistencies remain, for example, to do with the importance of different circulation changes for different aspects of SPNA salinity. Although coupled climate models project AMOC weakening in the 21st century under anthropogenic climate change, the SPNA changes seen to date are probably natural.

Arctic/sub-polar North Atlantic salt exchanges

Another useful perspective on the impact of Arctic freshwater export on the AMOC is the net exchange of salt between the Arctic and SPNA. Therefore, we examine this exchange in Fig. 5 using new results from ECCOv4r4 for 1992-2017. The SPNA is defined as the region between 45 and 65 o N and the Arctic is defined as north of 65 o N (i.e., it includes the Nordic Seas and CAA). In both cases, only the upper 200m of the water column is included. Fig. 5 shows the cumulative (time-integrated) contribution of various processes to the change in the total mass of salt in these reservoirs (see Methods section (d)). These processes are: advection across the faces of the reservoir, diffusion across the faces, and exchange with sea ice due to melting and freezing (sea ice has a salinity around 4g/kg). Note that there is no air/sea exchange of salt.

For the Arctic, Nordic Seas, and CAA, Fig. 5 shows that diffusion increases the salt content (because the water deeper than 200m is salty). Advection decreases the salt content (because the seawater outflow exceeds the seawater inflow by the water flux received from the atmosphere and land). Sea ice exchange also decreases the salt content (because, overall, the region exports salt in sea ice). Salt exchanges due to advection and sea ice have seasonal cycles. The effect on the total salt content is a decreasing trend over 1992-2017, which is due to an overall imbalance between sea ice, advection, and diffusion. 2 The total loss is about 0.35 ⇥ 10 15 kg. This salt mass corresponds to an increase of about 10,000km (assuming, reasonably, that the reservoir volume is constant). Thus, it is broadly consistent with the LFC increase discussed in section 2.

For the SPNA, Fig. 5 shows that diffusion increases salt content and advection decreases it; again, the main salt balance is between these two terms. Sea ice is a weak factor for the SPNA and no long-term trend is visible for the total salt content in Fig. 5.

Interannual variations in the total salt content exist for both the Arctic and, especially, the SPNA in Fig. 5. These variations are shown in detail in Fig. 6, which shows the same timeseries with linear trends removed. For the Arctic, Nordic Seas, and CAA, the variations have a magnitude of around 10 14 kg (corresponding to LFC variations of around 3000km 3 ). These variations are closely associated with variations in advection. For the SPNA, the variations have a similar magnitude, but they are associated with variations in both advection and diffusion. Salt content anomalies due to diffusion lead those due to advection, at least for the single fresh-to-salty-to-fresh cycle in ECCOv4r4 over 1992-2017.

The interannual SPNA salt content variations in Fig. 6 resemble the LFC variations seen in Fig. 2. The salt content minima in 1994 and 2016 correspond to the SPNA freshening events discussed in section 3. Fig. 6 shows that these freshening events were mainly associated with declining advection in ECCOv4r4. Diffusion counteracts them, but is weaker.

The contribution of advection to the SPNA salt anomalies in Fig. 6 is the sum of horizontal exchange across the two boundaries at 45 o N and 65 o N, and vertical exchange across 200m. Of these terms, the advective flux across 45 o N is relatively large and is strongly anti-correlated with advective flux across 200m (they nearly sum to zero; not shown). That means salt anomalies enter the SPNA control volume from the south, and mainly leave it by sinking across 200m. This exchange resembles the AMOC in the SPNA. In contrast, advective salt flux anomalies across 65 o N are relatively smaller, by a factor of about four. The sum of the advective fluxes across 45 o N, 65 o N, and 200m (red line in Fig. 6) is relatively small compared to these individual advective terms. For the diffusive salt flux anomalies in Fig. 6 (green line), the flux across 200m dominates.

Hence, for upper 200m SPNA ECCOv4r4 salt anomalies, Arctic/SPNA salt exchange is an important (although subdominant) process alongside vertical exchange and horizontal exchange from the south. The role of the Arctic decreasing salt content trend seen in Fig. 5 (upper panel, black line) on the SPNA is unclear, however. Further study of the advective exchange across 65 o N is required to elucidate it, such as decomposing the net 65 o N flux into southbound Arctic salt import into the SPNA, and northbound export.

Summary, open questions, and discussion

On the evidence from the published studies summarized above, and from the new results that provide a holistic context, the state of knowledge on freshwater variations in the Arctic and SPNA is as follows:

• Interannual Arctic freshwater fluctuations clearly exist, which appear to be natural. In addition, a decadal freshening trend exists, which appears to be anthropogenic. • Arctic Ocean freshwater export to the SPNA is known to fluctuate naturally on interannual periods with several export anomalies thought to have occurred in the last 50-100 years. • Interannual SPNA freshwater fluctuations (GSAs) clearly exist. They appear to be natural (not forced by anthropogenic effects), with no sign yet of a decadal freshening trend from the north. SPNA fresh anomalies seem to involve longer SPNA residence times, more Arctic water, and less subtropical water. Fluctuations in SPNA air/sea interaction and the AMOC are potentially important too. But the relative roles of these different processes, and their ultimate causes are still obscure. • Climate model projections suggest that Arctic freshwater accumulation will continue, and Arctic freshwater export fluxes will increase in the 21st century, which will freshen the SPNA. Projections suggest that the anthropogenic freshening signal will emerge in the 2020s (Davis Strait, freshwater flux; Fram Strait ratio of liquid to solid freshwater fluxes). • Climate model projections suggest that in the 21st century the SPNA AMOC will weaken. There is a low-likelihood, high-impact possibility that the AMOC will weaken irreversibly.

In the light of this knowledge, some leading open questions are:foot_3 (i) When will Arctic anthropogenic freshening be detected in the SPNA? (ii) What is the fingerprint of Arctic anthropogenic freshening in the SPNA and how will it be detected in the SPNA with the current observing network (if at all)? (iii) When will Arctic anthropogenic freshening affect SPNA circulation? (iv) What is the fingerprint of this circulation change and how will it be detected with the current observing network (if at all)?

To answer these questions on SPNA anthropogenic freshening we require improved understanding of the mechanisms of SPNA salinity variability. Mechanistic understanding is essential to distinguish natural from anthropogenic variations (among several reasons), and to thus characterize the fingerprints of anthropogenic freshening. We hypothesize the following sequence of events: (a) The first Arctic anthropogenic SPNA freshening signals to emerge will be of small amplitude and therefore dynamically passive (not affect the circulation, namely a kinematic mechanism). (b) Dynamically-active Arctic SPNA anthropogenic freshening signals will follow and will weaken the AMOC. As the initial dynamical freshening effects will be of small amplitude, they will affect the AMOC in a linear and, therefore reversible, way. (c) Any subsequent large amplitude Arctic SPNA anthropogenic freshening signals increase the risk of a non-linear irreversible AMOC weakening. The implications of SPNA freshening on the AMOC in steps (b) and (c) also need to be better understood, especially as they pertain to climate impacts.

It is important to recognize that the SPNA may freshen due to anthropogenic effects that are unrelated to Arctic Ocean freshwater export, such as forced Greenland Ice Sheet melt [Luo et al., 2016] or forced changes to the NAO [Kim et al., 2021] or changes associated with anthropogenic aerosols [Booth et al., 2012]. It remains to be established if the AMOC weakening in (b) will be detectable with the present or future observing network (we know of no studies on this question). It is also possible that the AMOC will weaken for reasons other than an Arctic SPNA anthropogenic freshening signal.

To address the open questions (i)-(iv) the community should:

• Maintain the current observing network, such as the Arctic and SPNA hydrographic measurements and gateway flux observatories. 4 No alternative method is known to observe the freshening signals. • Expedite data dissemination, analysis, and synthesis. In some cases, years have passed before data from in-situ instruments have been processed and made public. Support is needed to facilitate and accelerate this pipeline. • Extend and refine dynamically-consistent reanalyses, such as ECCOv4r4. These state estimates are our best (albeit imperfect and provisional) tools to track and understand the basin-scale, decadal stratification and circulation changes. • Study and refine coupled climate models to resolve Arctic Ocean biases, especially in the Atlantic Water, the halocline, and the surface Polar Water layer, and thereby decrease the model spread in projected salinity changes [Khosravi et al., 2022, Shu et al., 2023]. • Perform consistent, robust budget analyses (like those in Figs. 2,5,6). Some past studies have been plagued by ambiguities surrounding reference salinities [Bacon et al., 2015, Schauer andLosch, 2019]. Robust interpretation methods are now known, however, (for example, Tsubouchi et al. 2018); and should be universally adopted. Moreover, the sensitivity of budget analyses to choice of variable (LFC, salt), control volume (full-depth, upper ocean; whole SPNA, eastern SPNA), and data source (state estimates, circulation models) should be explored. • Observe and understand SPNA freshwater dispersion. In particular, the processes controlling transport of Arctic freshwater off the Greenland and Canadian shelves into the deep SPNA occur at small space-time scales and are poorly observed, modelled, and understood [Stolzenberger et al., 2022, Vellinga et al., 2008]. • Characterize the fingerprint of Arctic anthropogenic freshening in the SPNA and recommend strategies to observe it. An unprecedented opportunity exists to anticipate and observe fresh anomalies move through the system [Haine, 2021].

The aim of these activities is to elucidate the spread of Arctic anthropogenic freshening into the SPNA. They will establish the plausibility of the Arctic freshwater export process as an agent to change the SPNA, the AMOC, and thereby contribute to the wider debate on SPNA anthropogenic change.

profilers [Toole et al., 2011] and the Argo program are particularly valuable. The Overturning in the Subpolar North Atlantic Program (OSNAP) is important for SPNA fluxes and hydrographic changes [Li et al., 2021] . For a comprehensive framework to observe the Arctic Ocean, see Lee et al. [2019]. For a comprehensive list of observations used to constrain ECCOv4r4, see Fukumori et al. [2023Fukumori et al. [ , 2021b]]; Nguyen et al. [2021] is also useful.

Methods (a) ECCO Ocean state estimate

The Estimating the Circulation and Climate of the Ocean (ECCO) state estimate is a solution to the Massachusetts Institute of Technology general circulation model (MITgcm; Marshall et al. 1997). The solution is computed by fitting the MITgcm fields to several hundred million satellite (altimetry, sea surface temperature, sea surface salinity, gravimetry) and in-situ (temperature, salinity) ocean observations for the period of satellite altimetry [Forget et al., 2015, Wunsch and Heimbach, 2007, Wunsch et al., 2009]. To produce the state estimate, the surface forcing, initial conditions, and mixing coefficients are adjusted within their respective uncertainties. As the state estimate is a data-constrained solution to the free-running MITgcm, the solution is dynamicallyconsistent and it avoids unphysical nudges. Thus, closed, physically-realistic salt budgets can by computed, such as in Figs. 5 and 6. In this paper, we use ECCO version 4 release 4 (ECCOv4r4, Fukumori et al. 2023Fukumori et al. , 2018Fukumori et al. , 2021b)). The ECCOv4r4 solution is global and spans 1992-2017. The horizontal resolution is 1 o and there are 50 vertical levels whose thicknesses range between 10m near the surface and 450m near the bottom.

(b) Ocean reanalysis: EN4

EN4 is a gridded global dataset for ocean temperature and salinity compiled by the United Kingdom Met Office (Good et al. 2013; this paper also explains the origin of the "EN4" name).

It spans the period 1900-present with quality control checks and bias removal corrections applied following Gouretski and Reseghetti [2010]. We use EN.4.2.2 for our analysis. where Gauss' theorem has been applied to the divergent terms in (6.1) and the ? subscript indicates the component perpendicular to surface A. Integrating over time yields the mass of salt, M S (t):

where ⇢ 0 is the reference density of seawater. The four terms in this equation are called "total", "advection", "diffusion," and "sea ice" in Figs. 5 and 6.