Numerical simulations are run using a global configuration of the Nucleus for European Modelling of the Ocean NEMO; ocean model, which is coupled to the Los Alamos Sea-Ice Model CICE;. We use the model's ORCA1 configuration, which has a horizontal resolution of 1∘ (approximately 73 km) and 75 vertical levels, where the thickness increases vertically, from 1 m at the surface to 200 m at depth. We chose not to use a higher-resolution version because of the heavy computational requirements of the simulations. More complete descriptions of ORCA1 and a comparison of its performance with configurations with different horizontal resolutions can be found in and . ORCA1 also makes up the physical ocean component of the coupled UK Earth system model (UKESM1), contributing to Phase 6 of the Coupled Model Intercomparison Project (CMIP6), as described in .

This model configuration involves a vertical mixing scheme based on the turbulent kinetic energy model of , along with Redi isoneutral mixing with a diffusivity of 1000 m2s-1 and eddy parameterisation with a coefficient dependent on the local Rossby radius and Eady growth rate . Temperature, salinity, and tracers are advected by a second-order, two-step monotonic-flux-corrected scheme (FCT; ), which is the standard scheme used in current low-resolution NEMO models UKESM1; e.g.. The numerical mixing associated with this scheme may lead to an overestimate of Antarctic Bottom Water (AABW) production compared with more accurate but expensive advection schemes, such as the second-order-moment scheme , although this scheme is not implemented in NEMO.

Our ocean–ice simulation is forced with the JRA55-do surface atmospheric dataset that is based on the Japanese 55-year Reanalysis JRA-55;, and it is spun up following the Ocean Model Intercomparison Project (OMIP) protocol , which recommends running five cycles of the atmospheric forcing, starting from a motionless ocean state with climatological temperature and salinity distribution. Each cycle lasts 60 years (the length of the available atmospheric forcing for the version of JRA-55 used, from 1958 to 2017), and our diagnosis focuses on the last (fifth cycle), with the previous four cycles (240 years) used for spin-up. This OMIP protocol allows for meaningful comparison between different models e.g., although there may still be drifts in many ocean properties . All physical variables and those for the dye tracers are output and stored as monthly means.

Our model configuration gives an average AMOC (maximum in the overturning streamfunction at 1000 m at 26∘ N) of ∼12 Sv (where 1Sv=106 m3s-1) in the last 60 years (1958–2017) of the spin-up, which is lower than the latest observation-based estimates from the RAPID array at 26.5∘ N 17–20 Sv; but is not uncommon given the relatively coarse horizontal resolution of the model e.g.. The average transport through Drake Passage is also weaker (∼115 Sv) than the observation-based estimates of 173±11 Sv . Both the average AMOC and Drake Passage transport are weaker in our ocean-only simulation than in the coupled UKESM1 version of the model .

The representation of the mixed layer in the model is of particular interest for our analysis, given its key role in driving ocean ventilation . Therefore, we compare this simulated quantity from the NEMO output with the objectively analysed EN4 dataset and an optimally interpolated Argo dataset . For all datasets and for the 2004–2017 time period, the maximum mixed-layer depth (Fig. 1) is calculated at each grid point, using a variable density threshold associated with a 0.2 ∘C decrease in temperature, and representing the depth of the base of the winter mixed layer, as defined in .

The model reproduces the deep winter mixed layers both in the North Atlantic subpolar gyre and in the Sub-Antarctic Mode Water formation regions, as well as along the Antarctic coast (Fig. 1a); the latter is not captured in the EN4 and Argo datasets (Fig. 1b–d) due to limited observational capability under ice. However, it is known that the NEMO model is characterised by excessively strong convection in the Labrador and Irminger seas, down to depths that are much higher than what is measured in observations (Fig. 1c), even at higher horizontal resolutions , and overproduction of Labrador Sea Water is also found in other 1∘ ocean–ice models when compared with observations . This results in some overestimation in the mixed-layer depth in the North Atlantic subpolar gyre, but globally the model shows good agreement with observations; deep mixed layers can also be observed along the pathway of the Gulf Stream and Kuroshio Current, both in the model and in the observations, although in the Atlantic between ∼40 and 60∘ N, the simulated mixed layer is largely shallower than in the observations (Fig. 1c).

Anthropogenic transient tracers such as CFCs are often used for model validation and to evaluate ocean ventilation . These remain inert when absorbed by the ocean from the atmosphere, and due to their passive nature, they can be thought of as dye tracers. CFC-11, CFC-12, and SF-6 tracers are included in our simulations, and we show a comparison of their concentration along a mid-Atlantic section (Fig. 2) that will be used in the rest of the analysis. The tracers are implemented following the OMIP protocol and have also been used for the evaluation of the coupled UKESM1 simulation . The CFC-11 distribution in our simulations compares favourably to observations from the Global Ocean Data Analysis Project GLODAPv2.2020; along the WOCE/GO-SHIP A16 section (from occupations in 2003, 2005, 2013, and 2014; cruises 342, 343, 1041, and 1042) in the Atlantic Ocean (Fig. 2). The A16 section crosses the Atlantic from south of Iceland to the Southern Ocean and covers the eastern part of the basin in the Northern Hemisphere and the western side in the Southern Hemisphere, whereas the section in the model is taken in the central part of the basin at 25∘ W. Both in the model and in the observations, the highest concentrations can be found at high latitudes in both hemispheres, where CFC-11 has spread into the ocean's interior, especially in the subpolar North Atlantic (below 2000 m). The model also appears to be capturing the penetration of the tracer at depth in the Southern Hemisphere (below 4000 m), even though the concentrations are much lower in the model in this study than in the observations. The tracer also penetrates down to ∼2000 m around the Equator in the observations (Fig. 2b), but this is not captured in the simulation.

It is also worth noting that there are large differences in the simulation of the magnitude and variability of the (A)MOC in numerical models, both at lower and higher resolutions e.g.. There are also substantial discrepancies in simulating the mixed-layer depth, especially in high-latitude regions, and in the representation of water masses, as clearly shown for Labrador Sea Water . Climate models are also known to struggle with the representation of dense-water formation in the Southern Ocean, especially at lower resolutions , which will have an impact on the rates and dynamics of ventilation.

In this study, we aim to resolve the pathways and the inventories of ventilated waters after they leave the mixed layer. This is achieved by using a set of annually distinct dye tracers that are introduced in each year of the last (fifth) cycle through the surface forcing, meaning that the effective model spin-up is 240 years and the simulation with passive tracers is 60 years, which is the length of the available atmospheric forcing for the version of JRA-55 used (from 1958 to 2017).

In these simulations, the dye tracers are released uniformly across the global ocean, with a 6-month hemispheric offset, as tracer injection starts during the summer in each hemisphere (i.e. starts in January and ends in December in the Southern Hemisphere and starts in July and ends in June in the Northern Hemisphere). A transition zone is introduced between 20∘ N and 20∘ S, where the start and end of the release year increase day by day linearly moving northwards – i.e. the release year at a given latitude begins on the year day-number (days from 1 January) that increases linearly between 20∘ S and 20∘ N from 0 to 181 (the number of days between 1 January and 1 July), and the end of the release year is determined in a similar fashion.

Each dye tracer is injected throughout its release year (its “vintage”) by relaxing the tracer's concentration to a value of 1 throughout the top seven vertical levels (down to ∼10 m). The relaxation time is Tr=Tr01-ai, where Tr0=7200 s (the leapfrog time step) is the smallest relaxation time that still remains stable. To represent the ability of ice cover to insulate the ocean from air–sea gas exchange, the relaxation time is increased by the reciprocal of the water fraction 1-ai, where ai is the ice fraction. With the depth interval of 10 m, this implies a piston velocity of 1.39×10-3 ms-1, (120 md-1) without ice (much faster than a typical gas exchange piston velocity of 2.4 md-1), ranging down to a velocity of 2.4 md-1 in regions of maximum ice cover with ai=0.02. After injection into the interior, each tracer continues to propagate through the ocean, driven by advective and diffusive components of the simulated circulation. After its release year, each tracer is relaxed back to zero in the upper 10 m, resulting in a systematic loss of the globally integrated tracer inventory over the simulation. This is presented schematically in Fig. 3, where dye N is only injected in release (vintage) year N, whereas dye N+1 only starts being injected in release year N+1, and so on for the following years (from N+2 to N+59).

For the analysis presented in Sect. 3, we use a subset of dyes, injected in 1958 to 1993, so that we can follow their evolution from the year of injection and for 25 years of simulation for each one of the 36 vintages, allowing us to investigate the role of interannual variability and pathways from annual to multidecadal timescales. Note that the comparison of these simulated dye tracers to observed CFCs distributions (see Fig. 2) is not straightforward. While the CFCs' source behaves like a step function, our vintage tracers are best represented by a top-hat/delta function, so it is the sum of the concentration of all of the different vintage tracers that could be compared with CFCs.

The dye concentration, c, at any point (or in the model, in a grid box) represents the fraction of water at that point that was exposed to the surface in the dye's release winter (vintage). The natural unit for the dye concentration is, therefore, dimensionless (a fraction, so 0<c<1). Hence, the total globally integrated inventory of dye Cglobal=∭cdV represents the total volume of water exposed to the surface in the release year. Similarly, the “ventilation thickness” C(ϕ,λ)=∫cdz (where ϕ and λ are latitude and longitude) represents the volume of such ventilated waters per unit area and has dimensions of depth (m), even though it is not a physical depth but the column integral of the tracer. This metric can be thought of as the depth of a notional layer in which the vertically integrated inventory is concentrated with a dye concentration of c=1. In the first year, this represents the mixed-layer depth as c≈1 in the mixed layer and c≈0 below it. We find it useful to define globally (and hemispherically) averaged ventilation thicknesses that relate to the globally and hemispherically integrated inventories. In subsequent years, this ventilation thickness progressively decreases as the dye re-enters the mixed layer and is lost (set to zero).

The dye inventory evolves differently over time in each basin, and most of it can be found in the Atlantic on the timescales that we are examining, despite the substantially smaller volume of the Atlantic than the Indo-Pacific (Fig. 4). Over 60 years, the percentage of the global inventory held in the Atlantic increases. This is because the dye penetrates more deeply in the Atlantic, reaching depths where it is unable to re-enter the surface mixed layer, whereas the penetration into the deep Southern and Pacific oceans is less marked (Fig. 5a, b). This may not be fully realistic; as previously discussed, models are known to struggle with the representation of dense-water formation in the Southern Ocean, especially at the coarse resolution of this simulation, which may explain the low concentrations (and relatively small inventory) of tracer in the deep Southern Ocean (Figs. 4, 5).

Within 60 years (the end of the simulation), the core of the dye in the Atlantic has reached the deep ocean (down to ∼3000 m) between 20 and 50∘ N, while it has spread to ∼40∘ S in the top 1000 m (Fig. 5a). Looking at the dye distribution as a function of depth clearly indicates how important the Atlantic is for ventilating the deep ocean, especially on these timescales (Fig. 5b). The latitudinal distribution of the dye (Fig. 5c) illustrates the importance of the subtropical gyres, which on these timescales (60 years after injection) hold most of the dye concentration, especially in the Northern Hemisphere, with the North Atlantic clearly dominating the global zonal average.

In our set-up (see Fig. 3), we can also analyse the evolution of dyes injected in each year (vintages) separately. This can be effectively displayed using the “ventilation thickness” metric, as defined in Sect. 2.4 (Fig. 6). For each year, the dye concentration peaks during the winter in each hemisphere (where it is injected), and the ventilation thickness in the year of injection is always higher in the Southern Hemisphere (Fig. 6c). In each hemisphere, the interannual differences between each of the dyes largely derives from changes in the background ocean circulation and the effect of surface forcing on the mixed-layer depth at the time of injection, as the dyes are independent of each other and identify different seawater vintages for each year. After the first year of dye injection, the interannual variability in the peak in ventilation thickness between the different vintages mostly reflects the variability in mixed-layer depth in different years, driven by the surface forcing (Fig. 6).

Globally, during the first year when the dye is injected, the highest tracer concentrations can be seen in regions that correspond to the deepest mixed layers (see Fig. 1a), such as the subpolar North Atlantic near the locations of deep-water formation from the Labrador and Irminger seas to the Nordic Seas, as well as along the paths of the Gulf Stream and Kuroshio and in the Mediterranean Sea (Fig. 7a). Strong dye uptake can also be seen in the Sub-Antarctic Mode Water (SAMW) formation regions in the Southern Hemisphere and along the Antarctic coast and in the Weddell Sea, where dense water is formed (Fig. 7a). For the rest of the analysis, the main focus will remain on two chosen timescales, of 3 and 25 years, by using a subset of the dye tracers (as introduced in Sect. 2.3). Three years after injection, the vintages represent seawater that has moved below the base of the mixed later and been subducted, whereas after 25 years, they correspond to water that has flowed out of the upper ocean. Three years after injection, the dye is spreading prominently in the North Atlantic subpolar gyre (Fig. 7b); after 25 years, it has reached the entire basin and has also starting to spread southward along the western boundary (Fig. 7c). It is, however, worth remembering that boundary currents are not particularly well-represented at 1∘ horizontal resolution, which will affect the dye distribution e.g.. In the Southern Hemisphere, the uptake of dye can still be clearly identified in the SAMW formation regions after 3 and 25 years (Fig. 7b, c). Concentrations in the Arctic are likely too high (Fig. 7b and c), possibly as an artefact due to the model's resolution, meaning that the dye accumulates in this region due to restrictions in the flow through bathymetric features that are poorly represented at 1∘. However, these concentrations decrease over time, as the dye excess is slowly being ventilated out of the basin (not shown), which has a relatively small volume and a small contribution to the global inventory (see Fig. 4).

By using a subset of dyes, from 1958 to 1993, we can follow their evolution from the year of dye injection and for 25 years of simulation for each of the 36 vintages. Looking at the evolution of the dyes as the anomaly from the mean ventilation thickness (for the 1958–1993 time period) highlights the differences between the independent vintages that are due to interannual variability (Fig. 8). The strongest differences from the mean (up to ∼10 m in the Southern Hemisphere) develop within the first 3 years, but these reduce substantially or at least stabilise by 3 years after injection in both hemispheres. However, after 3 years of the simulation, the differences remain relatively large in the Northern Hemisphere (Fig. 8a), whereas they fall off in the Southern Hemisphere (Fig. 8b). After 25 years, the ventilation thickness still varies by up to ±3 m between vintages in the Northern Hemisphere, whereas differences decrease to within ∼±1.5 m in the Southern Hemisphere (Fig. 8). Positive anomalies (i.e. ventilation thickness higher than the mean) characterise the later years/vintages (1980s/1990s) in the Northern Hemisphere, whereas the opposite is observed in the Southern Hemisphere, where this is the case for earlier years (1960s); similar behaviour is noted for the negative anomalies (Fig. 8).

For all vintages, the absolute ventilation thickness is higher in the Southern Hemisphere after 3 years than in the Northern Hemisphere (Fig. 9). Vintages with a ventilation thickness that is higher than the mean are not necessarily the same in both hemispheres, representing the different responses to the surface forcing and the background circulation (e.g. stratification) and the local processes at play. On this timescale, the vintages represent seawater that has been subducted after injection and has then moved below the base of the mixed later. In the Northern Hemisphere, the vintages from the early 1990s have relatively high values (Fig. 9a), which correspond to years of observed strong convection in the Labrador Sea e.g.. Values in the Northern Hemisphere are actually above or very close to the mean for the entire period from the early 1980s to the early 1990s, whereas in the Southern Hemisphere, ventilation thicknesses higher than the mean can mainly be seen for the earlier period until the late 1970s (Fig. 9a). Even though the mean hemispheric ventilation thickness values are much closer to one another 25 years after injection, the early 1990s vintages in the Northern Hemisphere are now the highest, as well as those for the early 1980s (Fig. 9b), which also stood out at the 3-year timescale. This suggests that the response after 25 years, when the vintages represent water that has now flowed out of the upper ocean, is still strongly affected by the processes shaping the mixed layer at the time of dye injection and for the subsequent 2–3 years.

To further investigate this apparent link between the processes affecting subduction close to the time of dye injection and over the following 2 decades, we correlate the ventilation thickness for the two timescales of 3 and 25 years (Fig. 10). These show a high correlation (R2≥0.7) for both hemispheres, which confirms that the conditions close to the time of injection (i.e. mixed-layer depth and background circulation) are driving the amount of seawater being subducted, but also that this signal persists over time and that its inventory over 25 years is strongly related to that initial forcing.

Ventilation in the Northern Hemisphere appears to be twice as persistent as in the Southern Hemisphere (see the slope for the correlations in Fig. 10a and c), which could be thought of as a rate of erosion of the ventilated water masses. This means that subducted waters are exported (and isolated) away from deep mixed-layer regions faster in the Northern Hemisphere than the Southern Hemisphere. The residuals of the correlations (Fig. 10a, c) also highlight some of the longer-term variability, particularly in the Northern Hemisphere, where the residuals for the “later” vintages corresponding to the early 1990s appear to be rising (Fig. 10b).

Dyes that were injected in years characterised by stronger convection result in higher ventilation thickness after 3 and 25 years (Fig. 9), but this also impacts the evolution of the tracer's vertical distribution over time. This is shown for seven of the vintages (highlighted in Fig. 10) analysed so far, covering a range of higher and lower (than the respective hemispheric mean) ventilation thicknesses (Figs. 11, 12).

The vertical distribution of the tracer (Fig. 11a) is characterised by two prominent peaks, where the shallower one at around 500 m is present in all ocean basins but dominated by the inventory in the Pacific (not shown). The deeper peak below 2000 m is driven by the variability in the North Atlantic (not shown), and the highest values are in fact reached in 1992 and 1982. The strongest differences in the tracer's latitudinal distribution between different vintages develop in the Northern Hemisphere subtropical gyres (Fig. 11b) and are dominated by the North Atlantic (not shown), which can be expected on these timescales (i.e. 25 years after injection). The 1992 vintage stands out, and it corresponds to a period of strong convection in the Labrador Sea, as discussed in Sect. 3.2 and shown in Fig. 9, but 1982 and 1972 also have a relatively high peak around 40∘ N. In the Southern Hemisphere, there are smaller differences between the different vintages, but as expected (see Fig. 9a), the highest peak corresponds to the dye injected in 1962 (dominated by the signal in the Pacific; not shown).

Note that Fig. 11 a and b are equivalent to Fig. 5b and c respectively, but the different dyes are shown 25 years after injection (to allow the comparison between different vintages), whereas Fig. 5 shows the dye distribution at the end of the simulation, 60 years after dye injection.

Differences in the Atlantic are also shown along a north–south section in the centre of the basin (same as Figs. 2a and 5a) for two of the vintages 25 years after their injection (Fig. 12): one from a strong Northern Hemisphere ventilation year (1992) and one from a weak Northern Hemisphere ventilation year (1987). The tracer reaches deeper and with higher concentrations when it is injected in years characterised by strong convection in the subpolar North Atlantic (Fig. 12a), and the distribution is lower in the top ∼1000 m in both the Northern and Southern hemispheres for the year with weaker convection (Fig. 12b).

The dye uptake in the first (injection) year largely reflects the state and variability of the mixed layer during the season of active convection, which is driven by the surface forcing in that year (Figs. 1a, 7a) and the stratification in that year (“preconditioning”). Three years after injection, the amount of dye that has reached below the base of the mixed layer is also dependent on other factors, linked to both lateral mixing and the surface forcing in the years immediately following injection see also. This determines how much dye is retained, as a deepening of the mixed layer in the winter following the injection year (N+1; see Fig. 3) will ventilate a larger portion of the vintage from the previous year (N; see Fig. 3) and effectively reduce the dye concentration (due to the fact that it will be reset to zero in our set-up when ventilated). This contributes to the interannual variability on this timescale.

The correlation between dye retention after 25 years and the background conditions close to the time of injection (just after the strongest interannual differences have decreased; see Fig. 8) highlights the key role of the surface atmospheric forcing in driving long-term ocean ventilation and, more broadly, in determining the distribution of passive tracers over time (Fig. 10). As the variability in ventilation near the time of dye injection sets the long-term variability for the dye inventory, there is potential for forecasting how the distribution of a tracer in the ocean will evolve in the future, from a prior knowledge of the surface air–sea fluxes and mixed-layer properties.

Finally, the strong correlations in ventilation thickness between 3 and 25 years after injection in both the Northern and Southern hemispheres (Fig. 10; see slope of correlations) imply that, given the strong interannual variability in the initial surface forcing, it is this variability that will continue to dominate on longer timescales, largely overriding the different processes that drive how passive tracers are removed or taken up in the two hemispheres. The Northern Hemisphere is characterised by more persistent anomalies, as the ventilated waters penetrate more deeply where they are better isolated from surface influence, whereas the anomalies are initially stronger in the Southern Hemisphere (Fig. 8), but then dissipate faster than in the Northern Hemisphere, partly due to the more effective mixing along sloping isopycnals in the Southern Ocean. This means that the tracer eventually gets mixed back and ventilated even when the initial amount that is subducted is substantially higher than the mean, while the dye remains in the interior for longer in the subpolar North Atlantic once it has reached a deeper horizon (Figs. 11, 12). In other words, subducted waters are exported (and isolated) away from deep mixed-layer regions faster in the Northern Hemisphere than in the Southern Hemisphere.

The strong interannual variability that characterises ventilation in the Northern Hemisphere on these timescales (Fig. 9) is largely driven by the Irminger, Nordic, and Labrador seas (Fig. 7a, b), which are the sites of most active deep convection in the winter months e.g. and are characterised by ventilation anomalies that persist for longer than in the Southern Hemisphere (Fig. 8). In other words, anomalies near the time of dye injection in the Southern Hemisphere result in smaller longer-term changes than in the Northern Hemisphere (i.e. the “ventilation persistence” is lower).

There is coherent structure in the residuals of the correlation between Northern Hemisphere ventilation thickness close to the time of dye injection and 25 years later, and the residuals deviate from the trend (rise) for the vintages corresponding to the early 1990s (Fig. 10b). We expect that the role of surface buoyancy forcing through air–sea fluxes, as well as modes of climate variability that may affect convection in the subpolar North Atlantic (e.g. North Atlantic Oscillation – NAO – or Atlantic Multidecadal Variability – AMV) should already be captured by the correlation itself (Fig. 10a). However, these will, in turn, also affect the background circulation. We examine whether there is a relationship between the residuals and the strength of the large-scale circulation (AMOC). The hypothesis is that a stronger circulation (AMOC) might also be linked with moving water more effectively away from the ventilation site and reducing the rate at which dye is returned to the mixed layer and, thus, removed from the system. We consider the correlation between the residuals in the Northern Hemisphere and the AMOC at 26∘ N at a depth of 1000 m (to be comparable to estimates for the RAPID array; Fig. 13). There is a correlation (R2=0.45) between the residuals and the AMOC in the year of injection whereas that with the AMOC 25 years later is much weaker (R2=0.2).

The mechanism behind the connection that we find between the strength of the AMOC at 26∘ N and the residuals of the correlation for the Northern Hemisphere (Fig. 13) is not fully clear. To check this potential link further, we also correlated the AMOC in the year of injection with the absolute values for ventilation thickness after 25 years, rather than the residuals of the correlation. While both correlations are significant, the correlation of the AMOC with the residuals describes more of the variance (Fig. 13) than that with the ventilation thickness itself (R2=0.37; not shown). We also tested the correlation of the residuals with the AMOC at higher latitudes (e.g. 45∘ N; not shown); however, despite being closer to the sites of deep convection in the subpolar North Atlantic, the correlation is much weaker. It is, however, harder to assess and interpret AMOC changes at these higher latitudes, especially in depth rather than density space . There are also large differences in the simulation of the magnitude and variability of the (A)MOC across different numerical models, at both lower and higher resolutions e.g., as well as substantial discrepancies in simulating the mixed-layer depth, especially in high-latitude regions, and in the representation of water masses, as clearly shown for Labrador Sea Water . In both models and observations, the relationship between the hydrographic variability in the subpolar North Atlantic and the AMOC has also been shown to quickly deteriorate downstream of the Labrador Sea e.g..

There is also some structure in the residuals of the correlation for the Southern Hemisphere (Fig. 10d), perhaps reflecting how ventilation here appears to be stronger before the 1980s and consistently lower in the later period (Fig. 9a). This could highlight background changes in the strength of the subtropical gyres, driven by changes in the Southern Hemisphere winds, affecting SAMW formation e.g.. While there are more opportunities to test the model's performance in the Northern Hemisphere, given the richness of observations from the North Atlantic subpolar gyre, recording years of weaker and strong convection, a more prominent focus on Southern Hemisphere processes and changes in SAMW would be the desirable outcome of a future study exploiting our set-up. This could be achieved for the more recent vintages (from the 1990s onwards; only partly used here, due to the focus on the 3- to 25-year timescales and the constraints due to the length of the forced simulation). In fact, recent hydrographic observations have highlighted ventilation changes due to wind forcing and atmospheric modes , and other modelling studies have explored the different pathways followed by SAMWs and their sensitivity to wind changes , providing better estimates of their combined effect on heat and carbon uptake in the Southern Hemisphere, which could be integrated with our dye tracers.

Finally, while it would also be desirable to perform longer simulations with passive tracers and assess their uptake on centennial timescales, our results highlight how this would be problematic. In fact, a tracer's pathways, inventory, and distribution will be strongly dependent on the initial surface forcing, when the tracer enters the ocean, especially for the Northern Hemisphere (see Figs. 11, 12). This means that the cumulation of the inventory of a simulated tracer over time will provide an aliased view of its evolution. At the same time, it is currently too computationally expensive to introduce interannually varying tracers to resolve the full variability on such long timescales.