Surface atmospheric forcing as the driver of long-term pathways and timescales of ocean ventilation

. The ocean takes up 93% of the excess heat in the climate system and approximately a quarter of the anthropogenic carbon via air-sea ﬂuxes. Ocean ventilation and subduction are key processes that regulate the transport of water (and associated properties) from the surface mixed layer, which is in contact with the atmosphere, to the ocean’s interior which is isolated from the atmosphere for a timescale set by the large-scale circulation. Using numerical simulations with an ocean-sea-ice model using the NEMO framework, we assess where the ocean subducts water and thus takes up properties from the atmosphere and


Mixed layer depth
The representation of the mixed layer in the model is of particular interest for our analysis, given its key role in driving ocean 125 ventilation (Pedlosky and Robbins, 1991). Therefore, we compare this simulated quantity from the NEMO output with the objectively-analysed EN4 dataset (Good et al., 2013) and an optimally-interpolated Argo dataset (updated following Desbruyeres et al., 2017). For all datasets and for the time period 2004-2017, the maximum mixed layer depth (Figure 1) is calculated at each gridpoint, 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 (Clément et al., 2020). 130 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 ( Figure 1a) which is not captured in the EN4 and Argo datasets (Figures 1b,c,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 (Figure 1c), even at higher horizontal resolutions (MacGilchrist et al., 2020;Marzocchi 135 et al., 2015;Rattan et al., 2010) and overproduction of Labrador Sea Water is also found in other 1 • ocean-ice models when compared to observations (Li et al., 2019). 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 ∼40-60 • N the simulated mixed layer is largely shallower than in the observations (Figure 1c).

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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. Hirschi et al., 2020;Li et al., 2019). 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 (Li et al., 2019). Climate models are also known to struggle with the representation of dense water formation in the Southern Ocean, especially at lower resolutions (Heuzé et al., 2013), which will have an impact on the rates and dynamics of 145 ventilation.

Dye tracer injection
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 150 is the length of the available atmospheric forcing for the version used of JRA-55 (from 1958 to 2017).
In these simulations, the dye tracers are released uniformly across the global ocean, with a 6-month hemispheric offset, given latitude begins on the year day-number (days from 1 January) that increases linearly between 20 • S and 20 • N from zero to 181 (the number of days between 1 January and 1 July), and similarly for the end of the release year.
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 ∼10m). The relaxation time is T r = Tr0 1−ai , where T r0 =7200 s (the leapfrog timestep) is the smallest relaxation time that still remains stable. To represent the ability of ice cover to insulate the ocean from 160 air-sea gas exchange, the relaxation time is increased by the reciprocal of the water fraction 1-a i with a i the ice fraction. With the depth interval of 10 m, this implies a piston velocity of 1.39 x 10 −3 m s −1 , (120 m day −1 ) without ice (much faster than a typical gas exchange piston velocity of 2.4 m day −1 ), ranging down to a velocity of 2.4 m day −1 in regions of maximum icecover with a i =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 10 165 m, resulting in a systematic loss of the globally integrated tracer inventory over the simulation. This is presented schematically in Figure 2, where dye N is only injected in release (vintage) year N, while 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 section 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 170 interannual variability and pathways from annual to multidecadal timescales.

Dye diagnostics
The dye concentration, c, at any point (or in the model, in a gridbox) 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). Then the total globally-integrated inventory of dye C global = c dV represents the total volume of results correlating ventilation depth on different timescales and highlighting the dominant role of surface forcing in setting the evolution of the tracersistribution and inventory.

The fingerprint of surface atmospheric forcing
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 (Figures 1a and 4a) and the stratification in that year 290 (reconditioning. 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. This determines how much dye is retained, since a deepening of the mixed layer in the winter following the injection year (N+1; see Figure 2) will ventilate a larger portion of the vintage from the previous year (N; see Figure 2) and effectively reduce the dye concentration (since in our setup it will be reset to zero when ventilated). This contributes to the interannual variability 295 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 Figure 6) 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. Since the variability in ventilation near the time of dye injection sets the long-term variability for the dye inventory, there is potential for 300 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.
Finally, the strong correlations in ventilation depths between 3 and 25 years after injection in both the Northern and Southern hemispheres ( Figure 8) imply that, given the strong interannual variability in the initial surface forcing, it is this variability that will continue to dominate on longer time scales, largely overriding the different processes that drive how passive tracers are 305 removed or taken up in the two hemispheres. The Northern Hemisphere is characterized by more persistent anomalies, since the ventilated waters penetrate more deeply where they are better isolated from surface influence while in the Southern Hemisphere the anomalies are initially stronger ( Figure 6), 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 310 interior for longer in the subpolar North Atlantic once it has reached a deeper horizon (Figures 9 and 10).

Longer-term and large-scale signals
The strong interannual variability that characterises ventilation in the Northern Hemisphere on these timescales (Figure 7) is largely driven by the Irminger, Nordic and Labrador Seas (Figures 4a,b), which are the sites of most active deep convection in the winter months (e.g. Lozier, 2010) and are characterised by ventilation anomalies that persist for longer than in the Southern 315 Hemisphere ( Figure 6).
There is coherent structure in the residuals of the correlation between Northern Hemisphere ventilation depth 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