Seasonal overturning variability in the eastern North Atlantic subpolar gyre: A Lagrangian perspective

. Changes in the high-latitude Atlantic Meridional Overturning Circulation (MOC) are dominated by water mass transformation in the eastern North Atlantic Subpolar Gyre (SPG). Both observations and ocean reanalyses show a pronounced seasonality of the MOC within this region. Here, we investigate the nature of this seasonal overturning variability within the eastern SPG using Lagrangian water parcel trajectories evaluated within an eddy-permitting ocean sea-ice hindcast simulation. Our analysis highlights the critical role of water parcel recirculation times in determining the seasonality of overturning 5 measured in both the traditional Eulerian and complimentary Lagrangian frames of reference. From an Eulerian perspective, we show that the minimum of the MOC seasonal cycle in autumn results from a combination of enhanced stratification and increased southward transport within the upper East Greenland Current. This convergence of southward transport within the MOC upper limb is explained by decreasing water parcel recirculation times in the upper Irminger Sea, consistent with a gyre-scale response to seasonal wind forcing. From a Lagrangian perspective, we find that upper limb water parcels flowing 10 northwards into the eastern SPG participate in a recirculation race against time to avoid wintertime diapycnal transformation into the lower limb of the MOC. The majority of water parcels, sourced from the central and southern branches of the North Atlantic Current, are unsuccessful and thus determine the mean strength of overturning within the eastern SPG (8.9 ± 2.2 Sv). The seasonality of Lagrangian overturning is explained by a small collection of upper limb water parcels, recirculating rapidly ( ≤ 8.5 months) in the upper Irminger and Central Iceland Basins, whose along-stream transformation is dependent on their 15

Concordant with the previous studies of Lozier et al. (2019) and Mercier et al. (2015), we find that MOC variability in the eastern SPNA is most pronounced on monthly timescales (SD = ±2.7 Sv), where monthly MOC values range from 7.8 Sv in October 1978 to 28.7 Sv in January 1996. The simulated MOC variability at OSNAP East is weaker on interannual timescales (SD of annual means = ±1.0 Sv), in agreement with previous results from ocean models and reanalyses (Xu et al., 2014;  The seasonal cycle in the strength of the MOC at OSNAP East therefore corresponds to the expansion (MOC weakening in summer-autumn) and contraction (MOC strengthening in winter-spring) of the overturning streamfunction in density-space, which is consistent with seasonal variations in surface buoyancy forcing over the NAC upstream.

The Lagrangian perspective
The Lagrangian overturning framework provides us with an alternative view of the overturning variability at OSNAP East on 230 seasonal timescales. Whereas the Eulerian streamfunction integrates the meridional transports across OSNAP East in densityspace at a given point in time, the LOF measures the net diapycnal transformation that the total northward transport arriving at OSNAP East will go on to experience during its recirculation within the eastern SPG. As such, the meridional transports comprising the LOF belong to a single collection of water parcels (sharing a common inflow time), whereas the Eulerian streamfunction includes two unrelated collections of water parcels flowing northwards and southwards, respectively. We should 235 9 https://doi.org/10.5194/egusphere-2022-1334 Preprint. Discussion started: 5 December 2022 c Author(s) 2022. CC BY 4.0 License. therefore consider the LOF to be a complementary measure of the overturning at OSNAP East, which preserves knowledge of water parcel identity at the expense of integrating across water parcel recirculation times which can extend from days to years. Figure 3a presents the strength of the LMOC within the eastern SPG between 1976 and 2008, consistent with our earlier Eulerian analysis (Fig. 2a). We find that, on average, 8.9 Sv of transport flowing northwards across OSNAP East is transformed from the upper to the lower limb south of the Greenland-Scotland Ridge. Importantly, this transformation is stronger than 240 the mean eastern SPG Lagrangian overturning found in Tooth et al. (2022), because here we compute the average of the maximum Lagrangian overturning each month as opposed to taking the maximum of the mean LOF as in Tooth et al. (2022).
We attribute the remaining 6.5 Sv (15.4 Sv -8.9 Sv) of overturning at OSNAP East to water parcels which are transformed north of the Greenland-Scotland Ridge before returning via the deep pathways of Nordic Seas overflows. Although we do not resolve the overturning pathways of the Nordic Seas overflows in this Lagrangian experiment, the close correspondence 245 between the month-to-month Lagrangian overturning variability of the eastern SPG (SD = ±2.2 Sv) shown in Figure 3a and the total month-to-month variability of the MOC (SD = ±2.7 Sv) underscores the dominant contribution made by the eastern SPG to intra-annual overturning variability at OSNAP East.
In contrast with the seasonality of the Eulerian MOC, the seasonal cycle of Lagrangian overturning within the eastern SPG shows a steady increase from a minimum of 6.4 Sv in May to a maximum of 11.5 Sv in November. While the phase difference 250 between the seasonal cycles of the MOC and the LMOC may initially appear counter-intuitive, recall that the strength of the Lagrangian overturning in Figure 3b quantifies how much of the total northward transport initialised along OSNAP East each month is transformed from the upper to the lower limb in the Irminger and Iceland-Rockall Basins. Interestingly, the seasonal cycle of the LMOC strength corresponds closely with the seasonality of both σ LM OC and σ M OC (see Figs. 2b and 3b), suggesting that the potential density of upper limb water parcels on flowing northward across OSNAP East is an important 255 indicator of their future contribution to the overturning north of the section. This relationship can also be seen in Figure 3c, which shows how the LOF evolves over the duration of the mean seasonal cycle. Here, we find that the maximum of the LMOC in November occurs when the largest number of relatively light upper limb water parcels are able to integrate sufficient wintertime surface buoyancy loss to enter the lower limb before returning to OSNAP East. Meanwhile, in May, we find that denser upper limb waters, previously transformed by wintertime cooling in the NAC, experience substantial summertime 260 buoyancy gain north of OSNAP East to become lighter downstream. This negative diapycnal transformation manifests in The seasonal cycle of Lagrangian overturning within the eastern SPG therefore reflects the seasonality of the surface-forced water mass transformation within the Irminger and Iceland-Rockall Basins north of OSNAP East. The strengthening of the 265 LMOC in summer-autumn corresponds to increasing diapycnal transformation across σ LM OC , owing to intense surface buoyancy loss along particle trajectories during the ensuing winter. Meanwhile, the weakening of the LMOC through winter-spring reflects a decreasing volume flux into the lower limb as water parcels in the upper limb gain buoyancy along their trajectories during the ensuing summer. 4 Timescales and origins of seasonal Lagrangian overturning 270 We have demonstrated that variations in the Lagrangian overturning evaluated at OSNAP East are most pronounced on seasonal timescales. However, the magnitude of seasonal variability (SD of seasonal cycle = ±2.1 Sv) remains small compared with the mean strength of overturning (LMOC = 8.9 Sv), suggesting that the majority of water parcels flowing northwards across OSNAP East in the upper limb are transferred into the lower limb before returning to the section. Since wintertime surface buoyancy loss greatly exceeds summertime buoyancy gain over the eastern SPG (Xu et al., 2018b), the mean strength of 275 the LMOC is governed by the fraction of water parcels which fail to return to OSNAP East before the onset of winter and therefore integrate sufficient surface buoyancy loss to be transferred into the lower limb during their recirculation. In contrast, the seasonality of Lagrangian overturning is determined by rapidly recirculating water parcels whose transformation north of OSNAP East is dependent on the time of year that they arrive at the section. The minimum of the LMOC seasonal cycle (Fig.   3b) is due to the coldest upper limb water parcels arriving at the section in spring, which experience summertime warming 280 before returning to OSNAP East prior to the onset of wintertime densification. The maximum of the LMOC seasonal cycle, corresponding to the largest volume flux into the lower limb, is due to the warmest upper limb water parcels flowing northwards across the section in autumn, which experience the largest wintertime surface buoyancy loss downstream. This qualitative description of seasonal overturning variability raises two important questions. Firstly, what is the maximum amount of time a water parcel can spend north of OSNAP East and still contribute to the seasonal cycle of Lagrangian overturning? Secondly, are 285 the water parcels responsible for seasonal variability sourced from distinct inflow regions along OSNAP East when compared with those contributing substantially to the mean state of overturning? To address these questions, we decompose the LOF according to both the time water parcels spend north of OSNAP East (herein referred to as the water parcel recirculation time, τ ) and the distance from the East Greenland coast that water parcels flow northward across the section (Fig. 4). (difference between November-May LMOC monthly composites) accumulated as a function of the time water parcels spend north of OSNAP East (τ ). We find that the entire LMOC seasonal cycle and 25% of the mean strength of Lagrangian overturning can be explained by water parcels which spend less than 8.5 months recirculating within the eastern SPG. Interestingly, the absence of any further accumulation of seasonal Lagrangian overturning variability after 8.5 months following northward inflow across OSNAP East implies that, irrespective of its time of arrival, once a water parcel has experienced wintertime 295 surface buoyancy loss it can no longer imprint onto the seasonal cycle of Lagrangian overturning. Thus, the remaining 75% of the mean LMOC strength is accounted for by water parcels which spend between 8.5 months and 5 years recirculating within the eastern SPG, and experience at least one winter north of OSNAP East. We should note, however, that the accumulation of the mean Lagrangian overturning is not linear over this period; 91% of the volume flux from the upper to the lower limb is owed to water parcels recirculating in 2 years or less (Fig. 4a).

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To understand how the recirculation time of a water parcel is related to its inflow position along OSNAP East, we next calculate the average recirculation time of water parcels within the eastern SPG as a function of their northward crossing locations along the section. Figure 4b indicates that, on average, the recirculation times of the major upper ocean currents intercepted by OSNAP East are shortest in the upper ocean and increase strongly with depth. This is consistent with observations in the eastern SPNA, which show that northward transport is surface intensified in the NAC branches (Holliday et al., 2018;Houpert 305 et al., 2018Houpert 305 et al., , 2020 and the Irminger Current (de Jong et al., 2020;Fried and de Jong, 2022) since isopycnals in the upper ocean shoal strongly westward. A prominent feature of Figure 4b is the transition from upper limb pathways which contribute to the seasonal cycle of the LMOC (orange, τ ≤ 8.5 months) in the Irminger and Central Iceland Basins to longer pathways (blue, τ > 8.5 months), sourced from the central and southern NAC branches, which dominate its mean strength. Figure 4c quantifies this distinction, highlighting that 74% of the mean strength of the LMOC is due to water parcels originating from 310 the Sub-Arctic Front and the Rockall Trough and Plateau, whereas 96% of the mean seasonal cycle of Lagrangian overturning can be explained by water parcels sourced from the Irminger and Central Iceland Basins (x ≤ 1250 km). This finding is further supported by the recent results of Li et al. (2021a), who found that changes in the observed velocity and density fields between the East Greenland coast and the Central Iceland Basin can explain 75% of the monthly MOC variance across OSNAP East between 2014-16. To summarise, we have identified a threshold recirculation time of 8.5 months which governs whether water parcels will contribute substantially to the mean strength of the LMOC or determine its seasonal signal at OSNAP East. Seasonal overturning variability is sourced from the upper Irminger and Central Iceland Basins, where the rapid recirculation of water parcels in less than 8.5 months yields along-stream transformations which are dependent on their time of arrival at OSNAP East. Conversely, the mean strength of the LMOC is determined by water parcels, originating from the central and southern NAC branches, 320 whose longer recirculation time (τ > 8.5 months) guarantees their transformation into the LMOC lower limb through intense wintertime buoyancy loss. Concordant with our earlier analysis, Figure 5 shows a clear distinction between the circulation pathways responsible for the seasonality of the LMOC and those governing its mean state. We find that the two pathways crossing the Reykjanes Ridge north of OSNAP East account for 70% of the mean strength of the Lagrangian overturning within the eastern SPG yet exhibit 335 negligible variability on seasonal timescales (Fig. 5c). This is because the recirculation times of water parcels advected across the ridge north of OSNAP East consistently exceed the critical 8.5 month threshold required to be irreversibly transferred into the lower limb of the LMOC. Water parcels advected along the Ic-RR-Irm pathway typically experience 1.1 years (  shows that water parcels recirculating exclusively within the Irminger Basin (Irm-Irm) explain 75% of the amplitude of the LMOC seasonal cycle at OSNAP East (Fig. 4). However, our use of a single Irm-Irm pathway obscures two separate pathways that circulate cyclonically within the Irminger Sea, namely the Irminger Current IC and the Irminger Gyre 345 IG. Therefore, to isolate the Lagrangian overturning occurring along each of these pathways, we define the boundary between the IG, recirculating within the basin interior, and the IC, positioned on the western flank of the Reykjanes Ridge, to be 500 km from Cape Farewell, following Våge et al. (2011). We find that the northward inflows to the IG (x ≤ 500 km) make a disproportionately large contribution to the seasonality of Lagrangian overturning (26%) compared with their contribution to its mean strength (3%). Water parcels advected along the path of the IC (500 km < x ≤ 750 km) explain almost half (49%) 350 of the seasonal cycle of Lagrangian overturning whilst also accounting for approximately a fifth (19%) of the mean volume flux across σ LM OC . The larger overturning associated with the IC is explained by Figure 5d, which shows that water parcels typically spend 8.2 months recirculating within the IC compared with only 5.8 months within the IG. Since the median recirculation time of the IC pathway is comparable to the 8.5-month threshold required to avoid wintertime densification north of will be transformed across σ LM OC .
Although watermass transformation along the IcRo-IcRo pathway accounts for only a quarter of the LMOC seasonal cycle at OSNAP East, Figure 5c highlights its critical role in establishing the timing of the November maximum in the seasonal cycle of Lagrangian overturning. Notably, it is the rapid recirculation of water parcels from the northern NAC branch to the East Reykjanes Ridge Current (ERRC) within 4.8 months that dominates seasonal overturning variability along this pathway.

Transformation along seasonal overturning pathways
To understand how seasonal Lagrangian overturning variability results from diapycnal transformation along water parcel tra-370 jectories, we next calculate the net potential density change of water parcels between northward and southward crossings of OSNAP East, ∆σ, as a function of their inflow location along the section. Figure 6a  Since water parcels recirculating cyclonically along the boundary current of the Irminger Sea typically spend an additional 2.4 months north of OSNAP East compared with those circulating in the interior of the Irminger and Central Iceland Basins (Fig. 5), we next explore how the character of seasonal water mass transformation differs along boundary and interior pathways within the eastern SPG. We focus our analysis on the water parcels circulating in the upper 250 m of the Irminger Sea, since these collectively account for three quarters of the seasonal cycle of Lagrangian overturning at OSNAP East. To compare the 385 boundary and interior modes of seasonal overturning variability, Figure 6c-d presents the transport-weighted mean potential density of upper IG (pink box in Fig. 6a-b) and upper IC (purple box in Fig. 6a-b) water parcels on their northward (IG/IC inflow) and subsequent southward (EGC outflow) crossings of the OSNAP East section. We find the densest water flowing inflow, upper IG water parcels are consistently denser than those initialised in the upper IC (Fig. 6c-d) owing to their convective origins in the Labrador Sea interior (Lavender et al., 2000;Chafik et al., 2022). Moreover, upper IG water parcels exhibit a much narrower potential density range (27.52 -27.68 kg m −3 ) on southward outflow compared with those recirculating along the upper IC pathway (27.48 -27.59 kg m −3 ). This is because the longer recirculation time of the upper IC pathway (τ = 6.2 months) allows water parcels to undergo greater surface buoyancy loss along the boundary current, thereby damping the seasonality of their water mass properties on inflow. The additional time upper IC water parcels spend north of OSNAP East is also reflected by the shorter 2-month window (April-May in Fig. 6d) during which negative diapycnal transformation can occur, compared with the 5-month window (March-July in Fig. 6c) for the rapidly recirculating upper IG pathway (τ = 3.8 400 months).
To determine the relative importance of temperature and salinity changes along boundary and interior pathways, we further decompose the net diapycnal transformation (∆σ) north of OSNAP East into diathermal and diahaline components. We approximate ∆σ using a linearised form of the equation of state following the integral approach of Tamsitt et al. (2018):

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where θ denotes potential temperature, S denotes salinity, α represents the thermal expansion coefficient, and β represents the haline contraction coefficient. The values ofθ andS correspond to the average potential temperature and salinity of a water parcel on its northward and southward crossings of OSNAP East. August-January, mixing induced salinification acts to augment along-stream densification due to intense surface heat loss over 420 the basin interior. Although the predominant influence of boundary-interior exchange is year-round positive diahaline transformation, we should also note that the diathermal consequence of mixing is that summertime warming of IG water parcels exceeds their wintertime cooling (Fig. 6e).
Diahaline transformation along the upper IC pathway is characterised by the freshening of water parcels flowing northward across OSNAP East between February-August. Interestingly, Figure 6f shows that it is this substantial freshening, rather than 425 summertime heating, which is responsible for the negative diapycnal transformation along water parcel trajectories initiated in late spring -early summer. The largest freshening along the boundary current is associated with water parcels which flow we choose to decompose the net diapycnal transformation north of OSNAP East into two successive transformations taking place in the Iceland and Irminger Basins (Fig. 7c-d). Figure 7a shows that upper Ic-RR-Irm water parcels experience sufficient net diapycnal transformation north of OSNAP East to be transferred into the lower limb of the LMOC, irrespective of their 445 water mass properties on inflow. This is because water parcels typically recirculate on interannual timescales (τ = 1.1 years) and are therefore guaranteed to experience at least one winter within the eastern SPG. For the lightest water parcels flowing northward in autumn, this intense wintertime heat loss manifests as a large diathermal transformation (equivalent to ∼0.5 kg m −3 ) during their initial 6.8 months spent within the Iceland Basin (Fig. 7c). In contrast, the densest water parcels arriving at OSNAP East in spring experience wintertime diathermal transformation (equivalent to ∼0.5 kg m −3 ) during their final 450 6.5 months spent in the Irminger Basin (Fig. 7d). Thus, we find that wintertime surface buoyancy loss removes all seasonal thermohaline variability flowing northwards into the eastern SPG. Meanwhile, the transit times of upper Ic-RR-Irm water parcels through the Iceland and Irminger Basins account for the 7-month phase shift in the seasonal cycle in density as it decays downstream (Fig. 7a).
In addition to surface-forced diapycnal transformations, the remarkably consistent density of the upper Ic-RR-Irm pathway in the EGCC. A closer examination shows that this mixing (freshening) along water parcel trajectories is concentrated near the Kangerdlugssuaq Trough in the northern Irminger Basin, where observations have found substantial freshwater transports directed offshore from the East Greenland Shelf (Sutherland and Pickart, 2008;Sutherland et al., 2009;Foukal et al., 2020). We therefore propose that mixing between Arctic and Atlantic water masses along the western boundary of the Irminger Sea plays an integral role in maintaining the stable composition of the lower limb on seasonal timescales (see Fig. 3b where σ LM OC =  flowing northward across OSNAP East in the boundary current in spring exhibit substantial freshening along-stream due to 475 enhanced mixing with Arctic-origin waters in the EGCC during the ensuing autumn. The additional 2.4 months required for water parcels to be advected along the Irminger Current also reduces the variability of water mass properties on southward outflow compared with those rapidly recirculating in the Irminger Gyre. When advective timescales are increased further, as found along our dominant overturning pathway (Ic-RR-Irm), intense wintertime heat loss north of OSNAP East acts to damp the seasonality of water mass properties on northward inflow, thus forming lower limb water of remarkably consistent density. We conclude our analysis by using Lagrangian water parcel trajectories to cast new light on the mechanisms responsible for seasonal Eulerian overturning variability. We begin by decomposing the net volume flux in the MOC upper limb, determined directly from the simulated velocity and potential density fields along OSNAP East, into its constituent northward and southward components during April and October, corresponding to the extrema of the MOC seasonal cycle in Figure 2b. Figure 8   485 indicates that, in spite of the year-round net northward transport in the upper limb, the seasonal cycle of the MOC results from changes in the southward transport above σ M OC at OSNAP East. This is highlighted in Figure 8c, which shows that the total southward transport in the upper limb increases significantly from -8.7 Sv in April, when the Eulerian overturning reaches its seasonal maximum (18.5 Sv), to -14.4 Sv when the MOC seasonal minimum (14.4 Sv) occurs in October. Further decomposition of the seasonal upper limb transport according to the major currents crossing the OSNAP East array 490 (Table 1) indicates that the seasonal minimum of the MOC results from the combination of a 2.8 Sv strengthening of the EGC southward transport above σ M OC and a 1.1 Sv weakening of the southern NAC branch feeding the Rockall Trough and Plateau.
This agrees with the recent results of Wang et al. (2021), who demonstrated that variations in the southward transport along the western boundary of the Irminger Sea play a prominent role in modulating the seasonal cycle of overturning at OSNAP East.
Moreover, Wang et al. (2021) showed that the seasonality of the EGC upper limb transport is principally explained by seasonal 495 density changes in the upper Irminger Sea projecting onto the mean barotropic transport of the western boundary current.
To explore this further, Figure 9 presents the mean potential density field along OSNAP East in April (MOC maximum) and October (MOC minimum) and the corresponding location of σ M OC . In April, we find that the erosion of stratification, owing to intense wintertime heat loss, permits deep convective mixing in the Irminger Sea interior (de Jong et al., 2012;de Jong and de Steur, 2016;Piron et al., 2016), such that σ M OC (27.57 kg m −3 in April) outcrops at the surface (Fig. 9a). As a 500 consequence, the total northward transport above σ M OC along OSNAP East is reduced, since a substantial fraction of the water flowing northward in the Irminger Sea does so in the lower limb of the MOC (de Jong et al., 2020). Along the western 7 Discussion and conclusions In this study, we investigate the nature of seasonal overturning variability within the eastern North Atlantic SPG using Lagrangian water parcel trajectories evaluated within an eddy-permitting ocean sea-ice hindcast simulation. We employ the recently introduced Lagrangian Overturning Function (LOF) in density-space, complementing the traditional Eulerian over- Given the asymmetry between stronger wintertime surface buoyancy loss and weaker summertime buoyancy gain over the Iceland and Irminger Basins (de Boisséson et al., 2010;Brambilla et al., 2008;Xu et al., 2018b), it is also interesting to frame 585 seasonal Lagrangian overturning variability somewhat analogously to "Stommel's Demon" (Stommel, 1979;Williams et al., 1995). That is to say, water parcels advected northwards across OSNAP East in the upper limb of the LMOC are participating in a recirculation race against time to avoid wintertime diapycnal transformation into the lower limb. The majority of water parcels are unsuccessful and hence contribute to the mean strength of overturning within the eastern SPG. However, a small collection of water parcels at a specific time of year recirculate sufficiently quickly to imprint onto the seasonality of Lagrangian infer the contributions of air-sea interaction and mixing to the net densification along water parcel trajectories in this study, it would prove valuable for a future study to formally diagnose their respective contributions to the diathermal and diahaline transformations governing the densification of water masses within the SPG.
Our Lagrangian analysis also demonstrates how the longest circulation pathways within the eastern SPG maintain the consistent water mass properties of the lower limb flowing southward across OSNAP East. By examining seasonal water mass 625 transformations along the dominant Ic-RR-Irm overturning pathway, we show that, provided water parcels spend at least one winter north of OSNAP East, they will undergo sufficient surface-forced diathermal transformation to form upper ISIW, irrespective of their properties on inflow. We therefore propose that wintertime surface buoyancy loss over the Iceland and Irminger Basins acts as a crucial damping mechanism for seasonal thermohaline variability imported from the NAC upstream.
Meanwhile, the stable year-round composition of lower limb waters flowing southward in the EGC results from mixing with