To investigate the variability of dense-water formation along the path of the subpolar gyre, we use output from the eddy-rich, global ORCA0083-GO8p7 numerical ocean model configuration . This uses the Nucleus for European Modelling of the Ocean (NEMO) ocean circulation model version 4.0.4 implemented in the UK Global Ocean (GO) version 8 configuration. This is a pre-release configuration of the Global Ocean and Sea Ice (GOSI) version 9 developed by the UK Joint Marine Modelling Programme in preparation for CMIP7.

The NEMO ocean model is discretised on an Arakawa C grid with a nominal 1/12° resolution (equivalent to ∼8 km in the subtropical North Atlantic and ∼4 km in the Arctic). The extended version of the quasi-isotropic ORCA12 orthogonal tri-polar grid (eORCA12) is used, with poles located on land in Canada, Siberia, and Antarctica. In the vertical, the model uses 75 unevenly spaced z*-partial-step coordinate levels with unperturbed depth increments ranging from 1 to 250 m. The depth increment of the grid cells at each vertical level varies through time due to the implementation of a non-linear free surface . Within the NEMO framework, the NEMO Ocean Engine (NEMO-OCE) is coupled to the SI³ sea ice model . For a comprehensive description of the ORCA0083-GO8p7 model configuration, users are referred to .

The ORCA0083-GO8p7 integration is initialised from rest with temperature and salinity from the climatology of an Argo-based observational objective analysis EN4; covering 1995–2014. The model is forced by the Japanese 55-year atmospheric reanalysis JRA55-do; for the period 1958–2021. We disregard the initial 18 years of the integration when model adjustment is largest and make use of the monthly mean velocity and tracer field output between 1975–2021.

To assess the fidelity of the subpolar ocean circulation in the ORCA0083-GO8p7 hindcast, we compare the simulated diapycnal overturning to OSNAP observations between 2014–2020. Figure a and b shows the time mean Eulerian diapycnal overturning stream functions at the OSNAP East and OSNAP West sections calculated using both the model and observations. Overall, we find good agreement between the modelled and observed overturning stream functions in density space at the OSNAP array. At OSNAP East, the maximum of the time mean diapycnal overturning stream function in the model (13.5±2.3 Sv at 27.51 kg m⁻³) is slightly weaker than observed (14.5±3.0 Sv at 27.55 kg m⁻³). However, this is primarily due to the weaker time mean net northward transport across the section in the model (0.8±1.1 Sv) compared to the 1.6 Sv imposed in the OSNAP observational calculation. Figure b shows that there is also close agreement between both the magnitude and isopycnal of maximum diapycnal overturning in the model (2.1±2.8 Sv at 27.70 kg m⁻³) and observations (2.2±1.8 Sv at 27.69 kg m⁻³) at OSNAP West. This is particularly encouraging, given that many eddy-rich models considerably overestimate the time mean strength of diapycnal overturning in the Labrador Sea e.g.. Once we account for the larger net southward flow across the OSNAP West section in the model (-2.4±0.8 Sv) compared with that imposed in the OSNAP observational calculation (-1.6 Sv), we do find that the modelled diapycnal overturning is slightly stronger than observed.

Figure c and d show the time series of diapycnal overturning strength at OSNAP East and OSNAP West as determined by calculating the maximum of each monthly overturning stream function. Although we find a significant correlation (r=0.55, p<0.01) between the modelled and observed diapycnal overturning strength at OSNAP East, it is clear that the model (monthly SD = 2.6 Sv) underestimates the monthly overturning variability captured in observations (monthly SD = 3.0 Sv). In contrast, at OSNAP West, we find a much weaker correlation (r=0.27, p<0.05) since the observed diapycnal overturning strength is less variable than that found in the model, especially on seasonal timescales. The stronger overturning seasonality in the model is due to the presence of warmer (+0.14 °C) and saltier (+0.1 g kg⁻¹) waters in the western Labrador Sea compared with OSNAP observations, which experience less density compensation between wintertime cooling and year-round freshening .

In addition to reproducing much of the observed strength of and monthly variability in overturning along the OSNAP array, we also find reasonably good agreement between the modelled (6.5±1.0 Sv) and observed 5.8±0.7 Sv; overturning strength at the Greenland–Scotland Ridge (1995–2015). Given our focus on the formation of dense water along the boundary current of the SPG in this study, we also highlight the close agreement between the time mean top-to-bottom strength of the East Greenland Current (-33.8±2.7 Sv) in the model and that observed by (-33.1±2.6 Sv) between 2002–2012 along the OVIDE section. However, in the Labrador Sea, the model (-27.4±5.8 Sv) slightly underestimates the time mean (1997–2014) strength of the Deep Western Boundary Current (DWBC) at 53° N as, reported by (-30.2±6.6 Sv, where σθ≥27.68 kg m⁻³).

In spite of these differences, we consider the broad overall agreement between the strength of both the SPG and the diapycnal overturning circulations simulated in the ORCA0083-GO8p7 hindcast and that observed along trans-basin arrays to be sufficient justification for using this model to investigate the nature of dense-water formation along the path of the SPG.

We evaluate the Lagrangian trajectories of virtual water parcels advected by the time-evolving velocity fields of the ORCA0083-GO8p7 hindcast using TRACMASS version 7.1 . TRACMASS belongs to the inaugural family of Lagrangian particle tracking tools, which allow users to quantify the volume transport pathways of a steady, incompressible flow field by modelling water parcel trajectories as individual stream tubes e.g.. Here, we use the stepwise stationary scheme, which divides the duration between successive monthly mean velocity fields into 100 intermediate time steps during which volume transports are assumed to be constant. We calculate purely advective water parcel trajectories without attempting to parameterise the effects of vertical convective mixing in the surface mixed layer. This is because showed that introducing random vertical displacements along water parcel trajectories inside the surface mixed layer did not influence the strength and variability of along-stream diapycnal transformation.

To investigate the extent to which thermohaline anomalies arriving in the eastern SPG influence the formation of dense water along-stream, we evaluate the forward-in-time trajectories of water parcels sampling the full-depth northward transport across a subsection of the OSNAP East array extending from the Reykjanes Ridge (RR, 30° W) to the Scottish Shelf (SS). This approach differs from previous studies e.g., which employ backward-in-time trajectories to identify the sources and export pathways of NADW flowing southward in the lower limb.

We consider only a subsection of the OSNAP array to focus our analysis on the waters which flow northward across OSNAP East in the northern, central, and southern branches of the North Atlantic Current (NAC) and to avoid sampling the recirculating upper-limb waters which return northward in the Irminger Current (see Fig. ). One limitation resulting from this decision is that we do not quantify the contribution of upper-limb water parcels which flow directly into the Irminger Sea via the northernmost NAC branch e.g. to NADW formation along the path of the SPG.

Water parcels are initialised every month for 456 consecutive months between 1975–2012. Water parcels are assigned to each grid cell along the model-defined OSNAP East array in proportion to the northward volume transport across the grid cell face. Each water parcel represents a volume transport ≤ 2.5 mSv to ensure that a sufficiently large number of water parcels are initialised to calculate robust Lagrangian diagnostics .

In total, more than 12.5 million water parcels are advected forward in time using monthly mean velocity fields for a maximum of 9 years to determine their future trajectories. Water parcel trajectories are terminated on reaching the maximum advection time (τmax) or upon meeting any one of the following geographical criteria (Fig. ): (i) crossing (southward) a subsection of the OSNAP West array (53° N), (ii) crossing the Greenland–Scotland Ridge, (iii) crossing the Davis or Hudson straits, or (iv) crossing 51° N. Figure a and b show that the 9-year maximum advection time is sufficient to capture the SPG circulation because the accumulated volume transports reaching OSNAP West and the Greenland–Scotland Ridge have stabilised within this period. The location, conservative temperature, and absolute salinity along each water parcel trajectory are calculated through linear interpolation using the monthly mean model tracer fields. The potential density referenced to the sea surface (σθ) is calculated along each trajectory using the TEOS-10 equation of state as implemented in the ORCA0083-GO8p7 hindcast .

To quantify the amount of dense water formed along the path of the North Atlantic SPG, we calculate the Lagrangian diapycnal overturning stream function  F(σθ,t) in density coordinates using only the subset of water parcel trajectories initialised at time t which transit from OSNAP East (NAC) to OSNAP West (53° N) within the τmax = 9-year maximum advection period (i.e. 0<τout≤τmax, where τout is the transit time for each water parcel). We focus on this particular subset of water parcels since the overwhelming majority of water parcels which exit via the southern boundary at 51° N or remain inside the domain following 9 years of advection are already contained within the lower limb on flowing northward across the OSNAP East section and therefore are not involved in dense-water formation. The Lagrangian diapycnal overturning stream function for each monthly ensemble of N(t) water parcels initialised across the OSNAP East section at time t is calculated following : 1Fσθ,t=∑σθ*=σminσθVNAC,σθ*(t)-V53°N,σθ*t+τout, where VNAC,σθ* and V53°N,σθ* represent the absolute volume transport distributions of SPG water parcels in density coordinates on their initial northward (NAC) and final southward (53° N) crossings of the OSNAP array.

In order to investigate the downstream evolution of thermohaline anomalies, we additionally define the volume-weighted mean of a specified quantity q (e.g. potential density) for each monthly ensemble of N(t) water parcels at some time τ following their initialisation: 2q‾(t,τ)=∑n∈N(t)Vnqn(τ)∑n∈N(t)Vn, where Vn is the volume transport conveyed by an individual water parcel with index n, and qn(τ) represents the value of q recorded along its trajectory at time τ following initialisation, where t≤τ≤t+τout.

To characterise the nature of dense-water formation along the path of the SPG, we begin by describing the circulation pathways of water parcels flowing northward into the eastern SPG between 1975–2012 (Fig. ).

On average, 52.7±9.0 Sv flows northward across the OSNAP East array between the Reykjanes Ridge and the Scottish Shelf via the branches of the NAC. Of this total northward transport, 24.8±4.2 Sv (47.0±3.1 %; Fig. ) circulates around the SPG before flowing southward across the OSNAP West array at 53° N (between the Labrador coast and basin interior), which we shall herein refer to as the SPG pathway. The remaining northward transport across OSNAP East is distributed between pathways crossing the Greenland–Scotland Ridge (27.0±4.5 %) and the Davis and Hudson straits (0.5±0.4 %) and 51° N (12.4±4.2 %), with a small fraction remaining within the SPG interior following 9 years of advection (11.4±2.0 %).

Figure d shows that the 14.5±2.3 Sv flowing northward into the Nordic Seas is dominated by relatively light (σθ≤27.3 kg m⁻³) water parcels, sourced almost equally from the upper 500 m of the central and southern NAC branches, which typically reach the Greenland–Scotland Ridge in less than a year. Interestingly, although this inflow is larger than the observed Atlantic inflow into the Nordic Seas , we find reasonable agreement between the modelled (6.5±1.0 Sv) and observed 5.8±0.7 Sv; Eulerian diapycnal overturning strength at the Greenland–Scotland Ridge (1995–2015), suggesting that a substantial fraction of northward transport across the ridge is recirculated within the upper limb in the model.

As a typical water parcel flows cyclonically around the SPG, it forms dense NADW by cooling (ΔθSPG=-4.0±0.2 °C) and freshening (ΔSSPG=-0.36±0.03 g kg⁻¹) along-stream (Fig. ). Figure b shows that, on average, the total light-to-dense transformation of SPG water parcels peaks across the σθ=27.66 kg m⁻³ isopycnal, which we herein refer to as σ‾DWF. We hence define the along-stream dense-water formation (DWF) as the total volume flux of water parcels across this constant isopycnal between their initial release along OSNAP East and their final southward crossing of OSNAP West (i.e. DWFSPG(t)=F(σ‾DWF,t)). Notably, σ‾DWF agrees closely with the isopycnal of maximum overturning recorded in OSNAP observations (σ‾MOC=27.63 kg m⁻³ during 2014–2020 in ), although we acknowledge that this lies outside of our study period. We herein refer to water parcels with a potential density less than or greater than σ‾DWF as being found in, respectively, the upper or lower limb of the AMOC. Furthermore, we refer to lower-limb water parcels collectively as NADW throughout the study since σ‾DWF constitutes the time mean upper isopycnal limit of NADW.

Of the 24.8±4.2 Sv circulating around the SPG, Fig. b indicates that 12.7±1.9 Sv forms dense NADW (i.e. σ53°N≥σ‾DWF) prior to crossing OSNAP West. However, 5.6±1.4 Sv of the water flowing northward across OSNAP East is already in the lower limb, and this 12.7±1.9 Sv of NADW formation represents a significant fraction of the 19.2±3.0 Sv flowing northward across OSNAP East in the upper limb.

We additionally decompose the total DWF along-stream into the separate contributions made in the eastern and western SPG by calculating partial Lagrangian overturning stream functions using the properties of water parcels during their northward crossing of the OSNAP West array via the West Greenland Current (WGC; Fig. a). In agreement with OSNAP observations , we find that the time mean DWF_SPG is dominated by NADW formation in the eastern SPG (9.0±1.7 Sv; Fig. b). In contrast, DWF is much weaker in the Labrador Sea (3.7±0.9 Sv) since there is greater density compensation between cooling and freshening along-stream (Fig. c and d). The mean strength of along-stream DWF in the Labrador Sea agrees well with the magnitude of diapycnal overturning observed along OSNAP West (3.0±1.5 Sv during 2014–2020 in ). An equivalent comparison of DWF with observations in the eastern SPG is impeded by the contribution of the Nordic Sea overflows in the Eulerian diapycnal overturning stream function calculated at OSNAP East. However, we note that our finding that the eastern SPG accounts for 9.0±1.7 Sv of the total along-stream DWF agrees closely with both the results presented in and previous estimates from observations and ocean reanalyses, which suggest that between 9–10 Sv of diapycnal transformation takes place in the Iceland and Irminger basins e.g..

Figure a shows that the amount of dense NADW formed along the path of the SPG varies substantially across seasonal to decadal timescales. We next explore whether the initial properties of an upper-limb water parcel on release across OSNAP East have any influence on the likelihood of forming dense NADW downstream.

Consistently with , we find that variability in the composition of the upper limb at OSNAP East is dominated by seasonality (Fig. b); upper-limb water parcels are, on average, lighter when crossing OSNAP East northward during autumn and denser when crossing during spring. However, Fig. b shows that DWF_SPG is not significantly correlated (p>0.05) with the volume-weighted average potential density (or with the conservative temperature or absolute salinity) of water parcels flowing northward across OSNAP East in the upper limb. Furthermore, we find no statistically significant relationship between annual means of DWF_SPG and upper-limb potential density (buoyancy), suggesting that along-stream DWF is not influenced by the arrival of upper-limb buoyancy anomalies into the eastern SPG on either seasonal or interannual timescales. In contrast, we find a strong positive correlation (r=0.86, p<0.01) between DWF_SPG and the total northward upper-limb transport flowing cyclonically from OSNAP East to OSNAP West (53° N), such that a larger volume transport of upper-limb waters into the eastern SPG results in greater NADW formation along-stream (Fig. c).

There are several important reasons why this enhanced DWF along the path of the SPG may not necessarily project onto Eulerian diapycnal overturning variability diagnosed along the full OSNAP array. Firstly, as we shall later see in Sect. 3.4, the formation of dense water occurs at many different locations around the SPG, meaning that there is a wide range of transit times for newly formed NADW to reach 53° N (Fig. a). Second, when calculating the Eulerian overturning along the full OSNAP array, the properties and volume fluxes of water parcels whose histories include dense-water formation in the Nordic Seas and the Arctic Ocean are convolved with those transformed within SPG. The thermohaline properties of water parcels enter this Eulerian overturning calculation because it involves integration within density classes.

To better understand the relationship between upper-limb volume transport and along-stream diapycnal transformation, we can express the total DWF along the path of the SPG as follows: 5DWFSPG(t)=κ(t)VSPG[UL](t), where VSPG[UL](t) represents the SPG upper-limb volume transport arriving at OSNAP East, and κ(t) represents the fraction of this upper-limb volume transport that will form NADW prior to reaching OSNAP West. We recall that the time t refers to the shared time when water parcels flow northward across OSNAP East and not the time at which they subsequently form NADW downstream. Furthermore, by decomposing each term into its steady and fluctuating components (i.e. κ(t)=κ‾+κ′(t) and VSPG[UL](t)=V‾SPG[UL]+VSPG[UL]′(t)), we can clearly see that variations in DWF_SPG are potentially due to a complex combination of changes in the amount of upper-limb water flowing northward across OSNAP East (VSPG[UL]′(t)) and changes in the efficiency with which water parcels are transferred from the upper to the lower limb along-stream( κ′(t)): 6DWFSPG(t)=κ‾V‾SPG[UL]+κ‾VSPG[UL]′(t)+κ′(t)V‾SPG[UL]+κ′(t)VSPG[UL]′(t).

Surprisingly, Fig. c suggests that the efficiency of along-stream diapycnal transformation κ′(t) is not the rate-limiting factor governing DWF along the path of the SPG. Instead, variations in DWF_SPG are proportional to the amount of upper-limb water imported into the eastern SPG via the branches of the NAC (i.e. DWFSPG(t)∝VSPG[UL]′(t)). This implies that along-stream diapycnal transformation is sufficient to transfer a steady fraction κ‾ of upper-limb water parcels into the lower limb, irrespective of their initial thermohaline properties on their northward crossing of OSNAP East. Furthermore, the SPG upper-limb volume transport is also strongly correlated with the total volume transport along the path of the SPG (r=0.97, p<0.01), indicating that DWF_SPG is closely related to the overall strength of the SPG circulation.

Since we have shown that DWF along the path of the SPG is proportional to the upper-limb volume transport imported into the eastern SPNA, next, we develop a simple linear model to predict the amount of dense NADW formed along-stream. By assuming that the efficiency of water mass transformation from the upper to the lower limb is time-independent (i.e. κ=κ‾), we can formulate a linear model for DWF_SPG as follows: 7DWFSPG(t)=κ‾VSPG[UL](t)+ϵ(t), where κ‾ is the constant fraction of the upper-limb volume transport which forms NADW along-stream, and ϵ(t) represents the residual error, which is given by 8ϵ(t)=κ′(t)V‾SPG[UL]+κ′(t)VSPG[UL]′(t). We find that κ‾=0.66, implying that, on average, 66 % of upper-limb waters flowing northward across OSNAP East are transferred into the lower limb prior to their southward crossing of OSNAP West (53° N). Figure a shows the strong predictive skill of the linear model on both monthly (RMSE = 1.1 Sv) and interannual (RMSE = 0.8 Sv) timescales, accounting for 74% and 68% of the variance in monthly and interannual (12-month running-mean filtered) DWF, respectively.

To better understand the sources of error in our linear model, we decompose the residual DWF ϵ(t) into its two components in Fig. b. We find that the residual DWF is almost exclusively explained by fluctuations in the efficiency of along-stream diapycnal transformation from the upper to the lower limb acting on the time mean volume transport of the SPG upper limb (κ′(t)V‾SPG[UL]). More specifically, the linear model overestimates the amount of dense NADW formed during the late 1970s and mid-1980s, indicating that the time-independent efficiency of diapycnal transformation of the linear model is too large during these periods (i.e. κ‾>κ(t)). In contrast, during the early and late 2000s, the efficiency of transformation is slightly underestimated (i.e. κ‾<κ(t)), resulting in an underestimation of the DWF downstream. Despite these differences, the high predictive skill of the linear model, especially on interannual to decadal timescales, suggests that changes in diapycnal transformation efficiency play a secondary role in governing variations in DWF_SPG when compared to variability in the upper-limb transport imported into the eastern SPG.

Given that κ‾=66 % of the upper-limb waters arriving across OSNAP form dense NADW along the path of the SPG, we next consider what happens to the remaining (1-κ‾)=34 % of upper-limb waters which do not form dense NADW before crossing OSNAP West at 53° N. Of the 6.4±1.7 Sv of upper-limb water which does not form dense NADW along the path of the SPG, we find that 1.5±0.5 Sv becomes lighter through entrainment into the fresh Labrador Coastal Current. Meanwhile, the majority of outstanding upper-limb transport (5.0±1.4 Sv) becomes denser but not dense enough to be transferred into the lower limb on crossing OSNAP West via the Labrador Current. To determine the fate of these denser water parcels remaining in the upper limb at 53° N, we extend our original Lagrangian experiment by continuing to track upper-limb water parcels after they cross the OSNAP West section. We find that almost all of the denser upper-limb water parcels (94 %) are either transformed into dense NADW south of the OSNAP West section or return to OSNAP East via the NAC to continue circulating around the SPG. Thus, of the total upper-limb transport imported into the eastern SPG, we would expect that, on average, almost 92.5 % will form dense NADW during one or more additional circuits of the SPG, whereas 7.5 % will join the fresh, estuarine circulation confined to the shelves of the SPNA.

We have demonstrated that the total DWF along the path of the SPG can be skilfully predicted with knowledge of only the northward upper-limb transport, which flows cyclonically around the SPG, and a time-independent parameter κ‾, representing the efficiency of diapycnal transformation along-stream.

Figure  reveals that there are, in fact, two distinct pathways by which dense water is formed along the path of the SPG. By decomposing DWF_SPG into the separate contributions made by the NAC branches flowing northward in the Iceland Basin and in the Rockall Trough (Fig. a), we find that upper-limb water parcels sourced from the Iceland Basin (DWF_IB) account for almost three-quarters (9.3±1.8 Sv) of the time mean DWF_SPG and 88 % of its variance on interannual timescales (Fig. b). This contrasts with upper-limb water parcels flowing northward in the Rockall Trough, which account for 3.4±0.7 Sv (DWF_RT) of along-stream DWF and around 31 % of the interannual variability in DWF_SPG. These differences in along-stream DWF are partly explained by the larger northward transport entering the Iceland Basin across OSNAP East (21.2±4.0 Sv) compared with the Rockall Trough (3.9±0.8 Sv in Fig. c). However, this is far from the complete picture, given that these two dense-water pathways are also characterised by distinct modes of diapycnal transformation (Fig. c and d), resulting in markedly different efficiencies in the transformation of water parcels from the upper to the lower limb.

We find that 59 % (κ‾IB=0.59, Fig. ) of upper-limb waters entering the Iceland Basin via the northern and central branches of the NAC form upper NADW downstream (σ‾DWF<σ53°N<27.80 kg m⁻³). Consistently with the dominant Lagrangian overturning pathway identified in , we find that upper-limb water parcels undergo progressive diapycnal transformation along-stream (Figs. a and c). In contrast, practically all (κ‾RT=0.97, Fig. ) of the upper-limb waters arriving in the subsurface in the Rockall Trough form dense lower NADW (σ53°N>27.80 kg m⁻³) by intense, localised diapycnal transformation near the exit of the Faroe-Bank Channel (Fig. d). This finding is consistent with previous studies e.g., which identify a “short-cut” pathway for subtropical-origin waters to penetrate the deep ocean on sub-decadal timescales by diapycnal mixing with overflow waters south of the Iceland–Faroe Ridge. The clear distinction between the character of dense water formed along these two pathways is evident from the two peaks in the conservative temperature distribution of SPG water parcels on their northward crossing of OSNAP West via the WGC in Fig. c.

Concordant with our earlier analysis in Sect. 3.2, Fig.  c and d show that potential density (buoyancy) anomalies conveyed by upper-limb water parcels arriving in both the Iceland Basin and the Rockall Trough are strongly damped along-stream. This increasing homogeneity of water parcel properties on reaching 53° N is particularly evident in the Iceland Basin (Fig. c), where we find that variations in the average potential density of upper-limb water parcels can only explain around 30 % of their downstream variability at 53^∘N (i.e. r(σIB,σ53°N)=0.56, p<0.01).

We have seen that the amount of dense water formed along the path of the SPG exhibits substantial variations on decadal timescales (Fig. a), which principally result from changes in the transport of upper-limb water arriving across OSNAP East via the branches of the NAC. More specifically, we find that DWF_SPG transitions from a relatively strong period between 1975–1987 (13.7±2.0 Sv) to a weaker, less variable period extending from 2000 to 2012 (12.1±1.5 Sv; see Fig. b). Since the amount of upper-limb water flowing northward in the NAC is also strongly correlated with the total volume transport circulating around the SPG, next, we investigate the mechanisms responsible for generating variability in the strength of the SPG and, hence, DWF on decadal to multi-decadal timescales.

Previous numerical modelling studies have highlighted the important role of localised surface buoyancy forcing, driven by low-frequency changes in the NAO, in modulating decadal variability in the subpolar ocean circulation . Consistently with the mechanisms proposed in these studies, we find that the generation of subsurface density anomalies and the densification of the AMOC lower limb are both important precursors to sustained positive anomalies in DWF along the path of the SPG. In particular, Fig. a and b show that persistent positive phases of the NAO during the mid-1980s and early 1990s were responsible for enhanced surface heat loss and, therefore, an intensification in deep convection in the SPG interior. This resulted in anomalously strong surface-forced water mass transformation in the LSW density range (i.e. σ2>37.0 kg m⁻³ in Fig. b), which increased the thickness of the LSW layer in the central Labrador and western Irminger seas (Fig. c). The densification of the SPG interior also manifests at the surface through a depression in the sea surface height (SSH) field (see Fig. d), which induces a delayed spin-up of the SPG circulation by steepening the SSH gradient across the basin . In agreement with recent studies , we find that SSH (density) anomalies in the Irminger Sea interior play an important role in determining the northward geostrophic transport of the upper limb by modulating the pressure gradient across the NAC. Specifically, Fig. e shows that the stronger upper-limb transport arriving in the Iceland Basin between 1975–1987 is associated with a period of anomalously low sea surface heights in the Irminger Sea interior, whereas elevated sea surface heights are concomitant with the weaker upper-limb transport recorded during 2000–2012 (Fig. d).

To further demonstrate that multi-decadal variations in the upper-limb transport entering the Iceland Basin are concordant with low-frequency changes in SPG dynamics, Fig. f shows the average transit times taken for upper-limb water parcels to circulate around the SPG. We can clearly see that the greater upper-limb volume transport across OSNAP East during 1975–1987 coincides with a faster SPG circulation. Meanwhile, during 2000–2012, the slower SPG circulation is responsible for the weaker upper-limb transport arriving in the NAC. Finally, since we have already shown that DWF along the path of the SPG depends linearly on the upper-limb transport flowing northward across OSNAP East, Fig. f shows that multi-decadal changes in SPG DWF are largely determined by the response of the gyre circulation to remote (i.e. Labrador Sea) surface buoyancy forcing. The strong interannual variability superimposed on this multi-decadal variability in DWF likely reflects the faster wind-driven response of the SPG circulation to changes in the NAO e.g.. For example, show that wind-stress-curl-induced variations in the transport of the NAC branches arriving in the Iceland Basin and the Rockall Trough play an important role in driving interannual variability in the upper-limb transport across OSNAP East.

In summary, we have shown that decadal surface buoyancy forcing anomalies in the central Labrador and Irminger seas can remotely influence NADW formation taking place along the path of the SPG by modulating the strength of the SPG circulation and hence the availability of upper-limb waters in an eddy-rich ocean hindcast.

In Sect. 3.3, we demonstrated that DWF along the boundary current of the SPG can be skilfully predicted using a simple linear model in which a constant fraction κ‾=66 % of the available upper-limb volume transport is transformed into NADW during each circuit of the SPG. We have seen that one interpretation of κ‾ is a measure of the efficiency of diapycnal transformation from the upper to the lower limb. However, this can also be conceptualised as a measure of the relative alignment between the gyre and diapycnal overturning circulations at subpolar latitudes. To illustrate this, we can consider the idealised case in which the SPG and overturning circulations are perfectly aligned (i.e. κ‾=100 %), such that all of the upper-limb waters flowing northward in the NAC are transformed into lower-limb waters on returning southward in the Labrador Current. In this case, the volume transport flowing around the SPG would be equivalent to the DWF along-stream, and we could quantify the subpolar overturning by simply measuring the strength of the SPG circulation via the total volume transport advected in the branches of the NAC. However, we know from observations that the Labrador Current transports both upper- and lower-limb waters southward see Fig. 4 in, indicating that, in reality, the SPG circulation projects onto a diapycnal overturning cell (and thus the formation of NADW) with a time-evolving efficiency characterised by κ(t)<100 %.

Since dense water is also formed via progressive diapycnal transformation along the boundary current encircling the Nordic Seas e.g., it would be interesting to extend the Lagrangian methodology introduced in this study to establish if a similar linear relationship can be found between the northward transport of Atlantic Waters across the Greenland–Scotland Ridge and the along-stream formation of lower NADW (i.e. DWFNS=κ‾NSVAW). Previous studies have estimated that approximately 70 %–75 % of the Atlantic Water inflow to the Nordic Seas participates in the thermohaline circulation to form dense overflow waters , suggesting that κ‾NS≈0.7–0.75.

We have also seen that the likelihood of downstream transformation into the lower limb is strongly dependent on where upper-limb waters arrive in the eastern SPG. In particular, we showed that upper-limb waters arriving in the subsurface in the Rockall Trough are almost guaranteed (κ‾RT=97 %) to form dense lower NADW via vigorous mixing with ISOW, whereas only κ‾IB=59 % of upper-limb waters arriving in the Iceland Basin will form upper NADW along-stream. In agreement with the conclusion of , we found that the amount of dense water formed along each pathway is independent of the initial properties of water parcels arriving in the NAC on seasonal to interannual timescales, indicating that upper-limb potential density anomalies do not feed back onto the strength of DWF in this eddy-rich ocean model.

To better understand this decoupling between the strength of dense-water formation and upper-ocean properties in the SPNA, we consider the length scales on which upper-limb thermohaline anomalies evolve along their path from the Iceland Basin to the western subpolar North Atlantic. For an idealised boundary current which exchanges buoyancy with both the overlying atmosphere and the basin interior (Fig. a), temperature and salinity adjust exponentially along-stream toward equilibrium values . The cyclonic boundary current will therefore reach an equilibrium density provided that its length exceeds the adjustment length scales with respect to both temperature and salinity. Following and assuming that the inflow into the Iceland Basin is ∼200 km wide, with a temperature relaxation coefficient of 80 W m⁻² and an exchange rate between the boundary current and basin interior of M=2.0m² s⁻¹, we estimate the adjustment length scales for the upper-limb waters sourced from the Iceland Basin to be approximately 2400 and 7100 km for temperature and salinity, respectively. Note that, in the case of salinity, this estimate is an upper limit because we have assumed that the along-stream addition of freshwater F is small compared with the freshwater exchanged with the basin interior. Comparing these length scales with the typical path length of upper-limb water parcel trajectories travelling from the Iceland Basin to OSNAP West at 53° N (approximately 6000 km), we expect that the boundary current is fully adjusted in terms of temperature but not in terms of salinity.

The temperature of water reaching 53° N is therefore virtually independent of both the volume transport and initial temperature of upper-limb waters flowing northward across OSNAP East, whereas some signature of salinity anomalies arriving in the Iceland Basin may persist. Figure b shows that upper-limb potential density anomalies arriving in the Iceland Basin are dominated by temperature rather than salinity fluctuations on monthly to decadal timescales (i.e. r(-αθIB′,σIB′)=0.82, p<0.01). This dominance of thermal anomalies in the upper limb, combined with their efficient damping by air–sea fluxes and mixing during their transit of the gyre, explains both the strong decoupling between decadal changes in upper-ocean properties and SPG DWF e.g. and the narrow potential density range of upper NADW in observations 27.68–27.74 kg m⁻³;. On longer, centennial timescales, it is possible that the persistence of salinity anomalies will become the dominant control on NADW formation (via the salt advection feedback) as highlighted in previous coupled climate modelling studies e.g..

The use of monthly mean model velocity and tracer fields to evaluate Lagrangian water parcel trajectories is an important limitation of this study, albeit one that is necessary to make our calculations tractable. This is because we are likely to underestimate the dispersive nature of Lagrangian trajectories and, hence, the volume exchanges between the boundary current and the interior of the Labrador and Irminger seas . By using daily or 5 d mean velocity and tracer fields, we would expect shorter circulation times and greater boundary–interior exchanges along the path of the SPG . However, the effects of eddy exchange between the boundary current and the basin interior are implicitly captured in the tracer fields, sampled along water parcel trajectories , and are therefore included in our estimates of along-stream DWF.

A further implication of the strong decoupling between the properties of upper-limb waters arriving in the eastern SPG and the strength of NADW formation is that potential density anomalies advected along the path of the SPG do not play an active role in driving subpolar overturning variability on seasonal to decadal timescales since they are unable to persist downstream. This supports the conclusion of that, although decadal AMOC variability can generate upper-ocean thermohaline anomalies, these anomalies are not responsible for generating decadal subpolar overturning variability themselves. Instead, decadal variations in the DWF along the path of the SPG are driven remotely by surface buoyancy forcing localised in the central Labrador and Irminger seas in this model.

Concordant with recent studies e.g., we find that enhanced surface buoyancy loss during persistent positive phases of the NAO drives a geostrophic increase in the northward upper-limb transport into the Iceland Basin, which is consistent with an intensification of the cyclonic SPG circulation in response to the densification of the Irminger Sea interior. Since along-stream DWF is proportional to the amount of upper-limb water flowing northward across OSNAP East, we might anticipate that this spin-up of the SPG circulation would directly translate into an increase in the strength of the basin-scale diapycnal overturning circulation. However, in order for DWF to imprint onto the Eulerian overturning at lower latitudes, lower-limb waters must also be exported out of the SPG and into the subtropical North Atlantic . By comparing the long-term mean subpolar AMOC strength (∼16 Sv) to the typical southward transport of NADW at 53° N ∼30 Sv;, estimate that only around half of all NADW is exported to the subtropics, whilst the remainder recirculates in the SPG. Although it is beyond the scope of this study, it would be interesting to investigate whether decadal changes in DWF can influence the rate at which NADW is exported to the subtropical North Atlantic and, hence, act to modulate the advective propagation of overturning anomalies downstream.

We also recognise that model biases may play a role in amplifying the relationship between remote surface buoyancy forcing and DWF along the path of the SPG in this ocean model. For example, the larger-than-observed lower NADW formation (>27.75 kg m⁻³ in Fig. b) north of OSNAP West in this hindcast is indicative of excessive Labrador Sea deep convection (a well-established bias in eddy-rich models; ), which would enable the deeper penetration and greater persistence of density anomalies originating from surface buoyancy forcing .