Observation-based estimates of volume, heat and freshwater exchanges between the subpolar North Atlantic interior, its boundary currents and the atmosphere

The Atlantic Meridional Overturning Circulation (AMOC) transports heat and salt between the tropical Atlantic and Arctic Oceans. The interior of the North Atlantic Subpolar Gyre (SPG) is responsible for the much of the water mass transformation in the AMOC, and the export of this water to intensified boundary currents is crucial 10 for projecting air-sea interaction onto the strength of the AMOC. However, the magnitude and location of exchange between the SPG and the boundary remains unclear. We present a novel climatology of the SPG boundary using quality controlled CTD and Argo hydrography, defining the SPG interior as the oceanic region bounded by 47° N and the 1000m isobath. From this hydrography we find geostrophic flow out of the SPG around much of the boundary with minimal seasonality. The horizontal density gradient is reversed around 15 West Greenland, where the geostrophic flow is into the SPG. Surface Ekman forcing drives net flow out of the SPG in all seasons with pronounced seasonality, varying between 2.45 ± 0.73 Sv in the summer and 7.70 ± 2.90 Sv in the winter. We estimate heat advected into the SPG to be between 0.14 ± 0.05 PW in the winter and 0.23 ± 0.05 PW in the spring, and freshwater advected out of the SPG to be between 0.07 ± 0.02 Sv in the summer and 0.15 ± 0.02 Sv in the autumn. These estimates approximately balance the surface heat and freshwater fluxes 20 over the SPG domain. Overturning in the SPG varies seasonally, with a minimum of 6.20 ± 1.40 Sv in the autumn and a maximum of 10.17 ± 1.91 Sv in the spring, with surface Ekman the most likely mediator of this variability. The density of maximum overturning is at 27.30 kgm -3 , with a second, smaller maximum at 27.54 kgm -3 . Upper waters (σ 0 < 27.30 kgm -3 ) are transformed in the interior then exported as either intermediate water (27.30-27.54 kgm -3 ) in the North Atlantic Current (NAC) or as dense water (σ 0 > 27.54 kgm -3 ) exiting to 25 the south. Our results support the present consensus that the formation and pre-conditioning of subpolar Mode Water in the north-eastern Atlantic is a key determinant of AMOC strength.


Introduction
The AMOC (Atlantic Meridional Overturning Circulation) is the zonally integrated system of currents transporting heat and salt between the South Atlantic and the Arctic Mediterranean. It is a key component of the 30 global thermohaline circulation, transporting approximately 25% of the global ocean-atmosphere heat transport.
To evaluate the importance of these boundary processes to the SPG AMOC, we calculate a budget for the exchange of water between the SPG interior and boundary/shelf regions, and through a zonal transatlantic 75 section at 47° N (Fig. 1). We construct a new temperature-salinity (TS) climatology along the 1000 m depth contour of the SPG and closing at 47° N (12,000 km path, Fig. 1) covering the Argo era (2000 onwards).
The 1000 m isobath was selected for numerous reasons. Firstly, the 1000 m contour encircles the key features of the SPG, including the Rockall, Iceland, Irminger and Labrador Basins, partitioning basin interior processes from shelf sea processes. Secondly, at 47 °N the simulated maximum overturning in depth space is roughly 80 1000 m depth (Hirschi et al., 2020), so this choice allows us to approximately distinguish upper and lower limb processes. Thirdly, Argo trajectories allow us to estimate currents at 1000 m depth which we later incorporate into our analysis.
We quantify regionally and in density space where the volume transports into and out of the SPG interior occur.
We then validate and extend our analysis using the VIKING20X model (Biastoch et al., 2021;Fox et al., 2022), 85 which, when combined with our new climatology provides novel insights into the functioning of the AMOC in the SPG. We present the overturning, heat and freshwater fluxes associated with the observed water properties and transports. Finally, we investigate which processes determine how volume continuity is maintained in the SPG and summarise in a schematic (Fig. 12).

Materials and methods
Here we describe the datasets and methods used for the core analyses in the study. Information on other datasets used is provided in Supplementary Materials S2.

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We construct our TS climatology along a narrow strip defined by the 1000 m isobath around the basin of the SPG. CTD and Argo profile data from post-2000 (Argo era) were downloaded from the WOD on 03/09/2019 (Boyer et al., 2018). The isobath was smoothed using a 100 km along-contour bracket to remove undesired complexity in the contour and profiles of conservative temperature ( ) and absolute salinity ( ) were gathered between 0 and 75 km offshore as shown in Fig. 2. We required data coverage between surface and 1000 m so 105 profiles with poor vertical resolution (< 50 observations), and those sampling only part of the water column, were excluded. Further QC steps were performed and are detailed in Supplementary Materials S1.

Gridding of profile data
Profiles were first separated into four seasons: Winter (JFM); Spring (AMJ); Summer (JAS); and Autumn (OND). They were gridded vertically in 20 dbar pressure bins and then horizontally. For the horizontal gridding 120 we used cells spaced at regular 150 km intervals and employed a variable search radius centred on each cell.

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The along-slope property gradients were weaker and decorrelation scales larger (e.g. Davis, 1998) than those in the across-slope direction, so we considered a larger grid size and search radius in the along-slope direction to be appropriate. For a given grid cell, an initial search radius of 150 km was used, and the number of profiles found in this radius of a cell evaluated. If 75 raw profiles were not found, this search radius was incrementally 125 expanded up to a maximum of 300 km. Thus, most profiles are used in more than one grid cell. Most grid cells are populated using the minimum search radius (150 km), but it was necessary to expand the search radius up to the maximum 300 km to achieve good coverage in 5 % of cells during the summer, rising to 22 % during the autumn. No centre-weighting was attempted. Profiles were averaged on pressure levels to create the gridded product of ϴ and S. A schematic of the gridding workflow is provided in Supplementary Materials S1. 130 2.3. EN4 data at 47° N We use temperature and salinity data from the Met Office EN4 product (Good et al., 2013) for the zonal section to close the boundary at a latitude of 47° N. We considered this to be the most appropriate source of data for the zonal transect: first, whilst our boundary dataset benefitted from an 'along-boundary' gridding methodology, the zonal transect is aligned to EN4's grid, so the benefits of independently gridding the profile data are largely 135 negated. Second, EN4's climatology provides coverage deeper than 2000 m in the North Atlantic, a region where observational data is sparse due to the depth limit of most Argo floats.
We found excellent agreement between gridded profiles and EN4 grid cells in <2000 m waters, and no unusual horizontal gradient in properties (which could translate into an anomalous geostrophic transport) between the end of the boundary dataset and the beginning of the EN4 transect. The location of WOD profile data and EN4 140 grid cells is shown in Fig. 2. We found that below 1000 m, geostrophic velocities calculated from EN4 data overestimated the strength of the Gulf Stream and underestimated the Deep Western Boundary Current and other southward flows across 47° N due to data coverage limitations in the abyssal ocean. In Section 2.4.5 we discuss this weakness and the steps taken to limit its impact on the results.

Geostrophic velocities
We first compute the geostrophic shear between each gridded station, and between the final station and the first to complete the loop. Note that when integrating to the same depth around the loop, the net transport between the interior and exterior of the SPG is constrained to be near-zero because there is no net change in dynamic height around the closed circuit. A small residual transport remains because of variations in the Coriolis 150 parameter f as the latitude of the stations changes around the boundary (the 'beta effect').
When computing overturning transport and heat and freshwater fluxes in Sect. 3.4 and 3.5, we require a measure of transports to the seabed so that volume is conserved on completion of the boundary loop. Geostrophic velocities across the >1000 m depth of the 47° N transect result in a net gain in volume by the SPG interior, so we enforce the conservation of volume using a small negative reference velocity applied to this region. The

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EN4 dataset is known to poorly resolve the deep western boundary current in this region (Fraser and Cunningham, 2021) which explains some of this imbalance. The implementation of this reference velocity, and its impact on computed values for fluxes and overturning is discussed in Sect. 2.4.5. 6 Dynamic height at each profile is computed relative to the surface and referenced to the gridded Absolute Dynamic Topography (ADT) derived from satellite altimetry (Eq. (1)). We consider the use of satellite SSH-160 derived velocities to be a robust reference method for our application given the large spatial scales and the long temporal averages associated with the study. The gridded ADT data were temporally averaged over the same periods as the profile data coverage (2000-2019, split into four seasons) and interpolated values extracted at the station locations. They were then smoothed using a 5-point running average to mimic the smoothing inherent in the hydrographic gridding process.

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Where Φ is the dynamic height relative to the sea surface, calculated as the integral of the specific volume anomaly from the gridded pressure to the surface. is the satellite-derived ADT and g is acceleration due to gravity. The time-mean geostrophic velocity assigned to locations mid-way between hydrography stations is computed from: where x is the (anti-clockwise) distance along the 1000 m contour.

Geostrophic transports
Transports for each grid cell ( ) were computed by integrating Eq.
(2) over the cross-sectional area between each station, and between adjacent pressure levels (the 20 dbar pressure intervals are taken to 175 approximate 20 m): The vertically integrated transport between 0 and 1000 m can then be computed by summing the transports of cells at each station. Further, the accumulated transport around the basin can be obtained using a horizontal integral. We estimate statistical uncertainties based on the variability inherent in the datasets contributing to the 180 study. This is accomplished by repeating the analysis multiple times with the gridded TS profiles randomly perturbed. The perturbation of each gridded value is scaled by the standard deviation of profile data contributing to that grid cell, thus giving an indication of the sensitivity of the conclusions to the scatter of 'raw' profiles. For the EN4 transect, the uncertainty is supplied with the gridded variables, and we use this to scale the perturbations. The satellite altimetry has a large standard deviation on day or month timescales. As our analysis 185 spans two decades, we considered it appropriate to first calculate annual means of ADT, then compute the standard deviation of these annual means for the uncertainty estimate. The ADT accounts for about 60 % of the uncertainty for the heat and freshwater fluxes, and about 30 % of the uncertainty for the overturning results.
The analysis was repeated 100 times with the boundary climatology, altimetry, and surface Ekman transports CTDs are typically accurate to ± 0.001 °C and ± 0.002 psu, and delayed-mode calibrated Argo floats are accurate to ± 0.005 °C and ± 0.01 psu. Errors in SSH in the gridded ADT product are typically around 1-2 cm in the North Atlantic but are up to 7 cm in the Gulf Stream. As these measurement errors are generally not systematic, the long averaging periods in our analysis mean that they make a negligible contribution to the total 195 uncertainties.
At some locations the boundary contour is by necessity oriented along the boundary current, which implies the along-contour isopycnal slope is small compared to the across-contour slope in these regions. As such, the across-contour geostrophic transports for these grid cells will be small residuals of the along-contour transports.
We would expect these regions of the boundary product to be particularly sensitive to temporal or spatial biases 200 in the sampling. However, as we accumulate the geostrophic transports around the basin the distances over which the along-contour isopycnal slope is evaluated are large relative to the across-contour slope. Therefore, while along-contour flows may contaminate the signal for individual grid cells, they should have minimal impact on the accumulated transports. The uncertainties arising from our perturbation experiments provides some insight into the sensitivity of the results to local sampling errors (e.g. Fig. 5).

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We investigated the gridded ANDRO dataset as a complementary source of 1000 m velocities but found that the small across-slope component of flow described above, coupled with the proximity of the continental slope made the product unsuitable for our investigation.

Surface Ekman transports
Wind stress data were obtained from the ECMWF ERA5 reanalysis product (Hersbach et al., 2020). The wind

Model-derived transports in VIKING20X
We recreate the boundary transect in VIKING20X to support the observational analysis and help diagnose the transports and fluxes which may not be resolved by geostrophic or surface Ekman calculations. Output of the VIKING20X-JRA55-short model hindcast (Biastoch et al., 2021) is used to compute transports into the SPG.

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VIKING20X is a 0.05° ice/ocean model of the Atlantic Ocean (33.5° S to ∼65° N) nested within a 0.25 degree global ice/ocean model. The run used here is driven from 1980-present using JRA55-do atmospheric forcing and runoff (Tsujino et al., 2018). In the vertical, VIKING20X uses 46 geopotential z-levels with layer thicknesses from 6 m at the surface gradually increasing to ∼250 m in the deepest layers. Bottom topography is represented by partially filled cells allowing for an improved representation of the bathymetry (Barnier et al., 2009). In the 225 SPNA VIKING20X has horizontal resolution of 3-4 km. Hindcasts of the past 50-60 years in this eddy-rich configuration show that it realistically simulates the large-scale horizontal circulation, the distribution of the 8 mesoscale, overflow and convective processes, and the representation of regional current systems in the North and South Atlantic (see Biastoch et al., 2021 for full details).
To preserve the volume conservation in VIKING20X, rather than mimicking the observational data sampling

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The stepped model topography results in two potential approaches for estimating geostrophic transports. The first stops strictly at 1000 m but leaves a small gap beneath over complex bathymetry. This approach obeys the beta constraint on geostrophic flow, so is most comparable to the observations but some 'leakage' below 1000 m on the boundary remains. The other approach extends to the bed around the boundary. This means that all across-boundary flow is captured, but the beta constraint on total geostrophic transport is slightly relaxed as 240 there is now an undulating bed with along-section pressure differences.  Heat and freshwater fluxes across the boundary were calculated as follows. Heat flux ( ) across each grid cell 265 is defined as: Where is the nominal potential density of seawater, is the specific heat of seawater, ( , ) is the sum of the geostrophic (Eq. (1)) and Ekman velocities (Sect. 3.2.2) perpendicular to the section, ( , ) is the 270 conservative temperature and ̅ , the reference temperature, is the mean temperature for the full-depth SPG interior (4.03 °C). Following Lozier et al., (2019) we use a value of 4.1 x 10 6 Jm -3 K -1 for .
Freshwater flux ( ) is defined as: Where ( , ) is the absolute salinity of a grid cell, ̅ , the reference salinity, is the mean salinity for the full-275 depth SPG interior (35.14 g kg -3 ). As before the convention for and is positive into the SPG.
We estimate the average surface freshwater and heat fluxes for 2000-2019 using ERA5 monthly means (Hersbach et al., 2020). For freshwater we compute evaporationprecipitation for each grid cell, then integrate over the total surface area enclosed by the 1000 m contour and 47° N (4.6x10 6 km 2 ) using an area-weighted mean. We calculate downward surface heat flux as the sum of sensible, latent, shortwave, and longwave heat 280 fluxes. Surface flux errors are estimated as the standard error of the annually averaged timeseries for the summed components following Li et al., (2021a).

Eddy Kinetic Energy and boundary topography
Eddy kinetic energy (EKE) was calculated from satellite ADT for the period of study using where ′ and ′ are the high-frequency components (150-day highpass filtered) of the unsmoothed surface geostrophic velocity components along the SPG boundary contour. The overbar denotes seasonal averaging to form climatologies.
Seabed slope angle was calculated from 30 arc-second GEBCO bathymetry on the native grid (GEBCO compilation group 2019) then interpolated onto ~1 km horizontal resolution rendition of the 1000 m depth 290 contour (derived from the same GEBCO data set). A 480-point moving mean was applied along contour. Slope is a scale-dependent quantity: at the visual map scale a 480-point running mean does not equate to a 480km straight line moving average since at 1 km scale the 1000 m contour is highly irregular.

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The cyclonic evolution of water properties around the closed SPG boundary is shown in Fig. 3, and a full-depth section across 47 N is shown in Fig. 4. These figures depict the annual average water properties; seasonal anomalies are supplied in Supplementary Materials S3.
In general, the density at a given depth level increases with progress along the 1000 m isobath. By the thermal wind relation, the geostrophic shear is therefore typically negative (i.e. increasing density in a cyclonic direction 300 driving export across the boundary out from the interior). Between the boundary start near the Bay of Biscay and the Faroe-Shetland Channel (FSC) the water column is thermally stratified and this controls the density distribution (salinity changes only gradually with depth). Between 1000 and 2000 km (European Shelf), the along section density gradient at a fixed depth is positive shallower than 750 dbar and is negative deeper than 750 dbar. This is consistent with the expected density evolution of the adjacent slope current in this region 305 (Huthnance et al., 2022). The horizontal density gradient increases at the entrance to the FSC. Between here and Iceland, a persistent negative geostrophic flow, strongest near the surface, is associated with a thermally driven positive density gradient. Between Iceland and Cape Farewell, further cooling, freshening and densification occurs throughout the water column. Geostrophic flow is largely out of the SPG shallower than 500 dbar, and into the interior below 500 dbar. This implies an export of light surface waters from the SPG, 310 their external conversion to denser classes, and their re-import at depth. We do not see the very cold (< 3 °C) and dense (> 27.8 kgm -3 ) waters suggestive of the Faroe Bank Channel overflow or the Denmark Strait Overflow (DSO) at their expected locations along the boundary (approximately 3000 and 5000 km respectively, Johnson et al., 2017;Mastropole et al., 2017). We return to this point and discuss the significance of the overflows later in the manuscript.

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Cape Farewell marks the beginning of a pronounced change to the water column structure. West of Cape Farewell (i.e. along West Greenland) there are positive geostrophic flows associated with the introduction of a cold, fresh, low density surface layer shallower than 250 dbar. This change in water properties may be associated with offshore fluxes of freshwater from the Greenland shelf into the Labrador Sea interior near Cape Farewell (Lin et al., 2018) and farther north where the WGC becomes unstable (Fratantoni, 2001;Prater, 2002).

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The positive geostrophic flow may also partly result from the WGC moving into deeper water and thus crossing our perimeter contour in this region. There is also a negative horizontal density gradient below 250 dbar, but this is driven by an increase in temperature with progress around the gyre. In the north-western Labrador Sea, the trend towards increasing density is resumed, this time driven by further cooling below 250 dbar.
Geostrophic flow in the north-western Labrador Sea is into the SPG and is greatest at depth. The influence of   shelf and shelf edge (Lavender et al., 2000). Note that it is not possible to exclude the boundary currents entirely from the SPG by choosing a deeper boundary reference contour. A large portion of flow in the WGC and Labrador Current occurs offshore of the 2000 m isobath, and the choice of a deeper contour has other drawbacks, as discussed in Section 1. At 53° N (the western OSNAP crossing) for example, the core of the Labrador Current is inshore of the 1000 m isobath but the southward flow extends 75-100 km offshore of the 375 1000 m isobath (e.g. Zantopp et al., 2017). This portion of the boundary current must exit the domain to the south and west. From about 7800km to west of the Gulf Stream sustained outflow results in a net export of 12 Sv, of which about half is onto the shelf (Fig. 1, Fig. 5a). The outflow through the Flemish Pass and around the Flemish Cap accounts for the remainder (Petrie and Buckley 1996).
Along 47° N east of the Gulf Stream inflow there is a narrower region of recirculating outflow, then a weak 380 inflow across most of the section to the east. The net cumulative transports into and out of the SPG return to near-zero on completion of the circuit, with a small positive residual in all seasons (+2.13 to +2.58 Sv) due to the beta effect. Cumulative geostrophic transports above 1000 m are shown in Table 1.
Seasonal transport variations are relatively small (Fig. 5b). Between the FSC and the western Irminger Sea (5500 km) autumn and winter transports out of the SPG are 1-2 Sv greater than spring and summer before 385 converging at Cape Farewell. Similarly, along the Labrador Seaboard autumn and winter transports out of the SPG tend to be greater than those in spring and summer but converge when crossing the Gulf Stream.

Surface Ekman transport perpendicular to boundary
Due to the prevalent cyclonic weather systems over the SPNA surface Ekman transport is generally directed out of the SPG, with winter exhibiting the largest transports and summer the weakest (Fig. 6). South-westerly winds in the north-eastern Atlantic result in net transports out of the SPG onto the continental shelf west of the British Isles. Between Scotland and Iceland there is little surface Ekman transport across the boundary, due mainly to 400 the prevailing surface Ekman transport being roughly parallel to the boundary contour rather than lower wind speed (e.g. Laurila et al., 2021). Conversely, very high transports out of the SPG off south-east Greenland are due both to energetic storm systems and to the boundary contour being approximately perpendicular to prevailing surface Ekman flow. There is strong seasonality off south-east Greenland, with cumulative transports varying from -0.5 Sv in the summer to -2 Sv in the winter. Off south-west Greenland there is net inflow into 405 the SPG, except in summer. This is the only location that sees seasonal sign reversal (+1 Sv in winter to -0.2 Sv in summer). While the Labrador Sea gains volume off south-west Greenland during the winter, between Cape Farewell and the OSNAP-West crossing at 8500 km there is a net loss of -

Bottom Ekman transport
Bottom Ekman transport is an essential dynamical feature of cyclonic ocean boundary (slope) currents 430 (Huthnance et al., 2020), and a significant transport mechanism from slope regions to adjacent ocean interior (Huthnance et al., 2022). Typical slope boundary current velocities range from a few to several 10s of cm s -1 .
We We make an approximate observation-based estimate of the bottom Ekman transport using the 1000 m drift characteristics of Argo floats contributing to the boundary dataset (Fig. 2b). The advection of floats around the SPG boundary is visible as diagonal stripes, particularly after 3000 km. We investigated the gridded ANDRO 435 dataset as a potential source of boundary current velocities but found that the proximity of the continental shelf made the interpolation scheme unsuitable in some areas. Instead, uUsing the temporal and spatial displacements of floats between successive profiles, we compute the average along-slope speed ̂ around the SPG boundary to be 8.5 cm s -1 (dashed red line, Fig. 2b).
We estimate the bottom Ekman transport into the SPG following theoretical arguments by Souza et al., (2001) 440 and Simpson and McCandliss, (2013). However, as there is a quadratic dependence of bottom stress on current speed, simply taking the mean along-slope speed of the floats will result in an underestimate of the bottom Ekman transport. To address this concern, we use the approach suggested by Zhai et al., (2012), in which a transport correction factor, , is computed given the magnitude of the variability as a fraction of the mean, α.
Here we take the variability to be the standard deviation of float speeds (7.5 cm s -1 ) so α has a value of 0.88.

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The bottom Ekman transport is then: Where β can be approximated as (1 + 2 ) = 1.77 (Zhai et al., 2012), is a bottom friction coefficient (taken as 0.0025 following Simpson and McCandliss, 2013), ̂ is the mean along-slope speed and is the local Coriolis parameter. As varies around the boundary we compute for each grid cell on the boundary and integrate 450 horizontally. This results in a total transport into the SPG of 2.5 Sv.
Given the large uncertainties associated with the observation-based bottom Ekman estimates we exclude this process in the transports contributing to the overturning and flux totals, however it is relevant to the discussion of the SPG volumetric budget. The potential contribution of bottom Ekman transport and other near-bed processes to the SPG volume budget is discussed in Sect. 4.4.

Transports perpendicular to the boundary in VIKING20X
The 20-year mean geostrophic volume transports into the SPG calculated from the VIKING20X model hydrography show broad agreement with the observation-based geostrophic transports at large spatial scales cross-boundary flow we are capturing. We can use the model results to look at details of the missing transports. Figure 7a shows two candidate processes: bottom Ekman layer frictional flows, and the remainder primarily driven by nonlinear and viscous processes. In Fig. 7b we examine the possible missing transports due to flows 20 beneath the base of our 1000 m contour and the bed (due to the observed climatology being on average offset from the continental slope, see Fig. 2). In VIKING20X this is achieved by integrating to the bed along the 1000 490 m contour, as opposed to using a strict 1000 m cutoff. The difference arises due to the stepped model topography and associated inability to follow the 1000m bathymetry precisely.
The results show that over most of the boundary the across-boundary flows are dominated by geostrophic flows (orange/dashed orange lines, Fig. 7a and b). The major exceptions are the deep overflow regions of the Denmark Strait (around 5000-5500 km), and, to a smaller extent, the Faroe Bank Channel overflow at around 3000 km.

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While these unobserved processes dominate the cross-boundary transports at two locations they account for the majority of the cross-boundary transport when integrated round the whole boundary above 1000 m (grey/dashed grey lines, Fig. 7a and b). We discuss this further in Sect. 4.5.

Ekmanbed Ekman). (b) Comparison between transports into the SPG in VIKING20X using a strict 1000 m cutoff, and integrating to the bed along the 1000 m contour (but still integrated to 1000 m across 47° N). The
difference is due to the stepped model topography and associated inability to follow the 1000m bathymetry 505 precisely.

Overturning in the Subpolar Gyre
Here we compute the density-space overturning circulation in the SPG using the sum of the observed geostrophic and surface Ekman fluxes. Note that in the context of this study, the term 'overturning' describes the transformation occurring within a closed contour, in contrast to studies computing overturning north of an 510 open section such as OSNAP. For this analysis it is necessary to integrate to the seabed across the 47° N transect so we apply a reference velocity below 1000 m on the 47° N transect to enforce the conservation of volume (Supplementary Materials S5). The full-depth transports are shown in Fig. 8. As the adjustment is applied to waters below 1000 m, it almost exclusively impacts lower limb flows, and is below the main features of the overturning stream function (Fig. 9).

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The full-depth transports in Fig. 8 are divided into upper, intermediate and lower layers based on density thresholds established using inflection points in the overturning stream function (Fig. 9). These density thresholds are also overlaid on the density and geostrophic velocity sections depicted in Fig. 3c

Advective fluxes
The SPG on average gains heat of 0.18 ± 0.05 PW via advection (Fig. 10, Table 3 (5)). There is some heat loss to the exterior between 0 and 1000 km due to outflow 24 combined with above average temperatures. There is very little seasonality in heat flux across the 1000 m 565 contour (0-9500 km).
Advection drives a net salinification of the SPG, with a net freshwater loss of -0.10 Sv. Freshwater flux is largely into the SPG up to 6500 km, driven by the net export of waters with salinity higher than the reference salinity. The NAC is responsible for the effective gain of 0.1 Sv of freshwater due to this effect. As for heat flux, there is little seasonality in freshwater flux around the boundary. An exception is off south-west 570 Greenland, where fresher upper waters during the winter (Fig. S2), in conjunction with increased surface Ekman transport ( Fig. 6)  water of higher salinity than the basin-mean ( ̅ , Eq. (6)).

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The local heat and freshwater fluxes and their signs depend on the reference values ̅ and ̅ used (Eq. (5) and (6)). For heat flux we use the mean temperature of the waters of the full-depth SPG interior enclosed by the boundary (4.03 °C). The heat fluxes thus have a physical meaning in that they show the level to which these waters warm or cool the SPG. Similarly, for freshwater flux we use the mean salinity of the full-depth SPG interior (35.14 g kg -3 ), thus showing the level to which the boundary fluxes freshen or salinize the SPG. As the 580 flux calculations use mass-balanced velocities, the net heat fluxes into the SPG (Table 3)  Spatially integrated (net) advective heat and freshwater fluxes into the SPG are shown in Table 3. Heat fluxes into the SPG range from 0.14 PW in winter to 0.23 PW in spring. Freshwater fluxes are negative in all seasons and are between -0.07 Sv (summer) and -0.15 Sv (autumn).

Surface heat and freshwater fluxes
In Table 3 we also show the seasonal and annual mean surface heat and freshwater fluxes derived from ERA5.
The seasonal range of surface heat fluxes is much larger than that of the advective fluxes; between -0.80 PW

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Steeply sloping margins are known to be rich in eddy activity (Spall andPickart 2000, Brüggemann andKatsman, 2019). It is conceivable therefore that eddy exchange of heat and freshwater may be significant contributors to SPG-boundary exchange. The slope angle of the SPG boundary and its relationship to the EKE along the 1000 m contour is shown in Fig. 11.
The spatial distribution of EKE along the 1000m contour appears relatively consistent between seasons but 605 during the autumn and winter EKE is about double that of spring and summer. EKE is greatest around Greenland and in the western Labrador Sea during all seasons, with the WGC values exceptionally high. The high EKE west of Greenland is consistent with previous studies (e.g., Fratantoni, 2001;Prater, 2002). A similar spatial structure emerges when examining the slope angle around the SPG boundary, with Fig. 11 showing the excellent agreement between the two parameters. Note that the extreme (>=20 °) slope west of Greenland 610 corresponds to the EKE maximum in the WGC.

Figure 11: Angle of continental slope (black) compared to EKE by region. Key locations around boundary
labelled as for Fig. 3, note x-axis excludes 47° N transect.

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An estimate of the diffusive heat flux between the interior and exterior of the SPG associated with eddy activity was made using satellite derived SST and surface geostrophic velocities and is detailed in Supplementary Materials S4. Heat is diffused out of the SPG along the 1000 m contour, and into the SPG along 47° N (Fig.   S3). A total of 0.0062 PW of heat energy enters the SPG via turbulent diffusion, roughly two orders of magnitude less than the contribution from advection so this process is not included in our heat budget. It was 620 not possible to estimate diffusive freshwater flux due to the lack of reliable satellite SSS observations.

Discussion
In this article we present the first comprehensive observational assessment of properties, transports and fluxes between the interior and exterior of the whole North Atlantic SPG. In conjunction with model data, we used this to identify the relative importance of processes driving fluxes across the boundary. Our observation-based 625 approach uses data from 2000 to 2019, so can be considered the present mean state of circulation on decadal timescales. By considering fluxes into and out of the SPG as a whole, this work provides a measure of which processes in the SPG interior contribute to the AMOC.

Overturning in the Subpolar Gyre
Here we discuss the overturning stream function for the boundary of the SPG, and what it implies for water 630 mass transformation within the SPG.
We found the maximum of the annual mean overturning stream function in density space to be 7.36 ± 1.48 Sv across the 27.30 kgm -3 isopycnal ( Table 2, Fig. 9a). To contextualise this value, the mean overturning measured across the 26° N zonal section by the RAPID-MOCHA array is 16.8 Sv (Smeed et al., 2018), while mean overturning across the ~60° N OSNAP section, which bisects the SPG, is 16.6 Sv (Li et al., 2021a). Other 635 estimates in the North Atlantic place the total overturning between 11.9-18.4 Sv (Caínzos et al., 2022;Fraser and Cunningham, 2021;Rossby et al., 2017;Sarafanov et al., 2012). Overturning estimates across the Greenland-Scotland Ridge vary from 5.5 to 5.7 Sv (Østerhus et al., 2019;Tsubouchi et al., 2021). However, estimates from transatlantic zonal sections only speak to water mass transformation north of the line in question.
Our overturning stream function for a closed boundary (Fig. 9a) represents the excess inflow at lighter densities 640 and excess outflow of denser water. We interpret these flows as water mass transformation in the interior of the SPG, an enclosed volume, and therefore as densification within the boundary (by surface fluxes). However, on seasonal timescales the inflow/outflow will be balanced by a combination of densification by surface fluxes and changing average density in the SPG. This density storage in the SPG interior will result in a lag before modified water is registered at the boundary curtain, thus attenuating the seasonal cycle in the overturning

665
The overturning maximum at σ0 = 27.30 kgm -3 therefore corresponds to the transformation of 7.36 Sv of upper water (σ0 < 27.3 kgm -3 ) which enters the SPG from the south before being cooled by the atmosphere to form SPMW (27.3-27.54 kgm -3 ). Around half (3.77 Sv) of this SPMW is then exported from the SPG (Fig. 9a) towards the Nordic Seas, where it is further transformed. This result supports the conclusions of Petit et al.
(2020) who found roughly equal rates of deep-water formation in the north-eastern SPG and the Nordic Seas. As 670 such, densification in the SPG preconditions further water mass transformation in the Nordic Seas and is thereby important for the North Atlantic overturning, but it is not appropriate to ascribe that part of the water mass transformation to overturning in the SPG. The transports by density layer (Fig. 8) reveal that the outflow in this (intermediate) density class is located between Iceland and Scotland, as it is carried northwards in the NAC.
The remaining SPMW is further transformed within the SPG, resulting in the broad plateau in the mean 675 overturning between 27.4 to 27.6 kgm -3 with a secondary overturning maximum at σ0 = 27.54 kgm -3 . This density range corresponds to isopycnals outcropping in the Irminger and Labrador Seas (e.g. Lozier et al., 2019), indicating that this secondary transformation occurs as the remaining SPMW circulates into the western SPG.
The resulting dense water (σ0 > 27.54 kgm -3 ) is then exported both via the Labrador Current and across 47° N (Fig. 8). Dense water also enters the SPG both at Cape Farewell, having presumably travelled south through the 680 Denmark Strait in the EGC (e.g. Holliday et al., 2007), and in the Gulf Stream, which partially cancels the outflow at 47° N. However, the net export in this layer indicates dense water is formed, at a rate of 3.59 Sv, in the SPG interior.
The overturning maxima at σ0 = 27.30 kgm -3 and σ0 = 27.54 kgm -3 are both much lighter than the isopycnal of maximum overturning reported for OSNAP (27.66 kgm -3 , Lozier et al., 2019) and are instead comparable with 685 the outcropping isopycnals implicated in SPMW formation (27.3-27.5 kgm -3 , Petit et al., 2021). This is because the GSR overflows which dominate the lower limb transport at OSNAP-East are formed outside of the SPG, and therefore contribute minimally to the overturning structure computed around our closed-loop boundary. The negative overturning values during autumn and winter (Fig. 9a) indicate that these overflow waters can become lighter inside the SPG. As the overflow waters in the Labrador Sea are too deep to be accessed by winter 690 convection (Yashayaev, 2007), this modification probably occurs through mixing and entrainment with adjacent water masses.
The deepest overflows (σ0 > 27.8 kgm -3 , Dickson and Brown, 1994) are not resolved by the boundary climatology (Fig. 9b). However, and in reality, these waters will flow southward through the SPG at depth with little exposure to the atmosphere. They therefore undergo minimal transformation within the SPG so their 695 inclusion would not significantly alter the structure of overturning we observe (Fig. 9a). We address the issue of deep overflows in Sect. 4.5.
The maximum overturning at σ0 ≈ 27.30 kgm -3 has significant seasonal variability (Fig. 9a), with substantially larger values in winter and spring (9.33 Sv,10.17 Sv) than in summer and autumn (6.59 Sv,6.20 Sv). This is in accord with the seasonal overturning cycle now apparent north of OSNAP, such that overturning lags the winter 700 surface cooling maximum by one season. For OSNAP, this lag results from surface Ekman forcing acting to reduce the northward transport in the upper layer during the winter due to the direction of prevailing winds relative to the transect (Li et al., 2021a;Petit et al., 2020;Petit et al., 2021). For our closed boundary, winter surface Ekman forcing has little impact on transport towards the Iceland-Scotland Ridge but maximally suppresses the import of upper layer water (σ0 < 27.3 kgm -3 ) across the 47° N transect (Fig. 6). In addition, the 705 winter mixed layer in the North-east Atlantic is too dense to contribute to the maximum overturning peak at σ0 ≈ 27.30 kgm -3 . The net result of these influences is to delay the peak in overturning until spring. We find that removing surface Ekman forcing results in maximum overturning occurring during winter instead (not shown).
The secondary maximum in the overturning at σ0 ≈ 27.54 kgm -3 displays a different class of seasonal variability (Fig. 9a). The transformation is strongest in spring and summer (5.46 Sv, 5.31 Sv), while the autumn value (4.13 30 Sv) is close to the mean (3.59 Sv). In winter this secondary peak is absent, indicating that some of the SPMW formed in the eastern SPG is exported before undergoing further transformation to dense water (σ0 > 27.54 kgminterior then exported, in approximately equal measure, as either intermediate water (27.30-27.54 kgm -3 ) in the NAC or as dense water (σ0 > 27.54 kgm -3 ) exiting to the south. These results support the findings of Petit et al., (2021); that the pre-conditioning of buoyant NAC waters into SPMW is a key stage in the transformation of water to successively higher densities and that it is therefore an important source of dense water masses for the lower limb of the AMOC.

Heat and freshwater divergence in the Subpolar Gyre
We find a net advective convergence of heat into the SPG of 0.18 ± 0.05 and a net divergence of freshwater of -0.10 ± 0.03 (Table 3). Are these compatible with atmospheric fluxes?
The annual mean net downward heat flux over the SPG is -0.24 ± 0.02 PW (Table 3). Thus, our estimate for the mean heat imported into the SPG through advection is approximately balanced by the mean loss to the 725 atmosphere. The seasonal range of surface heat fluxes (-0.80 PW in the winter to 0.33 PW in the spring) is much greater than that for advective heat fluxes (0.14 PW in the winter to 0.23 PW in the spring). The annual mean net downward freshwater flux is 0.06 ± 0.01 Sv with only minor seasonality.
A discrepancy of -0.06 ± 0.07 PW remains between the rate of heat entering the SPG through advection and that of heat leaving the SPG through surface cooling averaged over 20 years. This value is compatible with the 730 observed magnitude of cooling in the North Atlantic, for example Bryden et al., (2020) find cooling at rate of 0.04 PW for the region 26-70° N between 2008-2016. For freshwater, the discrepancy between the rates of advective freshwater export and surface freshwater import (-0.04 ± 0.04 Sv) implies a net salinification during the period 2000-2019 which again supports the findings of Bryden et al., (2020), who reported freshwater loss at a rate of 0.062 Sv for the region 26-70° N between 2008-2016. We note that for both heat and freshwater 735 fluxes, the discrepancy is within our error bounds so cannot be significantly distinguished from zero.
We find that a mean of 0.48 ± 0.05 PW crosses 47° N into the SPG (Fig. 10a). This is not directly comparable to other zonal transects (Fraser and Cunningham 2021;Li et al., 2021b;Lozier et al., 2019)  The contribution of the energetic EGC and WGC systems to the overall SPG heat and freshwater budgets is relatively small. While the region around Greenland contributes up to 0.02 Sv of freshwater, the melting from the Greenland ice sheet appears to play a minor role in the freshwater budget of the SPG. This may be because 750 much of the freshwater remains on the shelf rather than joining the EGC (De Steur et al., 2009). Near Cape Farewell, the ingress of 8 Sv of relatively dense water signals the import of various modified water masses across the Denmark Strait, entering the SPG chiefly through the EGC and WGC. The precise location of import is dependent on how our boundary intersects with the current cores and the EGC retroflection (e.g. Holliday et al., 2007) but the accumulated fluxes are robust to this effect. Net heat flux resulting from this interface is 755 minimal because local temperatures are near the reference temperature ̅ (Fig. 10a, Eq. (5)). Note that the impact of the poorly resolved overflows (see Sect. 4.5) on the SPG heat and freshwater budgets is likely to be minor. For example, an inflow of 3 Sv at 1 °C and 35 g kg -1 at the expected location of the DSO (e.g. Mastropole et al., 2017) results in a heat loss to the SPG of 0.04 PW which is smaller than our error bounds, and a negligible gain in freshwater.

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While turbulent diffusion does not play a significant role in the SPG heat budget, the highly energetic Gulf Stream eddy field does import 0.025 PW, or about 8 % of the total Gulf Stream heat input, though this is largely compensated by heat leaving the SPG on either side (Fig. S3). This value is still an order of magnitude smaller than the eddy heat flux estimated at 36° N (immediately after its separation at Cape Hatteras) by Tréguier et al.,

Buoyancy exchanges in the western Subpolar Gyre
It is clear from Fig. 3 that that density generally increases with progress around the SPG boundary, and that this is primarily caused by gradual cooling. This reflects the buoyancy loss in the interior and is also seen in the boundary current as it flows around the basin (Straneo, 2006). A notable exception to the increasing density 770 trend is south-western Greenland where an injection of freshwater (and warming below 250 m) leads to a marked reduction in density, along with a reversal of volume transports between the interior of the SPG and the boundary in this region (Fig. 5). While Liu et al., (2022) diagnose upwelling in this region, instabilities in the WGC and the associated formation of Irminger rings (e.g., Fratantoni, 2001;Prater, 2002) would appear to be likely sources for this signal in our 1000 m contour climatology. We note that the reversal of the prevailing 775 horizontal density gradient is a subtlety that is lacking from more idealised studies of boundary current dynamics which assume a continual decrease of density with progress counter-clockwise around the SPG (e.g. Brüggemann and Katsman, 2019).
The role of the EGC and WGC in water mass modification is undoubtedly enhanced by eddy activity, which is in part driven by the boundary current interacting with local topography. In Fig. 11 we show that the 780 exceptionally high EKE values in the WGC region are associated with a slope of 20° west of Greenland. This coherence suggests that EKE, and hence the diffusive flux of buoyancy between the boundary and SPG, is controlled by the steepness of the sloping margins. As we have already stated, diffusive fluxes have minimal significance for the overall boundary heat and freshwater budget, but in the WGC region we find that diffusive and advective fluxes are comparable. Studies citing eddy diffusion for communication between interior and 785 boundary tend to be located around southern Greenland (Brüggemann and Katsman, 2019;Le Bras et al., 2020;Liu et al., 2022) and our results highlight that this region is an exception to the rule around the gyre.
We do not see clear signs of true winter deep convection at the boundary of the Labrador Sea (Fig. S2, mixed layer depths of > 800 m are indicated by Lavender et al., 2000). While the boundary current system was ventilated during the severe winters of the early and mid-1990s (Pickart et al., 1997), these episodes occurred 790 outside our data temporal coverage (2000 onwards). Deep convection appears to have been largely confined to the basin interior in recent winters, communicated to the boundary and appearing as anomalies at the boundary in spring (Yashayaev and Loder, 2017, Fig. S2).

Subpolar Gyre volume budget estimation
Given the transports estimated in this study, we can make a first order estimate of the SPG volume budget given 795 the continuity constraint of zero net transport.
The SPG interior can be divided into an upper and lower volume partitioned at 1000 m depth. The upper volume is enclosed by the 1000 m boundary curtain and the 47° N section, the lower volume is completely enclosed except across 47° N (Fig. 12). A net inflow above 1000 m must be balanced by downwelling across the 1000 m 'surface'. In addition, model-based estimates of North Atlantic AMOC in depth space find 800 maximum overturning located near 1000 m (Biastoch et al., 2021;Hirschi et al., 2020)  Hence from Eq. (10) and (12),

≈ (13)
We estimate the mean to be 12.0 Sv using VIKING20X (dashed grey line, Fig. 7b). From Eq. (11), 820 this results in a net gain of +11.9 Sv above 1000 m, necessitating a downwelling flow of 11.9 Sv through the 1000 m surface, and an equivalent southward net flow across 47° N below 1000 m (Fig. 12). The depth space AMOC estimated by Hirschi et al., (2020) and Biastoch et al., (2021) is 10-15 Sv and therefore is of the same order as that inferred from the VIKING20X remainder term.  Between the UK and Greenland (Fig. 5) 12 Sv of geostrophic transport leaves the SPG. This is the same transport as was reported for the upper limb across OSNAP-East (Lozier et al., 2019) and implies that the return current in the lower limb is not captured in the geostrophic transports from the observational analysis. Another indication that the lower limb of the AMOC is not fully resolved in the observations is the lack of very cold (< 3 835 °C) and dense (> 27.8 kgm -3 ) waters where we would expect the Faroe Bank Channel overflow and DSO to bisect the boundary (Johnson et al., 2017;Mastropole et al., 2017). The dominant role of in Sect.
4.4 further highlights that some processes are not fully captured by the observational analysis. In this section we consider which regions and dynamical processes contribute to the term.
The region off south-east Greenland is responsible for over half the signal in VIKING20X (Fig. 7).

840
We surmise that the modelled DSO is primarily responsible for this transport. The model fields suggest a contribution by of 6.0-6.8 Sv entering the SPG in the Denmark Strait region, with the majority of the flow close to the seabed (dashed grey line, Fig. 7). For comparison, observational estimates of the volume transport in the overflow indicate that the DSO is responsible for 3.2-3.5 Sv (Girton et al., 2001;Harden et al., 2016;Jochumsen et al., 2012;Jochumsen et al., 2017;Käse et al., 2003). The transport across the sill may then 845 roughly double by entrainment as the dense water descends toward the abyssal plain (Dickson and Brown, 1994). By contrast, observational estimates of the Faroe Bank Channel overflow suggest an underestimation of its flow in VIKING20X (2.6 Sv, Johns et al., 2021). The volume transport of the overflows into the SPG interior in VIKING20X may therefore be approximately correct, although their physics and relative contributions are probably not simulated very realistically.

850
We have encountered modelling results suggesting that the overflows may have a significant ageostrophic and non-Ekman component and must therefore receive significant contributions from non-linear and viscous processes. For example, the DSO is manifest as a turbulent cascade released over the sill in pulses with a timescale of around 3-5 days (e.g. Käse et al., 2003;Lin et al., 2020;Spall et al., 2019). One would anticipate that small-scale, non-linear and ageostrophic processes would dominate in such an environment. It is beyond 855 the scope of this paper to quantitively assess these processes. However, our analysis demonstrates the importance of overflow dynamics in closing the overturning streamlines in the SPNA.
There are several reasons why our sampling strategy and analysis may result in poorly resolved overflows.
Firstly, the relatively low horizontal resolution along the boundary contour may be too coarse to clearly resolve overflow waters in the gridded profile data. Secondly, the profiles contributing to our dataset may on average 860 be too far from the continental slope to regularly capture the overflow (see schematic in Fig. 12). Thirdly, due to the transitory nature of the overflow waters, temporally-scattered CTD sampling may fail to sample them.
Finally, Argo floats may be actively deflected around the downslope-flowing boluses of dense water, thus not sampling the core properties.

865
A novel observational climatology of the entire SPG boundary has yielded new perspectives on overturning in the interior of the SPG. We find an average transformation of 7

870
These findings underline the findings of Petit et al., (2021): that the overturning of dense waters is reliant on the prior 'pre-conditioning' of lighter waters.
We find a mean advective convergence of heat into the SPG of 0.18 ± 0.05 PW, and a net divergence of freshwater of -0.10 ± 0.02 Sv, which are approximately balanced by surface fluxes. Net diffusive heat and freshwater fluxes into the SPG are negligible, but hotspots of eddy activity such as the Gulf Stream and western

875
Greenland result in localised diffusive heat fluxes approaching those of the advective contributions.
When considering the total transports into and out of the SPG volume, we find that the mean geostrophic (2.3 Sv), surface Ekman (-4.9 Sv) and bottom Ekman (2.5 Sv) terms approximately cancel, meaning that flow downwards across the 1000 m surface is dominated by ageostrophic (and non-Ekman) processes. This result highlights the requirement to better understand the overflows into the SPG, and the net sinking that occurs along 880 the boundary (e.g. Johnson et al., 2019;Spall and Pickart, 2000) and demonstrates that a geostrophic approach alone may not be sufficient for this.
Our investigation focused on the recent (20-year) climatic mean state, as was necessitated by observational data availability. However, given recent evidence of changes in large-scale circulation patterns (Biastoch et al., 2021;Fox et al., 2022;Zhang and Thomas, 2021) it is crucial to assess the decadal shifts in the basin-scale processes 885 outlined here, and establish to what extent this can alter the behaviour of the AMOC.

Data and code availability
Aggregated Argo and CTD profile data are available from the WOD at https://www.ncei.noaa.gov/access/world-

Author contribution
SJ conducted the core analyses and prepared the manuscript with contributions from all co-authors. NF 900 computed the surface Ekman transports and EKE values around the boundary and contributed to manuscript preparation and interpretation of results. SC secured the funding for the work, conceptualised the gyre boundary investigation, and contributed to the text and experiment design throughout. AF supplied the VIKING20X investigation and contributed to the text and interpretation of results. MI supplied the slope angle investigation and contributed to the text and interpretation of results.

Competing interests
The authors declare that they have no conflict of interest.