Y J Liu

D G Desbruyères

H Mercier

M A Spall

Observation-based estimates of Eulerian-mean boundary downwelling in the western subpolar North Atlantic

 The long-term mean full-depth density field of the subpolar North Atlantic's boundary is reconstructed from hydrography data  The along-boundary densification results in a 2.12 ± 0.43 Sv Eulerian-mean downwelling between Denmark Strait and Flemish Cap  A first observation-based regional and seasonal distribution of near-boundary Eulerianmean downwelling is provided

Introduction

Through its role in redistributing heat, freshwater, and chemical properties between low and high latitudes, the Atlantic Meridional Overturning Circulation (AMOC) is a critical component of Earth's climate system. Warm and saline waters flow from low latitudes towards the poles within the AMOC upper limb. Following significant mixing-driven and surface-forced water mass transformation, colder and fresher waters are returned southward as intermediate and deep-water masses within the AMOC lower limb. Climate model studies indicate that the AMOC could weaken significantly over the next century (IPCC, 2021), and significant efforts have been consequently made over the last decades to understand the processes maintaining the AMOC and the drivers of its variability (e.g., [START_REF] Lozier | Overturning in the North Atlantic[END_REF][START_REF] Buckley | Observations, inferences, and mechanisms of Atlantic meridional overturning circulation variability: a review[END_REF][START_REF] Johnson | Recent Contributions of Theory to Our Understanding of the Atlantic Meridional Overturning Circulation[END_REF].

The vertical connection between the upper and lower limb of the AMOC, as well as the underlying mechanism, are still under investigation (e.g., [START_REF] Spall | Where does dense water sink? a subpolar gyre example[END_REF][START_REF] Pedlosky | Thermally Driven Circulations in Small Oceanic Basins[END_REF][START_REF] Straneo | On the Connection between Dense Water Formation, Overturning, and Poleward Heat Transport in a Convective Basin[END_REF][START_REF] Spall | Dynamics of down welling in an eddy-resolving convective basin[END_REF]Brüggemann & Katsman, 2019). The location of this downwelling has long been associated with regions of intense open-ocean convection, such as the Labrador and Irminger seas, where dense and deep waters form because of convective mixing. However, deep convection regions have large vertical heat and salt transports (in density space) but a negligible vertical mass transport (in depth space) [START_REF] Marshall | Open-ocean convection: Observations, theory, and models[END_REF]Send and Marshall manuscript submitted to Geophysical Research Letters 1995;[START_REF] Spall | On the thermohaline circulation in at bottom marginal seas[END_REF][START_REF] Spall | Boundary Currents and Watermass Transformation in Marginal Seas[END_REF]. Instead, the Eulerian-mean downwelling connecting the AMOC upper and lower limbs should occur near continental boundaries, where geostrophy breaks down and a new balance between vertical stretching of planetary vorticity and dissipation of relative vorticity in a thin boundary layer emerges [START_REF] Spall | Dynamics of down welling in an eddy-resolving convective basin[END_REF]. Previous research has established that such downwelling through modification of the boundary current properties in a region is undergoing buoyancy loss (e.g., [START_REF] Spall | Where does dense water sink? a subpolar gyre example[END_REF][START_REF] Straneo | On the Connection between Dense Water Formation, Overturning, and Poleward Heat Transport in a Convective Basin[END_REF][START_REF] Spall | Dynamics of down welling in an eddy-resolving convective basin[END_REF][START_REF] Cenedese | Downwelling in basins subject to buoyancy loss[END_REF][START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF]. Notably, the dynamics of Eulerian-mean downwelling are primarily governed by the large-scale geostrophic flow, so that the details of the thin boundary layer where vorticity is ultimately dissipated do not need to be resolved for capturing the overall impact of downwelling [START_REF] Spall | Buoyancy-forced downwelling in boundary currents[END_REF].

Several studies have focused on the location and underlying mechanism of boundary downwelling. [START_REF] Spall | Where does dense water sink? a subpolar gyre example[END_REF] investigated the boundary sinking using a thermodynamic balance. During winter, the boundary current loses heat and buoyancy. As shown schematically in Figure 1, the resulting along-boundary density increase requires a vertically sheared crossshore baroclinic flow in thermal wind balance (V in ) fed by the boundary current itself (U in ; there is no exchange with the basin interior). Therefore, the flow rotates counterclockwise with depth along the boundary within a so-called "cooling spiral". To maintain local mass conservation, a net downwelling (W) is required to balance the mass flux towards the boundary. This causes a barotropization of the boundary current, with the upper part decelerating and the lower part accelerating [START_REF] Spall | Boundary Currents and Watermass Transformation in Marginal Seas[END_REF][START_REF] Spall | Buoyancy-forced downwelling in boundary currents[END_REF][START_REF] Straneo | On the Connection between Dense Water Formation, Overturning, and Poleward Heat Transport in a Convective Basin[END_REF] Several processes, including surface buoyancy flux or mean and eddy-driven heat advection, likely contribute to maintaining an along-boundary density gradient. While the respective contribution of these processes is regionally unknown, lateral eddy-driven heat exchangesgenerated by the lateral density gradients and baroclinic instabilityare widely acknowledged as important in densifying the boundary region, as seen for instance in the Labrador Sea [START_REF] Lilly | manuscript submitted to Geophysical Research Letters Observations of the Labrador Sea eddy field[END_REF][START_REF] Katsman | Boundary Current Eddies and Their Role in the Restratification of the Labrador Sea[END_REF]. Lateral eddy-induced heat fluxes are required to balance the heat loss to the atmosphere and restratify open-ocean water columns following deep convection events [START_REF] Katsman | Boundary Current Eddies and Their Role in the Restratification of the Labrador Sea[END_REF][START_REF] Hátún | Buoyant eddies entering the Labrador Sea observed with gliders and altimetry[END_REF][START_REF] Chanut | Mesoscale eddies in the Labrador Sea and their contribution to convection and restratification[END_REF][START_REF] Kawasaki | Effect of freshwater from the West Greenland Current on the winter deep convection in the Labrador Sea[END_REF]Tagklis et al., 2020). Additionally, eddies contribute to interior downwelling and boundary current barotropization through along-isopycnal water masses stirring and exchange between the boundary current and the interior [START_REF] Khatiwala | An estimate of the eddy-induced circulation in the Labrador Sea[END_REF][START_REF] Brüggemann | Dynamics of downwelling in an eddying marginal sea: Contrasting the eulerian and the isopycnal perspective[END_REF].

Recent studies have used realistic and high-resolution model simulations to investigate the net downwelling in the entire Subpolar Gyre (SPG) [START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF][START_REF] Sayol | Seasonal and regional variations of sinking in the subpolar North Atlantic from a high-resolution ocean model[END_REF] or in marginal seas characterized by high convective activity, such as the Labrador Sea [START_REF] Brüggemann | Dynamics of downwelling in an eddying marginal sea: Contrasting the eulerian and the isopycnal perspective[END_REF][START_REF] Georgiou | On the interplay between downwelling, deep convection and mesoscale eddies in the Labrador Sea[END_REF]. [START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF] and [START_REF] Sayol | Seasonal and regional variations of sinking in the subpolar North Atlantic from a high-resolution ocean model[END_REF] confirmed that the bulk of the vertical volume flux occurs along the boundary and that its spatial integral in the SPG is close to the magnitude of the AMOCthe zonally-integrated meridional flowat the southern exit of the SPG (i.e., near 45°N). [START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF] further demonstrated that the amount of boundary sinking is largely determined by density change, except the region where eddy-driven processes or hydraulic controls may become significant.

The role of eddy-driven processes was particularly studied by [START_REF] Brüggemann | Dynamics of downwelling in an eddying marginal sea: Contrasting the eulerian and the isopycnal perspective[END_REF] and [START_REF] Georgiou | On the interplay between downwelling, deep convection and mesoscale eddies in the Labrador Sea[END_REF], who showed the importance of eddies in balancing heat loss over the Labrador Sea and in triggering boundary downwelling along steepened isopycnal surfaces.

Estimates of boundary-focused sinking and its associated mechanisms from in situ observations are still lacking. Here, we use hydrography data from global ocean monitoring programs (e.g., Argo, Go-Ship) to estimate for the first time the long-term Eulerian-mean along-boundary downwelling and its spatial and seasonal distribution within the western SPG, from Denmark Strait (DKS) to Flemish Cap (FC). While such observations cannot resolve the intricate and small-scale dynamics of downwelling within the thin boundary layer where it is most likely to occur, they can be used to infer the large-scale geostrophic balance governing it.

We begin by introducing a specific optimal interpolation method to map temperature and salinity along the boundary, and then describe the method used for calculating cross-shore velocities and resulting vertical transport (section 2). Section 3 describes the reconstruction of the alongboundary density field, as well as the subsequent calculation of geostrophic velocity and associated downwelling. A summary and a discussion conclude this study (section 4). manuscript submitted to Geophysical Research Letters 2 Data and Methodology

Data

We use three datasets of temperature and salinity profiles to map the long-term mean (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) and seasonal cycle of hydrographic properties in the SPG (52-66°N; 30°W-66°W): the In Situ Analysis System-ISAS15 [START_REF] Kolodziejczyk | ISAS temperature and salinity gridded fields[END_REF][START_REF] Gaillard | In situ-based reanalysis of the global ocean temperature and salinity with ISAS: Variability of the heat content and steric height[END_REF], the Coriolis data set for ReAnalysis-CORA [START_REF] Szekely | CORA, Coriolis Ocean Dataset for[END_REF][START_REF] Cabanes | The CORA dataset: Validation and diagnostics of in-situ ocean temperature and salinity measurements[END_REF]EN4.4.2.2 (Good et al., 2013). Whereas ISAS15 only contains Argo profiles, EN4 and CORA include profiles from fixed moorings and shipboard full-depth CTD profiles. These profiles have undergone quality control checks in delayed mode, and we only use good profiles (i.e., fully acceptable).

Because most of Argo floats drift at 1000 m depth, ISAS15 exhibits an uneven distribution across the domain with decreasing near the shelf (see Figure S1). The EN4 and CORA provide adequate coverage of profiles near the shelf. The temperature and salinity fields are then used to derive the in situ (ρ) and potential (σ 0 ) density fields. Bathymetry is derived from ETOPO2.

Optimal Interpolation

Optimal interpolation (OI) is a frequently used technique for generating gridded property fields from sparse and irregular data [START_REF] Bretherton | A technique for objective analysis and design of oceanographic experiments applied to MODE-73[END_REF][START_REF] Kaplan | Reduced space optimal analysis for historical data sets: 136 years of Atlantic sea surface temperature[END_REF]. The conventional OI algorithms for climatological mapping use circle-shaped Gaussian correlation functions (see [START_REF] Gaillard | In situ-based reanalysis of the global ocean temperature and salinity with ISAS: Variability of the heat content and steric height[END_REF] for additional details), but we herein employ an elliptic Gaussian correlation function parallel to isobaths, with length scales of 67 km (cross-shore axis) and 145 km (alongshore axis) to account for the larger (smaller) correlation length scales in the along-shore (crossshore) directions. In other words, this provides data along the boundary current's primary path larger weights in the estimation. Based on convergence sensitivity tests, the horizontal resolution is set as 4km, which enables us to refine the properties along boundaries and topographic features (such as the sharpest portions of the continental slope). Interpolation is conducted at 152 levels independently between 0 and 2000 m; the vertical spacing is 5 m down to 100 m, 10 m down to 800 m, and 20 m below. The configuration of the OI is explained in more detail in [START_REF] Gaillard | In situ-based reanalysis of the global ocean temperature and salinity with ISAS: Variability of the heat content and steric height[END_REF]. The overall mapping methodology was eventually validated by good performance in estimating properties along the OVIDE and AR7W hydrographic lines (see Figure S2-S5). To estimate the vertical transport, the final multiproduct mappings of temperature and salinity for the four seasons (Winter (Jan-Mar), Spring (Apr-Jun), Summer (Jul-Sep), Autumn (Oct-Dec)) is the average of the fields derived independently from the three datasets.

The density below 2000 m is obtained by linear extrapolation from the above 2000 m. The threedimensional density field is eventually interpolated onto the locations of 100m-spaced isobaths spanning 700 m to 3000m from DKS to FC.

Computing cross-shore geostrophic velocity and the vertical transport

To calculate the absolute geostrophic cross-shore velocity, a local mass balance assumes equal inshore and offshore transport. Any horizontal recirculations between the boundary current and the interior are assumed to be mostly barotropic, with no effect on the cross-shore baroclinic density field. These assumptions are supported by laboratory experiments showing that water downwelling along a vertical wall returns offshore in the opposite direction [START_REF] Cenedese | Downwelling in basins subject to buoyancy loss[END_REF], and by observations of the strong barotropic nature of inner gyres and lateral entrainments (Våge et al., 2011). The baroclinic component of the cross-shore velocity relative to the sea surface manuscript submitted to Geophysical Research Letters (v baroclinic ) is firstly derived from the along-boundary density gradient and the thermal wind balance:

𝜕𝑣 𝑏𝑎𝑟𝑜𝑐𝑙𝑖𝑛𝑖𝑐 (𝑥, 𝑦, 𝑧) 𝜕𝑧 = - 𝑔 𝜌 0 𝑓 𝜕𝜌(𝑥, 𝑦, 𝑧) 𝜕𝑥 (1)
where x, y, and z represent the along-shore, cross-shore, and vertical directions, respectively. ρ is the in-situ density field derived from OI, ρ 0 is 1024 kg/m 3 , and 𝑓 is 1.26 × 10 -4 s -1 .

The reference velocity v reference is then obtained by applying the local zero-mass transport constraint:

𝑣 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑥, 𝑦) = -∫ (𝑣 𝑏𝑎𝑟𝑜𝑐𝑙𝑖𝑛𝑖𝑐 (𝑥, 𝑦, 𝑧))𝑑𝑧 0 𝐻(𝑥,𝑦) ∆𝑧 ( 2
)
where H (x,y) denotes the bottom depth and Δz the water depth.

We calculate vertical transport along the SPG at isobaths ranging from 700 to 3000 m with a 100-meter interval. The analysis focuses offshore of the 700 m isobath because of poorer sampling inshore. This has little effect on the maximum transport estimate, however, which is found across much deeper slope. For a given isobath (y 0 ), the vertical transport streamfunction 𝜓(𝑧) is estimated as follows:

𝜓(y 0 , 𝑧) = ∫ ∫ (𝑣 𝑏𝑎𝑟𝑜𝑐𝑙𝑖𝑛𝑖𝑐 (𝑥, 𝑦 0 , 𝑧′) + 𝑣 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑥, 𝑦 0 )) 0 𝑧 𝑑𝑧′𝑑𝑥 𝑥 𝑑 𝑥 𝑢 (3)
where 𝑥 𝑢 and 𝑥 𝑑 are the upstream and downstream locations along a given isobath y 0 . The maximum of 𝜓(y 0 , z) represents the net shoreward transport integrated along an isobath between 𝑥 𝑢 and 𝑥 𝑑 . The maximum vertical transport is thus defined as the maximum of the net shoreward transport 𝜓 max across the 100-m spaced isobaths between 700 m and 3000 m.

A Monte Carlo approach is used to add an uncertainty estimate to our mean vertical transport calculation. We use the errors estimated from the OI calculation, which depend on the distribution density and variability of adjacent profiles, to perturb the temperature and salinity fields randomly and re-compute overturning streamfunctions. 12000 bootstrap estimates of the streamfunctions in four seasons are calculated using 3000 iterations on the three datasets. The errors of the transport are considered as two times the standard deviation of the 12000 estimates (see Figure S6).

Results

Figure 2 shows the multiproduct long-term mean temperature field averaged over the upper 300 m depth. It depicts the cooling of the warm boundary current in the upper layer as it flows from DKS to FC. The full-depth surface-referenced in situ (ρ) and potential (σ 0 ) fields are determined along 100 m-spaced isobaths ranging from 700 to 3000m. The 2400m isobath is shown here (for the reason that will become obvious later) and labeled using the distance relative to the isobath's total length (4032 km), starting at s=0 near the DKS at -30°W and ending at s=1 near FC at -48°W.

manuscript submitted to Geophysical Research Letters Figure 3ab depicts the density and associated cross-shore geostrophic velocity sections following isobath 2400 m from DKS to FC (the along-isobath baroclinic and reference velocities in Equation 2 are shown in Figure S8). The density generally increases downstream (Figure 3a,c) and is primarily determined by the change in along-shore temperature (see Figure S7). The Upwelling, s = 0.33~0.5).

A vertical section of the DKS-FC along-shore average of the cross-shore velocity crossing different isobaths is shown in Figure 4a. It reveals a cell-like structure in the upper and lower layers, with a cell center in the isobath 2400 m at 100 m depth. In line with theory and experimental works [START_REF] Spall | Buoyancy-forced downwelling in boundary currents[END_REF][START_REF] Cenedese | Downwelling in basins subject to buoyancy loss[END_REF], the cross-shore velocity increases from the coast offshore to a maximum near the 2400 m isobath and then decreases offshore until the along-shore density gradient becomes insignificant at circa the 3000 m isobath. The mean maximum vertical transport along the SPG boundary is 2.12 Sv at 1088 m, with an uncertainty of for the three regions defined in Figure 1 and Figure 2c and for the four seasons: Winter (Jan-Mar), Spring (Apr-Jun), Summer (Jul-Sep), Autumn (Oct-Dec). The uncertainty estimates and maximum overturning depths for each region are represented in Table 1.

The cumulative transport (Figure 3c) along the 2400 m isobath reveals that the entire DKS-FC boundary can be divided into three distinct areas: a downwelling region in the Irminger Sea (ID, s=0 to s=0.33), an upwelling region in the eastern Labrador Sea (LU, s=0.33 to s=0.5), and a downwelling region in the western Labrador Sea (LD, s=0.5 to s=1). These downwelling/upwelling patterns result from the downstream density increase/decrease along the boundary (Figure 3a). The cross-shore velocities averaged along the isobaths in these three regions are shown in Figure 4dgj. They also capture cell-like structures within the boundary current system, with waters flowing inshore (offshore) in the upper layer and offshore manuscript submitted to Geophysical Research Letters (inshore) in the lower layer of the downwelling (upwelling) region. Maximum crossshore transports, which are consistently observed at the 2400-m isobath, are of comparable magnitude in each of the three regions with upwelling (2.17 Sv) along the western slope of Greenland balancing half of the total downwelling (4.28 Sv) (Figure 4ehk).

Water sinks (upwells) all year in the downwelling (upwelling) regions. The Eulerian-mean transport in the LD region is 2.23±0.71 Sv (Figure 4e and Table 1) at a depth of 986 m. The transport in the LU region (Figure 4h and Table 1) is 2.17±0.74 Sv at a depth of 1182 m. The ID has similar downwelling of 2.05±0.79 Sv to the LD (Figure 4k and Table 1) at a depth of 1304 m. The regional density-space transport follows a very similar pattern to that in depth-space, and the density level of maximum transport remains nearly constant at around 27.71 to 27.76 kg/m3.

The uncertainty estimates in Table 1 show the standard deviations calculated from 3000 iterations using the three datasets. Seasonal and regional errors are all between 0.3 and 0.8 Sv.

The seasonal variations are of the same magnitude as the uncertainties derived from the bootstrap estimates based on the three datasets, and the present estimates of seasonal changes of the Eulerian-mean downwelling are not statistically significant for the whole SPG or individual basins. This is in line with [START_REF] Li | Subpolar North Atlantic western boundary density anomalies and the Meridional Overturning Circulation[END_REF] 1. The maximum vertical transport (Sv) derived from the multiproduct mean in the LD, LU and ID regions (defined in Figure 2) and whole SPG. The errors are two times of standard deviation derived from the bootstrap simulations. The depths (m) of the maximum transport are displayed in parentheses.

Discussion and Conclusion

We have provided here a first observation-based estimate of the Eulerian-mean downwelling along the boundary of the SPG. Using in situ temperature and salinity profiles from sustained global ocean observational networks, we mapped the long-term mean density along the continental slope from the Denmark Strait to Flemish Cap. The cooling and resulting densification along the boundary region result in a geostrophic cross-shore flow and a downwelling above the continental slope, with a maximum value of 2.12 ± 0.43 Sv at 1100 m depth. The transport in density space, which is here representative of the cross-shore diapycnal flux, is very similar to the transport in depth space. Cross-shore velocity is found to increase manuscript submitted to Geophysical Research Letters offshore and peak near the 2400 m isobath, before eventually disappearing near the 3000m isobath, in good agreement with observation-based descriptions of the distinct circulation of the interior and the boundary current [START_REF] Pacini | Mean conditions and seasonality of the west Greenland boundary current system near cape farewell[END_REF], and with theoretical or modelling works suggesting limited mean advective exchanges between those two regimes [START_REF] Cenedese | Downwelling in basins subject to buoyancy loss[END_REF][START_REF] Brüggemann | Dynamics of downwelling in an eddying marginal sea: Contrasting the eulerian and the isopycnal perspective[END_REF]. Our analysis further reveals no strong or statistically significant seasonality in the magnitude of downwelling across the entire SPG.

Interestingly, the total Eulerian-mean downwelling from CF to FC is estimated as only 0.1±0.03 Sv due to compensation between upwelling along the western slope of Greenland and downwelling in the remaining portion of the Labrador Sea. Downwelling was estimated to be 1.4 Sv in that region by [START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF] in high-resolution simulations. Western Greenland is in fact generally described as a region with strong along-shore densification due notably to eddydriven heat flux, as described in several modelling works [START_REF] Katsman | Boundary Current Eddies and Their Role in the Restratification of the Labrador Sea[END_REF][START_REF] Georgiou | On the interplay between downwelling, deep convection and mesoscale eddies in the Labrador Sea[END_REF]. This apparent discrepancy could arise for several reasons. Warming in the intermediate layer might be overly represented due to an uneven distribution of profiles along western Greenland's narrowing boundary, which may be insufficient to represent the boundary current's features. It is also possible that the subsurface warming along western Greenland (also observed in other estimates, see, e.g., [START_REF] Palter | How does Labrador sea water enter the deep western boundary current?[END_REF] indicates a signal of restratification following baroclinic instability. The tilted isopycnals on the offshore side of an unstable current should deepen downstream and drive a warming signal in this portion of the water column.

Additionally, the cross-shore transport along the narrowing boundary might represent the deflection of upper layer water into the interior. An offshore mass flux, resulting from either a flux of less dense water off the shelf or a broadening of the boundary current due to baroclinic instability, would be diagnosed as upwelling because of the assumption of no net flow across the isobaths. Future work may focus on describing the properties in shallower depths further inshore when sampling is denser. Nevertheless, the net downwelling in SPG is not sensitivity to the distribution of boundary downwelling or upwelling, as demonstrated by the fact that the strong downstream warming and subsequent upwelling in the eastern Labrador Sea are compensated by the significant downstream cooling and subsequent downwelling in the western Labrador Sea. Indeed, the full-basin integrated downwelling only depends on the density variation between the DKS and FC and thus remains a robust estimate.

Further comparison with independent overturning estimates from cross-basin arrays or realistic modelling provides insights and confidence in the values reported herein. The Irminger Sea downwelling is estimated to be 2.05±0.79 Sv at 1200 m depth, in line with the high-resolution modelling estimates of 1.4 Sv from [START_REF] Katsman | Sinking of dense north atlantic waters in a global ocean model: Location and controls[END_REF] and 1.13 Sv from [START_REF] Sayol | Seasonal and regional variations of sinking in the subpolar North Atlantic from a high-resolution ocean model[END_REF].

Summer downwelling in the Labrador Sea is estimated to be 0.85±0.15 Sv at depth 685 m by integrating the transport between the two ends of the AR7W line (Figure 2), which agrees quantitatively with [START_REF] Pickart | Impact of Labrador Sea convection on the North Atlantic meridional overturning circulation[END_REF] observation-based meridional transports of about 1 Sv at depth 800 m. The annual mean downwelling rate in the Labrador Sea is estimated here as 0.72±0.07 Sv, similar to [START_REF] Holte | Seasonal overturning of the Labrador sea as observed by Argo floats[END_REF] and [START_REF] Lozier | A sea change in our view of overturning in the subpolar North Atlantic[END_REF] estimates, which amount to 0.9 Sv and 0.8 Sv, respectively. This also confirms that the majority of sinking occurs near the Labrador Sea's boundary, with little vertical mass transport occurring in the convective interior.

manuscript submitted to Geophysical Research Letters Furthermore, we quantify here only the western boundary downwelling downstream of DKS, omitting potential upstream contributions around Reykjanes Ridge (RR) or the Rockall Plateau, for instance. The zero-mass constraint used herein to estimate cross-shore overturning is likely inadequate in such regions where the vertical integral of the cross-shore geostrophic flow is not zero (consider for instance the net westward flow above the crest of RR). Additionally, overflows across the DKS or the Iceland-Scotland Ridge contribute significantly to the overall net sinking in the SPGabout 7 Sv [START_REF] Hansen | North Atlantic-Nordic Seas exchanges[END_REF] via hydraulically-controlled dynamics not captured by our geostrophic estimate. A refinement of the boundary sinking calculation is being investigated for these specific areas.

Ekman transport was estimated from the long-term mean (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) along-shore wind stress averaged from the NCEP/NCAR Reanalysis 1 and ERA5 dataset. It carries 0.7 to 0.9 Sv of water inshore of the DKS-FC boundary. Two-dimensional models require that this onshore flow returns to the basin interior (e.g. [START_REF] Lentz | The importance of nonlinear cross-shelf momentum flux during wind-driven coastal upwelling[END_REF][START_REF] Choboter | Exact solutions of wind-driven coastal upwelling and downwelling over sloping topography[END_REF], but threedimensional models with spatially variable winds (or coastlines) demonstrate that some of this water flows along the shelf (e.g. [START_REF] Allen | Some aspects of the forced wave response of stratified coastal regions[END_REF][START_REF] Suginohara | Coastal Upwelling: Onshore-Offshore Circulation, Equatorward Coastal Jet and Poleward Undercurrent over a Continental Shelf-Slope[END_REF]. It is difficult to determine a priori the partition of this downwelled water between along-shelf and interior pathways as it will depend on various factors such as stratification, topography, nonlinearity, wind pattern, etc. However, any of the Ekman transport that does flow back into the interior will remain relatively shallow and have a negligible effect on the deep overturning circulation, and so is not included in our estimate.

We finally emphasize that novel descriptions of the Eulerian-mean downwelling rooted in observations are critical for understanding AMOC variability in the current context of anthropogenic climate change (IPCC, 2021). Both upper-ocean warming and increased ice melting may significantly affect along-boundary density gradients and result in the reduced sinking and a consequent weakening of the AMOC. A better observation-based understanding of boundary-focused vertical transport may also help us to properly represent or parameterize the details of the underlying boundary dynamics in climate models. It can assist in not only describing the circulation and diagnosing its controls, but also in providing valuable insights into how to improve existing ocean circulation theories of overturning.

Figure 1 .

 1 Figure 1. The cooling spiral and associated boundary downwelling. Gray arrows represent the background boundary current. The blue-red shading depicts the horizontal density fields, with the distribution of light waters in red and dense waters in blue giving rise to a cross-shore baroclinic flow in thermal wind balance (V in ) fed by the boundary current (U in ). Local mass conservation lead to a downward flow at the wall (W), a deep entrainment in the boundary current (V out ), and a rapid along-boundary export (U out ). The overall effect in a net downwelling within and a barotropization of the boundary current.

Figure 2 .

 2 Figure 2. Observed multiproduct time-mean (2002-2015) temperature field averaged in upper 300 m as obtained from an OI tool specifically designed for the boundary region (see section 2.2). The isobaths 700 m and 3000 m are shown as thin black contours, and the isobath 2400 m (thick black line) used in Figure 3 to show along-boundary density and velocity fields, from s = 0 at Denmark Strait until s = 1 at Flemish Cap. Solid and dashed portions of this contour refer to (Eulerian) downwelling and upwelling regions. Key locations noted in the plot are Denmark Strait (DKS), Cape Farewell (CF), Davis Strait (DVS), and Flemish Cape (FC). Red line indicates the AR7W section, whereas the blue line indicates the OVIDE section.

  Figure 3. (a) OI-derived multiproduct density (σ 0 ) field along isobath 2400 m. (b) The crossshore geostrophic velocity field along isobath 2400 m. The positive (negative) values indicate inshore (offshore) flows. The green line indicates the depth at which the maximum (accumulated) vertical transport is found (i.e., levels of no motion). The σ o =27.6, 27.7, 27.8 kg m -3 isopycnals are contoured in black. (c) The density along the boundary from s = 0 to s = 1 averaged in the upper layer (1-300m, red curve) and the intermediate layer (301-1500m, blue curve). The maximum vertical transport (black curve) accumulated along the boundary from s = 0 to s = 1. The upward slopes indicate the downwelling (LD-Labrador Downwelling, s = 0.5~1, ID-Irminger Downwelling, s = 0~0.33), and the downward slope indicates upwelling (LU-Labrador

  0.43 Sv (2 times STD) estimated from 12000 bootstrap estimates. The transport in density space is 2.11 ± 0.28 Sv by crossing the nearly-horizontal 27.73 kg/m 3 isopycnal surface. Note that this manuscript submitted to Geophysical Research Letters does not fully account for water mass formation near the boundary since the diapycnal flux is also carried out by the along-stream densification in the upper layer and cross-stream eddy circulation in the deeper layer(Brüggemann & Katsman, 2019).

Figure 4 .

 4 Figure 4. (a) The along-shore average of the cross-shore velocity along the SPG averaged at the 100 m-spaced isobaths between 700 m and 3000 m. The x-axis represents distinct isobaths rather than the cross-shore distance. The dashed line indicates the isobath (2400m) where the maximum vertical transport is found. (b)(c) The corresponding geostrophic streamfunctions obtained by accumulating the vertical transport from the surface in depth space and density space. The errors in gray patch are one standard deviation derived from the bootstrap simulations. The dashed lines indicate the depth (density) of maximum overturning. Panels (d)-(l) are the same as (a)-(c), but

.14±0.47 (1044) Annual 2.23±0.71 (986) -2.17±0.74

  who did not detect a statistically significant signal cycle when estimating the composite monthly mean MOC transport using the OSNAP program's 46-month records. Furthermore,[START_REF] Sayol | Seasonal and regional variations of sinking in the subpolar North Atlantic from a high-resolution ocean model[END_REF] used a high-resolution model to find that seasonal variability in boundary sinking is rather insignificant in comparison to interior sinking, and that the variability is thought to be driven by ageostrophic dynamics that our large-scale geostrophic balance cannot capture. Nevertheless, based on our observations, a potential upper bound on the seasonal cycle amplitude has been established.

	Season LD	LU	ID	SPG
	Winter	1.97±0.30 (970)	-2.56±0.44 (1108) 2.57±0.31 (1190) 1.99±0.58 (975)
	Spring	2.27±0.31 (1274) -2.04±0.31 (1288) 1.92±0.61 (1278) 2.14±0.81 (1253)
	Summer 2.16±0.28 (923)	-1.81±0.34 (1301) 1.84±0.84 (1425) 2.19±0.82 (903)
	Autumn 2.54±0.51 (891)	-2.27±0.60 (1084) 1.88±0.45 (1372) 2

(1182) 2.05±0.79 (1304) 2.12±0.43 (1088) Table

Data Availability Statement

The In Situ Analysis System-ISAS15 dataset (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) is available from the SEANOE repository (https://www.seanoe.org/data/00412/52367/, last access: July 2021) and described in [START_REF] Gaillard | In situ-based reanalysis of the global ocean temperature and salinity with ISAS: Variability of the heat content and steric height[END_REF]. The Coriolis data set for ReAnalysis-CORA V5.2 (1950-to present) is available from the SEANOE repository (https://www.seanoe.org/data/00351/46219/, last access: September 2019) and described in Szekely et al. (2016). The EN4.4.2.2 dataset for years 1990 to present is provided by Met Office Hadley Centre and available at https://www.metoffice.gov.uk/hadobs/en4/ (last access: November 2021) and described in Good et al. (2013). The A25-Ovide and AR7W hydrography sections are available via the CLIVAR and Carbon Hydrographic Data Office (CCHDO) platform (https://cchdo.ucsd.edu/). The NCEP/NCAR Reanalysis 1 (1948/01/01 to present) is provided in National Centers for Environmental Prediction (/data/gridded/data.ncep.reanalysis.html). The ERA5 dataset (1950-to present) is available in Copernicus Climate Change Service Climate Data Store (CDS), manuscript submitted to Geophysical Research Letters https://cds.climate.copernicus.eu/cdsapp#!/home. The present analysis does not use new unpublished data.

Research Data Archive at NOAA/PSL: /data/gridded/data.ncep.reanalysis.html. Våge, K., Pickart, R. S., Sarafanov, A., Knutsen, Ø., Mercier, H., Lherminier, P. et al. (2011)


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de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.