Large-scale control of the retroflection of the Labrador Current

The Labrador Current transports cold, relatively fresh, and well-oxygenated waters within the subpolar North Atlantic and towards the eastern American continental shelf. The relative contribution of these waters to either region depends on the eastward retroflection of the Labrador Current at the Grand Banks of Newfoundland. Here, we develop a retroflection index based on the pathway of virtual Lagrangian particles and show that strong retroflection generally occurs when a large-scale circulation adjustment, related to the subpolar gyre, accelerates the Labrador Current and shifts the Gulf Stream northward, partly driven by a northward shift of the wind patterns in the western North Atlantic. Starting in 2008, a particularly strong northward shift of the Gulf Stream dominates the other drivers. A mechanistic understanding of the drivers of the Labrador Current retroflection should help predict changes in the water properties in both export regions, and anticipate their impacts on marine life and deep-water formation.


Retroflection index
A small number of virtual particles that leave the Labrador Current at the Grand Banks flow neither west towards the Slope Sea or the eastern American continental shelf, nor east towards the subpolar North Atlantic; rather, they go south from the tip of the Grand Banks.These represent approximately 7% of the particles, and their number shows little variability with time (Fig. S8).Since these particles do not affect the retroflection index significantly and for the sake of simplicity, we count them as retroflected.
Figure S8: Time series of the number of particles going south from the Grand Banks (blue line), the retroflection index (orange line), and the retroflection index from which the particles going south are removed (green line).
In addition to the retroflection index based on Lagrangian trajectories, we compute a retroflection index based on an Eulerian approach.The Eulerian index is computed from the difference in the volume transport across the WB and SESPB sections (Fig. S14a).Whereas the Eulerian index represents the total transport, the Lagrangian index only tracks waters of subarctic origin.We therefore chose the Lagrangian index to study what controls the retroflection, but the two indices show a similar variability (not shown), and the Eulerian index is simpler to calculate.

Eliminated variables
During our analysis, we identified some variables that are not significantly correlated with the retroflection index.Whereas these results do not identify the forcing mechanisms at play, they help us understand what the main drivers are.The retroflection index has a low correlation with the freshwater transport.Furthermore, there is no clear relation between the retroflection index and the buoyancy fluxes, the mixed layer depths and convection along the shelf or in the Labrador Sea.This suggests that the dynamics of the system is the main determinant of the retroflection, while thermohaline processes play an indirect role, e.g. by affecting the strength of the transport.The buoyancy fluxes across the air-sea interface are calculated as follows: where α and β are, respectively, the thermal expansion and the haline contraction coefficients, both functions of salinity and temperature, Q is the air-sea heat flux, c p is the heat capacity of water, and (E − P ) is the net freshwater flux from the ocean, or evaporation minus precipitation, neglecting the river run-off as we are far from the coasts [3].

Validation of the ocean reanalysis
The GLORYS12V1 outputs are evaluated against measurements of temperature, salinity and velocity provided by the Department of Fisheries and Oceans (DFO) Canada along selected hydrographic sections [1, see Fig. S14a].A visual inspection shows that the values, location and timing of the fronts, both associated with the Gulf Stream and that separating the Labrador Shelf from the Labrador Sea, are generally consistent with observations (Fig. S10).GLORYS12V1 reproduces the main features of the observed velocity field, including the structure and direction of jets on the continental shelf and the location of the shelf-break jet.It underestimates the velocity of the shelf-break jet at the latitude of the SI section, and the scarcity of the velocity data, with only one transect per summer, does not allow for a more quantitative estimate of this underestimation.The shelf-break jet is better resolved at lower latitudes, from the WB section downstream.Only the position of the NAC front at the SEGB section sometimes diverges from observations.

Comparison with trajectories of floats and drifters
The Lagrangian trajectories of virtual particles computed from the GLORYS12V1 ocean reanalysis are compared with trajectories of actual floats (Argo and RAFOS/SOFAR) and surface drifters.There are two important differences to note between the model-based and the observation-based trajectories.
(1) Most of the Argo and RAFOS/SOFAR floats drift deeper than our virtual particles, and are thus advected by the Deep Western Boundary Current (see section Method).( 2) While floats and drifters travel at a fixed depth, virtual particles can move vertically.Nevertheless, we use floats and drifters trajectories to perform a qualitative comparison with the virtual particle trajectories.A visual inspection suggests the pathways of the floats/drifters and of the virtual particles generally agree (Fig. 1b,c).Furthermore, similarly to the virtual particles, two major pathways emerge from the observational dataset in the area of the Grand Banks: a westward pathway into the Slope Sea, and an eastward (retroflecting) pathway towards the subpolar North Atlantic.The limited number of observational platforms drifting in the area and period of interest  to the Labrador Current diminishes dramatically as it flows south, reaching a few percents only on the Scotian Shelf.Given our interest in the fate of the fresh and well-oxygenated Labrador Shelf waters, the Lagrangian retroflection index is therefore more appropriate than the Eulerian index, as the latter contains the contributions from external sources.surface layer by the time they reach Flemish Cap.Most of the particles take 0-1 month to reach the WB section, 2-3 months to reach the FC section, 4-7 months to reach the SESPB section, and 8-15 months (a larger spread) to reach the HL section.These times equate to an advection velocity along the Labrador shelf of ∼7-11 cm s −1 .In comparison, [7] measured velocities of 6-23 cm s −1 in the Labrador Current, and [2] and [9] found an advection velocity of ∼20 cm s −1 by tracking salinity anomalies.

Figure S1 :Figure S2 :
Figure S1: (a) Full (grey) and smoothed (black) retroflection index (see Fig. 3 of the main paper).(b) Indices of NAO (bars, bottom panel) and AO (black line, bottom panel).(c) Salinity in the subpolar North Atlantic (SPNA, dashed line) and temperature and salinity on the eastern American continental shelf (EACS, continuous lines), averaged over the top 500 m (boxes in Fig.S4a).Correlation coefficients with the retroflection index are respectively of -0.58, 0.57, and 0.57.

Figure S3 :Figure S5 :
Figure S3: Composite maps in periods of strong (left) and weak (right) retroflection, for the anomalies of the same variables as Fig. 4. Composites are based on the periods identified in Fig. 3a. 3

Figure S6 :
Figure S6: SSH maps showing the evolution of the formation of a cyclonic eddy (yellow arrow) at the tip of the Grand Banks from the tongue of Labrador Current Waters.

Figure S7 :
FigureS7: Anomalous number of eddies (in percentage) near the tip of the Grand Banks during strong (red) and weak (blue) retroflection periods based on the ±1σ periods of the retroflection index, as a function of lag.We differentiate cyclonic (dotted) and anti-cyclonic (dashed) features.The grey band indicates the expected lag between the retroflection index and the time when eddies are counted.

Figure S9 :
Figure S9: Yearly averave of the smoothed Lagrangian retroflection index (dark blue), of the observed contributions of the Labrador Current Waters (LCW, red) to the deep waters at the mouth of the Laurentian Channel, on the 1027.3kg m −3 isopycnal [6], and of the freshwater content anomaly in the upper 1000 m of the subpolar North Atlantic (green), reproduced with authorization from [5].

Figure S10 :
Figure S10: Comparison between DFO observations (left) and the GLO-RYS12V1 reanalysis (right) along the SI section (see Fig.S14afor the location of the hydrographic section).For temperature and salinity, observations from the 2004 sampling campaign are compared with the average values in summer 2004 in GLORYS12V1.For the zonal velocity and meridional velocity, we show the average over the sampled days, in summers of 2008-2018.The black contour indicates the 34.8 salinity cut-off used to discriminate the Labrador Shelf waters from the Labrador Sea.

Figure S11 :
Figure S11: Observations from Argo floats (second row), RAFOS/SOFAR floats (third row) and surface drifters (bottom row) carried by the Labrador Current and passing through the Grand Banks region, in periods of weak (middle column) and strong (right column) retroflection identified from the retroflection index (see Fig.3).The top row presents the three data types combined, and the left column the trajectories over the complete 2000-2018 period.The retroflected floats and drifters appear in blue, and the westward-flowing ones in green (see Fig.1).The black and magenta lines in the first panel show the hydrographic line that the platforms have to cross to be considered.The black contour delineates the 350 m isobath.

Figure S12 :
Figure S12: Distribution of floats and drifters over 2000-2018 categorized by float type: Argo floats (magenta), RAFOS and SOFAR floats (blue) and surface drifters (orange).The colour shading indicates if the floats retroflect (vivid) or move westward from the tip of the Grand Banks (dull).On the x-axis, years are identified as periods of weak (green) or strong (red) retroflection based on the retroflection index presented in Fig. 3.

Figure S13 :
Figure S13: Time series of Labrador Current volume transport, computed from an Eulerian approach, on the shelf (a), at the shelf-break (b), and over both (c), at different sections, smoothed with a one-year moving average.For the location of the sections and the separation point between the shelf and shelfbreak branches, see Fig.S14a.