Within the framework of the global overturning circulation, the Atlantic meridional overturning circulation (AMOC) is a unique feature characterized by a net northward heat transport driving the variability of European climate (Sutton and Dong 2012;Moffa-Sánchez and Hall 2017). The northward limb of upper warm and salty waters entering the South Atlantic sinks in the Labrador Sea and Nordic seas to feed the southward lower limb, which exports cold and salty deep waters into the Indian and Pacific basins. Deep waters are then upwelled in the Southern Ocean before returning as lighter waters into the North Atlantic hence closing the middepth cell shown by red contours in Fig. 1. Upwelled waters exit the Southern Ocean and continue their journey in the Indo-Pacific sector before rejoining the upper limb of the AMOC either through Drake Passage (DP) south of South America or south of South Africa.
In the literature both pathways are named after their different thermohaline properties: the "cold" route through DP brings relatively cold and fresh waters into the South Atlantic (Rintoul 1991), whereas the "warm" route supplies comparatively warm and salty waters through the Agulhas system (Gordon 1986).
Due to their different thermohaline properties, the quantification of each route contribution is of major importance especially since the salinity transport into the South Atlantic is one of the factors controlling the AMOC stability (Drijfhout et al. 2011;Mecking et al. 2016): a larger contribution from the warm route implies salinity import into the Atlantic resulting in a potential instability of the AMOC. The relative contributions of both routes have thus been discussed by many numerical and observational studies: some suggests the cold route is the major source for the upper limb of the AMOC (Rintoul 1991;Schmitz 1995;Macdonald 1998;Sloyan and Rintoul 2001;Talley 2013) while most support the warm route prevalence (Gordon 1986;Holfort and Siedler 2001;Speich et al. 2001;Donners and Drijfhout 2004;Speich et al. 2007;Rodrigues et al. 2010;Cessi and Jones 2017;Rühs et al. 2019;Rousselet et al. 2020Rousselet et al. , 2021;;Xu et al. 2022).
The approach to quantify both routes using distinct hydrographic properties is challenged by some studies who identified an indirect cold route carrying a mixture of waters that traveled from DP into the Indian Ocean supergyre along with the Antarctic Circumpolar Current (ACC) before reentering the South Atlantic through the Agulhas system (Speich et al. 2001(Speich et al. , 2007;;Rousselet et al. 2020). Donners and Drijfhout (2004) also emphasize the discrepancy in route estimations due to methodological differences between Eulerian and Lagrangian approaches or with methods using observations at hydrographic sections such as inverse box model. So far, studies using Lagrangian analysis, although too scarce, all agree with a major warm route contribution: 85% in Speich et al. (2001) based on a relatively coarseresolution (28 3 0.58) simulation of the OPA Ocean General Circulation Model (OGCM); 95% in Rousselet et al. (2020) Denotes content that is immediately available upon publication as open access. estimated with the 18 state estimate from Estimating the Circulation and Climate of the Ocean, version 4, release 3 (ECCOv4r3) constrained with over 1 billion observations; and 60% in Rühs et al. (2019) based on a high-resolution eddy-resolving ocean model simulation (INALT20 at 1/208 resolution in the South Atlantic nested within a global 1/48 resolution model).
The variety of model outputs used in the previous Lagrangian studies raises the question of what determines the quantitative differences in the routes partition. One hypothesis is that Agulhas leakage (AL; i.e., the portion of waters from the Agulhas system injected into the South Atlantic) increases with resolution (Biastoch et al. 2008;Beal and Elipot 2016). More generally, the pathways and relative strength of the mean currents in the South Atlantic can be a factor governing the routes partition. Another hypothesis is that diffusivity associated with eddies may increase the exchanges across the South Atlantic supergyre boundaries. Prevailing diffusion over advection due to the currents in the South Atlantic would result in a more balanced partition between the cold and warm routes.
In this study we reconsider the relative contribution of the cold and warm routes for the AMOC upper limb using the Southern Ocean State Estimate (SOSE), which is the ocean state estimate with the highest resolution available (1/68 resolution). SOSE is an eddy-permitting general circulation model of the Southern Ocean assimilating a large observational dataset (Mazloff et al. 2010) to constrain initial conditions and surface forcings within observed uncertainties. Thus, it provides the closest fields from observations a numerical model can supply.
First, we review the characteristics of the main routes using a specifically designed Lagrangian experiment: following Blanke and Raynaud (1997) methodology, we interpret SOSE fields by means of Lagrangian analysis connecting two meridional sections, one at DP and one from south of the tip of South Africa to Antarctica, to one longitudinal section at 6.78S. This Lagrangian method, specifically designed with similar characteristics as previous Lagrangian studies (Rühs et al. 2019;Rousselet et al. 2020), allows for a quantitative estimate of the relative transport by the cold and warm routes. Transit times and thermohaline properties at sections of entry and exit are also examined and compared with the previous Lagrangian analyses. Then we consider the relative control of the mean flow versus the eddy flow on the routes partition by comparing them with a similar state estimate at lower resolution. Particularly, a direct and unambiguous comparison with coarser-resolution fields from ECCOv4r3 (;18) provides new insights on the influence of eddies on the routes partition while using state estimates that assimilate the same data. The main dynamical features of the South Atlantic are studied and compared using both Eulerian and Lagrangian time means. Additionally, the role of eddies is examined by mapping the mean and eddy kinetic energies as well as the diffusivity derived from particle trajectories and by estimating the advection/diffusion ratio, that is, the Péclet number, in the South Atlantic.
The methodology consists of Lagrangian analysis using three-dimensional numerical particle trajectories advected with high-resolution time-varying velocity fields of the SOSE model. The SOSE model configuration is detailed in section 2a while the particle trajectory integration and eddy diffusivity estimation methods are presented in sections 2b and 2c.
The SOSE model is a 1/68 eddy-permitting version of the three-dimensional Massachusetts Institute of Technology General Circulation Model (MITgcm) that satisfies exact conservation laws for mass, momentum, temperature, salinity, and sea ice. The model domain is restricted to the Southern Hemisphere with 52 vertical levels with varying thickness and a horizontal domain spanning from the equator to 808S. Similar to the ECCOv4r3 effort, the model inputs are adjusted to best fit to a large number of available observations including satellite products as well as in situ temperature and salinity profiles (Argo). SOSE fields are currently the ocean state estimate with the highest horizontal resolution available. SOSE output includes dynamically consistent time-evolving estimates of horizontal and vertical velocities, temperature and salinity archived at 5-day means.
The SOSE version (iteration 135) used in this study spans 7 years (from December 2012 to the end of 2019) and uses open boundary conditions (OBC) produced from ECCOv4r4 (i.e., release 4) through 2017 and the ECCOv4r4 climatology for 2018 and 2019 [SOSE OBCs use a more recent release of ECCO than the one analyzed in Rousselet et al. (2020)]. This 1/68 SOSE setup evolves from the 1/38 setup of Verdy and Mazloff (2017). Specific details of this SOSE configuration are given in Swierczek et al. (2021). A 4-month spinup period is removed restricting the dataset extent from 21 March 2013 to 20 March 2019. The 5-day mean velocities provide a representation of the eddying flow in the South Atlantic and adjacent Southern Ocean sector consistent with available observations. Overall, the sea surface height (SSH) field is consistent with that observed by satellite (see Wang et al. 2014). The SOSE estimate adequately represents the ACC transport (163 6 6 Sv; 1 Sv ≡ 10 6 m 3 s 21 ), which stands in the upper range of previous estimates: 134 6 11 Sv estimated from observations achieved in the framework of the International Southern Ocean Studies program in Cunningham et al. (2003); 141 6 3 and 173 6 11 Sv based on mooring measurements in Koenig et al. (2014) and Donohue et al. (2016) and an updated estimate of 157 6 5 Sv, which combines these observations and a high-resolution model Xu et al. (2020); 152 6 19.2 Sv estimated from an ensemble of ocean reanalyses in Uotila et al. (2019). SOSE also provides a qualitatively good picture of the two major jets within the ACC, the Polar Front (PF) and the Subantarctic Front (SAF) (see Firing et al. 2011 for a detailed comparison with current observations). The major current systems of the South Atlantic are also adequately represented: the Agulhas Current (AC) carries about 60 6 7 Sv at the Agulhas Current Time-Series Experiment (ACT) section from top to bottom [the section runs along 27.58-28.858E and 33.258-35.758S, as defined in the Agulhas Current Time-Series Experiment from Beal et al. (2015)]. The Malvinas Current (MC) transports about 43 6 15 Sv down to 5000 m (;39 Sv in the upper 1500 m) at 448S. These values are comparable to those of previous observational studies [84 6 24 Sv at the ACT section in Beal et al. (2015); 37.1 6 2.6 Sv at 418S in Artana et al. (2018)]. The mean net northward volume transports across 68S and across 308S, 12.5 6 3.5 and 12.6 6 3.3 Sv, respectively, are in agreement within uncertainties with previous estimates of the MOC ranging from 12 to 15 Sv at 308S (Cessi 2019; Table 1). They are also within the uncertainties of MOC observations from moored instruments at 34.58S (average 14.7 Sv in Meinen et al. 2018). The time series of the AMOC strength at 6.78S shown in Fig. 1 reveals TABLE 1. Summary of transport estimates (in Sv and as a percent of the net northward flow reaching the South Atlantic, i.e., sum of the warm and cold routes) and transit times (years) of the warm and cold routes of the AMOC upper limb quantified using Lagrangian analysis. For each study, the type of model used and its resolution are also provided. The most frequent (peak) and median (T50) transit times are given for the studies performed using roughly the same Lagrangian sections
. OCCAM 5 Ocean Circulation and Climate Advanced Modelling project model. Warm route Cold route Model (resolution) Transport (Sv) Percent Transit time Transport (Sv) Percent Transit time Speich et al. (2001) ORCA (;28 3 18) 12.6 85% } 2.3 15% } Donners and Drijfhout (2004) OCCAM (1/48) 15.4 95% } 0.9 5% } Speich et al. (2007) ORCA (;28 3 18) 15.8 99% } , 1 1% } R ühs et al. (2019) INALT20 (1/208) 6.3 58%-60% Peak: 7, T50: 9 4.7 40%-42% Peak: 12, T50: 18 Rousselet et al. (2020) ECCOv4r3 (18) 13 97% Peak: 6, T50: 9 0.4 3% Peak: 12, T50: 13 Xu et al. (2022) HYCOM (1/128 3 1/128) 13.3 90% } 1.5 10% } Our experiment SOSE (1/68) 12.3 88% Peak: 9, T50: 11 1.7 12% Peak: 11, T50: 20
interannual changes ranging from 1 to 25 Sv, which is a variability comparable to that observed at 118S (Herrford et al. 2021).
The sources of the AMOC upper limb are quantified with offline Lagrangian experiments using the Ariane tool (Blanke and Raynaud 1997;Blanke et al. 1999). Ariane is an opensource Fortran software designed to advect virtual fluid particles with three-dimensional volume-conserving velocity fields. The resulting trajectories represent the main pathways connecting an entry section to different exit sections. To quantify these connections a small amount of volume transport (maximum 0.01 Sv) is attributed to each particle during initialization so that the cumulative transport of all particles is representative of the total transport through the entry section. Subsequently particles are tracked until they first cross one of the exit sections closing the Lagrangian domain of integration. The individual particle integration stops once the trajectory goes back to the entry section or crosses one of the exit sections. This methodology contributes to saving some computational time, allowing for the advection of millions of trajectories, which can provide statistically robust results. Since the volume transport is conserved along the particle trajectory the total transport through each exit section is the sum of the transport carried by each particle reaching the section. Temperature and salinity are also linearly interpolated along the particle trajectory and saved for subsequent analysis.
In this study we released virtual fluid particles along an entry section at 6.78S (at the southern boundary of the grid cells) every 5 days using the SOSE velocity fields for a total over 2 million particles. The particles are seeded from the surface to the depth of the density surface s 2 5 36.6 kg m 23 , which represents the lower boundary of the upper limb of the AMOC (black dashed line of the top panel in Fig. 1). The particles are then tracked backward in time for a maximum of 90 years, and stored every 5 days, to identify the sources of the AMOC upper limb. Such a long integration time is reached by looping over the available 6-yr-long velocity data so that over 97% of the particles are intercepted on the Lagrangian domain boundaries. The looping technique introduces errors, represented by nonphysical jumps in the fields, that can be neglected if a sufficiently high number of particles is seeded (Thomas et al. 2015). However, the jumps in velocity and tracer fields do not induce any unphysical drift or real trend.
The predefined exit sections are located at DP (668W) and at the tip of South Africa in the AC region (228E) from top to bottom. These two sections define the origin of the AMOC upper limb from the cold and warm route, respectively. To reach the exit sections backward in time particles are seeded every five days in a number proportional to the northward transport through the entry section. Indeed, the grid cells with southward velocity at any time along the entry section are not sampled by Ariane since the particles advected backward in time exit the Lagrangian domain of integration at the first time step. The mean northward transport through 6.78S amounting to 45.96 Sv is accounted for with this technique.
A significant number of particles meander and exit the domain carrying 30.31 Sv back across 6.78S. These particles are removed from the calculation. In this way, the remaining Lagrangian net transport through 6.78S amounts to 15.65 Sv, and it can be attributed to the sources of the upper limb of the AMOC. This value differs from the Eulerian net transport (12.5 Sv) because the grid cells at 6.78S with southward velocity are not sampled by Ariane. Agreement between Lagrangian and Eulerian transports through 6.78S is obtained running two complementary experiments: 1) a backward in time experiment seeding only grid cells with northward transport along a section at 6.78S (total northward transport 5 45.96 Sv); and 2) a forward in time experiment seeding only grid cells with southward transport along 6.78S (total southward transport 5 33.35 Sv). The transport difference between both experiments is the net southward transport through 6.78S and amounts to 12.6 Sv, a value close to the Eulerian net transport (12.5 Sv).
Following Dö ös (1995) methodology, the cold and warm routes are evaluated by calculating Lagrangian streamfunctions representing the time-and depth-integrated ensemble-averaged volume transport pathways inferred from all trajectories reaching an exit section backward in time (particles still recirculating in the domain after 90 years are discarded from the calculation). The Lagrangian streamfunction measures the "center of mass" of the transport between exit and entry sections.
The following results are given in terms of transport (or relative transport %) since each particle is associated with a slightly different transport. The number of particles per grid cell is proportional to the transport in that cell, but because there is an integer number of particles per grid cell, particles in different cells carry a slightly different transport. Although the experiment is conducted backward in time, the resulting Lagrangian diagnostics are presented in a forward sense: from the sources (Agulhas section or Drake Passage) to 6.78S section.
To investigate the role of mesoscales with different resolutions such as SOSE and ECCO, three different Eulerian and Lagrangian diagnostics are used and detailed in the following.
Examining the distribution of the Eulerian-based mean kinetic energy (MKE) and eddy kinetic energy (EKE) provides a first insight toward determining the relative contributions of the mean flow and the mesoscale instabilities. The MKE is defined as the sum of the squared time-mean zonal and meridional velocities, u and y, respectively, [Eq. ( 1)], whereas the EKE equals the sum of the squared anomalies u and y from a multiyear averaged u and y [Eq. ( 2)]:
where the overbar indicates a time average.
Mesoscale (10-100 km) processes such as eddies and jets induce fluid particles to disperse quickly, consequently accelerating mixing and thus influencing large-scale circulation (1000 km) (LaCasce 2008). In a time-dependent velocity field, such as that of SOSE, individual Lagrangian trajectories are chaotic and thus very complex. The ensemble-averaged view offered by the Lagrangian streamfunction does not provide a measure of the dispersion of trajectories from the average paths. One quantitative measure of the dispersion due to eddies and chaotic divergence of trajectories is the Lagrangian eddy diffusivity. Several studies evaluate eddy diffusivity derived from drifter data (e.g., Krauß and Böning 1987;Davis 1991;Swenson and Niiler 1996;Poulain 2001;Lumpkin and Flament 2001;Bauer et al. 2002;Zhurbas and Oh 2004;Sallée et al. 2008;Koszalka et al. 2011;Zhurbas et al. 2014;Peng et al. 2015) or from simulated Lagrangian trajectories in eddy-resolving ocean models (e.g., McClean et al. 2002;Koszalka and LaCasce 2010;Griesel et al. 2010Griesel et al. , 2014;;Chen et al. 2014;Wolfram et al. 2015). Particle trajectories advected with SOSE fields offer an interesting opportunity to estimate the lateral eddy diffusivity due to mesoscales in SOSE. In our case study, the 3D trajectories are divided into three density classes representative of the surface (29.5-34 kg m 23 ), middle (34-35.5 kg m 23 ), and deepest (35.5-36.6 kg m 23 ) circulation of the upper branch of the AMOC. The density discretization is done on the initial position of each particle at 6.78S independent of their subsequent density along their trajectory. The density classes are chosen wide enough so that most of the particles travel almost exclusively within the same layer between entry and exit sections despite the property modifications experienced along trajectories. In this way we consider the trajectories as isoneutral, and we compute the isopycnal diffusivity in each of the three s 2 layers (hereafter referred as lateral eddy diffusivity).
The Lagrangian diffusivity, a second-order statistic of the probability density distribution of particles transport, is estimated from the Lagrangian trajectory positions and velocities (longitude, latitude, u, y), following a robust approach developed by Zhurbas and Oh (2003). This approach assumes that the velocity field can be decomposed into a large-scale mean and an isotropic eddy field so that a scalar value of lateral Lagrangian diffusivity K(x, y, t) is representative of the eddy transport. Assuming isotropy in diffusivities, Zhurbas et al. (2014) defines K(x, y, t) as half the sum of the minor principal component of the symmetric part of the Davis diffusivity tensor k davis p2 (x, y, t) and the half growth rate of the minor principal component of the dispersion tensor k davis p2 (x, y, t):
Only the minor principal component (p2) of the tensors are used in the K(x, y, t) estimate with Lagrangian trajectories as they are less biased by the shear of the average flow than the major principal components (Oh et al. 2000;Zhurbas and Oh 2003). The Davis diffusivity tensor k jk (Davis 1991) and its symmetric part, referred to as k davis jk , are defined as
where jk are the indices for the horizontal dimensions in Cartesian space; angle brackets indicate averaging over the ensemble of particles; d k (t 0 2 t|x, y, t 0 ) is the kth component of the residual displacement of a particle followed backward in time for the period (t 0 2 t, t 0 ) and y j (t 0 2 t|x, y, t 0 ) is the residual velocity of this particle at t 0 . The residual velocity and displacement are defined as the departures from the Lagrangian mean velocity and displacement. In practice they are computed as follows: every particle position, stored bimonthly, is binned into a 18 3 18 grid and considered to be the initial point (x 0 , y 0 , t 0 ) of a pseudotrack.
Backward displacements d(t 0 2 t|x, y, t 0 ) are calculated and Lagrangian velocities at the pseudo-origin v(t 0 |x, y, t 0 ) are obtained by central timedifferencing of the discrete displacements. The mean value of displacement hd(t)i and Lagrangian velocity hv (t 0 )i are estimated by ensemble averaging. The residual displacements and velocities are then derived: d (t|x, y, t 0 ) 5 d(t|x, y, t 0 ) 2 hd(t)i and v (t|x, y, t 0 ) 5 v(t 0 |x, y, t 0 ) 2 hv(t)i. The half-growth rate of the dispersion tensor k disp jk is defined as k disp jk 5 1 2 ds jk dt , with
where d (t 0 1 t|x, y, t 0 ) represents the forward residual displacement computed similarly to the backward displacement defined previously but for the time period [t 0 , t 0 1 t].
The minor principal components of k davis jk and k davis jk are obtained with k p2 (x, y, t) 5 k xx (x, y, t)sin 2 u 2 k xy (x, y, t)sin2u
In practice, maps of eddy diffusivity are produced as follows: 1) particle trajectories are binned on an horizontal grid (18 3 18); 2) residual velocities and displacements are computed for each bin for each pseudotrack within the bin; 3) ensemble mean of k davis p2 , k disp p2 , and K are computed for each bin with a time lag t 5 10 days chosen as the best time interval to capture the looping trajectories within eddies. Even though diffusivity estimates are time varying, we decide to show time-averaged diffusivity estimates since the route pathways are also computed from timeaveraged particle trajectories. In the following we only show maps of k davis p2 and K since Davis (1991) suggests estimating the diffusivity directly from (4) while Zhurbas et al. (2014) states ( 3) is the most robust estimate of eddy diffusivity.
The influence of eddy-diffusion versus mean flow advection can be evaluated using the Lagrangian diagnostics derived from particle trajectories via the Péclet number. The notion of advection versus diffusion is important because if diffusion dominates over the mean Lagrangian flow advection then the partition between the cold and warm route would tend to an equal distribution. The Péclet number is a bulk measure of the prominence of advection versus diffusion. If the Péclet number is equal to 1 then diffusion balances advection, whereas if the Péclet number is .1 (,1) advection (diffusion) dominates. Here the Péclet number is based on the mean flow and is defined as the ratio between the total time-mean and depthintegrated Lagrangian streamfunction (m 3 s 21 ) computed in the SOSE Lagrangian experiment and the depth-integrated diffusivity (K in m 3 s 21 , i.e., the depth-weighted sum of the three density layers). Since both Lagrangian streamfunction and diffusivity are set to 0 where there is no particle, the Péclet number is consistent.
In this section we summarize the main properties of the cold and warm route pathways estimated with the SOSE ocean state estimate. The diagnostics [Lagrangian streamfunctions, transit times, and temperature-salinity (u-S) diagrams] are specifically chosen to compare with previous Lagrangian studies from the literature (Speich et al. 2001;Donners and Drijfhout 2004;Speich et al. 2007;R ühs et al. 2019;Rousselet et al. 2020). Hence, we also provide, at the end of the section, a review of the quantitative results obtained by different Lagrangian studies of the routes partition.
Of the Lagrangian time-average net transport across 6.78S, amounting to 15.65 Sv, 12.30 Sv (79%) stems from the AC section and can be attributed to the warm route, whereas 1.73 Sv (11%) originates from DP, representative of the cold route.
The remaining 1.57 Sv are still recirculating in the domain after 90 years of integration. A small number of particles, representing 0.3% of the total Lagrangian transport (5 3 10 22 Sv), is intercepted by a surface section marking fluid parcels that try to exit the Lagrangian domain into the atmosphere. The total Lagrangian net transport through 6.78S due to the cold and warm routes only is thus estimated to 14.03 Sv from which 88% originate from the warm Indian Ocean and 12% from the Pacific Ocean directly through Drake Passage.
The AMOC upper limb pathways are shown by mean Lagrangian streamfunctions for each route computed with the respective trajectories and their associated volume transport (Fig. 2). The overall pathways agree with the well-known concept of cold and warm routes. Particles enter from the Indian Ocean via the narrow Agulhas Current (between 358 and 388S) as already shown in previous Lagrangian studies. From there, waters steered by the South Equatorial Current (SEC) take a nearly zonal path until they veer north into the North Brazil Current (NBC) along the Brazilian coast (Fig. 2a). Some particles paths, characterized by the contours of weak transport (between 22 and 0 Sv, blue color shading), recirculate in the subtropical gyre before joining the NBC. A small number of particles (less than 0.1 Sv) enters the South Atlantic along the Antarctic coast with the southern branch of the Weddell Sea Gyre before veering northeast into the ACC and then in the subtropical gyre. This pathway appears due to the geography of the AC section reaching the Antarctic margin but should not be counted as part of the warm route but rather as part of the cold route. However, as it represents such a small amount of transport, the partition between the routes remains robust. On the western side of the domain, particles enter the South Atlantic from the northern part of Drake Passage (north of 608S) and follow a path through the MC before veering east along the South Atlantic Current just north of 458S (Fig. 2b). Most of the transport (streamlines , 20.2 Sv) thus travels north of the South Atlantic Subtropical Front (STF) located along 458S that marks the limit between the South Atlantic Subtropical Gyre and the northern boundary of the ACC (Smythe-Wright et al. 1998). During this eastward path a significant amount of transport (between streamlines 21 and 20.8 Sv) recirculate near the Mid-Atlantic Ridge at about 108W. Once the eastern part of the South Atlantic in the Agulhas retroflection area is reached, waters take a similar path as the warm route in the westward SEC and then NBC.
Figure 3 shows the typical transit times of each route from their entrance in the South Atlantic to 6.78S. The most frequent transit times are similar in both routes with 9 and 11 years for AC and DP sections, respectively. However, the median time and 90th percentile are significantly longer for the cold route (20 and 54 years) than for the warm route (11 and 31 years). The longer median transit time is explained by the additional detour taken by waters entering through DP into the MC and the southern branch of the subtropical gyre, whereas the AC directly leaks in the SEC. In both routes, the long tails in the time distributions suggest some particle may recirculate for a long time in the subtropical or tropical gyres before reaching 6.78S. Those slow particles are evidenced by the contours of weak transport (blue shading) on both panels of Fig. 2. We identify that 0.47 Sv (0.14 Sv) make the connection between the AC (DP) and 6.78S sections in 60-90 years with an average of 0.02 Sv yr 21 (4.6 3 10 23 Sv yr 21 ). It is thus impossible to attribute the remaining 1.57 Sv to one or the other route without considerably increasing the integration time. However, the long transit times represent 8% of the total transport of the cold route but only 4% of the total transport of the warm route, indicating the contribution of the cold route may slightly increase. These are small differences, and the overall partition is robust.
The Lagrangian streamfunctions clearly show that both routes share a common path in the SEC and NBC before joining 6.78S suggesting water mass mixing as already noted by R ühs et al. ( 2019). This becomes clear when visualizing the transport distribution in potential temperature-salinity (u-S) space both at source (AC or DP) and at 6.78S for each route (Fig. 4). Both histograms at 6.78S (right panels) cover the same range of temperature (48-308C) and salinity (34.5-37.5) with a maximum frequency at densities between 34 and 36.6 kg m 23 . At AC section, 99% of the waters are relatively salty (34.5-36) and spans a broad range of temperatures (48-258C) and densities (31-36.8 kg m 23 ) indicating that the warm route is not only fed with warm surface waters but also with fresher and colder intermediate waters (Beal et al. 2006). Those colder waters probably originate from a mix with the cold indirect route, identified in Speich et al. (2001) and Rousselet et al. (2020), carrying cold waters in the ACC before veering and warming into the Indian Ocean and the AC. The vast majority (.99%) of waters originating from DP is fresher (33-34.5), colder (from 228 to 88C) and consequently spans a density range from 35 to 36.8 kg m 23 typical of Antarctic Intermediate Waters (AAIW; Talley 1996). The u-S diagrams also show that waters entering through DP experience more thermohaline transformations along their path in the South Atlantic with a global increase in temperature and salinity.
Our results are in general agreement with almost all previous studies identifying the relatively warm waters entering FIG. 3. Distribution of transit times from (top) AC or (bottom) DP section and 6.78S weighted by transport. The inset also shows the median, the 90th percentile, and the e-folding time scales fitted to the distributions between 9 and 90 years.
through the AC section as the major contributor to the AMOC upper limb. Indeed, most Lagrangian analysis estimate the warm route contribution above 90% of the net northward transport into the North Atlantic (Donners and Drijfhout 2004;Speich et al. 2007;Rousselet et al. 2020;Xu et al. 2022; see Table 1), whereas Speich et al. (2001) quantifies a smaller contribution at 208N (85%). Recently, R ühs et al. ( 2019), using Lagrangian analysis in high-resolution eddy-rich velocity fields (INALT20 model at 1/208), suggested that the warm versus cold route contributions might be more balanced than previously stated (58%-60% originating from AC and 40%-42% from DP). The comparison with previous estimated transit times can only be made with other Lagrangian analysis performed using similar entry and exit sections. Table 1 reveals comparable connection times, but the cold route is slower with higher resolution, probably due to the intense mesoscale recirculations. All these previous studies used similar methodologies with similar locations for entry and exit sections. Hence the large range of volumetric contributions (from 1% to 42% for the cold route) can only be attributed to the differences in the model characteristics, parameterization used for each study as well as the time periods considered. These differences make it almost impossible to clearly identify the factors controlling the partition. The unambiguous comparison between SOSE (1/68 resolution) and ECCOv4r3 (18 resolution, used in Rousselet et al. 2020) allows analyzing the relative influence of the mean versus the eddy transport on the partition, using ocean state estimates.
SOSE and ECCO state estimates result from different horizontal resolutions of very similar MITgcm configurations. SOSE uses OBCs at its northern boundary (68N) derived from ECCO fields. Therefore, a direct comparison between the two configurations can provide insights into how the mean flow or the eddies can influence the routes partition.
The top panels of Fig. 5 show the total Lagrangian streamfunctions (i.e., combining the origins from AC and DP), computed with ECCO (more details on the Lagrangian configuration in Rousselet et al. 2020) and SOSE, superimposed with the depth of the 36.6 kg m 23 surface. As shown in Table 1, the ECCO state estimate carries more waters (;13 Sv) than SOSE (;12.3 Sv) from AC to 68S resulting in a relatively higher contribution from the warm route (97% and 88%, respectively). It is important to note that this contribution is a Lagrangian estimate of the Agulhas Leakage that is defined as the part of the AC transport persisting in the South Atlantic after ejection from the AC FIG. 4. Thermohaline properties binned in potential temperature/salinity space and shown as relative transportweighted frequency (color bar; %) following trajectories from the sources [(top) AC section and (bottom) DP section) to 6.78S. Dotted lines show contours of constant s 2 . Initially 99% of the AC (DP) transport can be found at temperature warmer (colder) than 48C (88C) and at salinities greater (lower) than 34.6 (34.5) as shown by the thick (dashed) black line.
retroflection. Both configurations highlight the same qualitative pathways, though more tortuous due to higher resolution in the SOSE configuration, from the entry sections to 6.78S. However, the Lagrangian contours are more spread (i.e., spanning a larger latitude range) at each entry sections in the case of the low-resolution (ECCO) configuration probably indicative of relatively less intense horizontal velocity gradients at DP and in the AC region. Another major difference is the route followed after entering through DP: in the low-resolution case, the particles follow a northeastward path within the ACC before joining the southern part of the South Atlantic Subtropical Gyre, whereas in the high-resolution case the particles are directly pumped into the MC and then flow eastward within the southern branch of the subtropical gyre. The northeastward path from DP is indicative of a less sharp STF at low resolution that is more easily crossed by particles in ECCO than in SOSE.
The depth of the 36.6 kg m 23 s 2 surface delimits the vertical extent of the subtropical gyre and is thus a marker of its intensity (Ridgway and Dunn 2007). The subtropical gyre in ECCO reaches maximum depths of 1200-1300 m in a region confined to the western part of the South Atlantic (608-108W). In SOSE the subtropical gyre is stronger (reaching 1500-1600 m) and extends farther east (08). The SOSE streamlines of the cold route strictly follow the subtropical gyre edges, which is also indicative of relatively stronger velocities. The AC region also expands farther west (158E) and deeper (maximum depths of 1500-1600 m) in SOSE than in ECCO (maximum depths of 1300-1400 m). The intense and narrow AL revealed by the deeper extension of the 36.6 kg m 23 s 2 surface matches the narrow streamlines of the SOSE Lagrangian experiment. The western spread and strengthening of the AC in SOSE are also visible at the surface on the sea surface height (middle panels of Fig. 5). No other significant differences can be drawn from the surface fields.
The Eulerian streamfunctions computed by time-averaging the horizontal velocities from ECCO and SOSE, and integrating from the surface to the depth of s 2 5 36.6 kg m 23 , are also indicative of the strength of the South Atlantic main features including currents and gyres (bottom panels of Fig. 5). To ease comparison, a constant was removed from SOSE's streamfunction so that the value on the solid boundary of South America is the same as ECCO's one (less than 0.1 Sv difference). Bottom panels of Fig. 5 show similar but more tortuous streamlines with narrower and more intense currents in the higher-resolution SOSE model. The vertically integrated AC expands farther west to 108E and the ACC carries a larger transport as shown by the saturated red color. The 0-Sv contour located at 458S delineates the position of the STF that is similar in both models but more intense in SOSE as revealed by streamlines closer together. We can also note the Mid-Atlantic Ridge recirculation at 108W in the SOSE configuration that was also previously identified on the Lagrangian streamlines (Fig. 2). Although the Eulerian streamfunction shows the same field as the Lagrangian, the warm and cold routes are obscured by the recirculating gyres carrying much larger transport. Hence the Lagrangian streamfunction provides a complementary and more detailed information on the routes as it is limited to the paths from exit to entry sections. A close examination of the Eulerian streamfunction (bottom panels of Fig. 5) allows picking out the streamline with a contour value of 0 Sv, which connects the entry and exit sections.
All diagnostics indicate a strengthening of the South Atlantic main features when resolution increases. Indeed, the mean ACC transport estimated at 668W amounts to 163 6 6 Sv in SOSE and 150 6 3 Sv in ECCO. The AC transport computed at the ACT section from top to bottom reaches 60 6 7 Sv in SOSE against 57 6 2 Sv in ECCO (magenta line in bottom panels of Fig. 5). The MC estimated from 0 to 5000 m at 448S for longitudes of northward transport is also more intense in SOSE (43 6 15 Sv) than ECCO (24 6 3 Sv). The large difference in the MC transport between SOSE and ECCO is also due to a less northward penetration of the latter, placing the maximum MC transport in ECCO farther south than 448S (cf. the bottom panels of Fig. 5). The increase in resolution also leads to higher variability in the main current transports. This overall strengthening is also visible on the SOSE narrow Lagrangian streamlines. The particles mostly circulate along the strong currents and the exchanges among them are reduced.
The Eulerian mean flow estimates reveal an increase of the AC with increased resolution. The AL is another important component of the Agulhas system since it injects the warm and salty waters from the AC into the South Atlantic. A complementary portion of the AC veers east and reenters the Indian basin forming the Agulhas Return Current (AR). Although the AC transport is increased in the high-resolution case, the AL can have a different dynamic as shown by Loveday et al. (2014). Quantifying the AL is thus essential to fully understand the mean dynamic of the Agulhas system and the transport of the warm route.
We follow the systematic Lagrangian methodology established to estimate the transport of the AC, AL, and AR (Durgadoo et al. 2013;Biastoch et al. 2009Biastoch et al. , 2015;;Schwarzkopf et al. 2019), using an additional Lagrangian experiment, designed to overcome the high spatiotemporal variability of the Agulhas system (Biastoch et al. 2009). We release transportweighted virtual particles for one year along a section at 328S across the AC. They are advected forward in time by SOSE velocity fields for a maximum of 5 years. The particles reaching the section referred to as the Good Hope line are considered part of the AL (green line on Fig. 6). The particles crossing the section at 358E provide an estimate of the AR (purple line on Fig. 6). Repeating this procedure for each year of the SOSE time series gives the transport variability through the sections. This methodology is further detailed in the appendix.
Figure 6 shows the mean Lagrangian streamfunction connecting the AC section to the AL and AR sections. The Lagrangian-based AC transport (60.7 6 2.3 Sv) is comparable to the Eulerian estimates in ECCO and SOSE (57 6 2 and 60 6 7 Sv, respectively). The mean Lagrangian-based AR from SOSE amounts to 30.6 6 2.4 Sv and is centered around 408S. The location of the AR is consistent with previous observations, but the transport is much lower than the estimate using hydrographic data (Lutjeharms and Ansorge 2001). SOSE simulates a more intense AL (21.1 6 2.1 Sv) than ECCO (15.1 6 3.6 Sv in Qu et al. 2019, defined as a long-term average of meridional integral of monthly westward flow in the upper 2000 m). The latter is close to the AL estimate from Richardson (2007, 15 Sv) using subsurface floats down to 1000 m. However, a recent study from Daher et al. (2020) using both observations and simulations of Lagrangian floats and FIG. 6. Mean (2013-19) Lagrangian streamfunction representing the net volume transport (Sv) across the AC section (red) toward the AL section (green) or the AR section (purple).
drifters down to 2000 m estimates the AL to be 21.3 6 4.7 Sv, a value similar to SOSE's. In summary, the increased resolution in SOSE versus ECCO results in enhanced AC and AL transports.
Both Eulerian and Lagrangian estimates demonstrate a global relative increase of the mean flow transports when resolution increases. The Lagrangian-based cold and warm route evaluations evidence an increased cold route contribution in the higher-resolution state estimate (SOSE). In the following we summarize how these increases can influence the partition. Two mechanisms can play in favor of a larger warm route contribution. The first one is the increase in the AL that results in a larger portion of Indian waters reaching 6.78S. The second one is the increase of the ACC transport: a more intense ACC results in a sharper STF acting as a boundary that prevents exchanges between the ACC and the subtropical gyre. As a consequence, particles traveling south of the STF cannot reach the subtropical gyre and are eventually swept away from the South Atlantic. This pathway, enhanced by a stronger ACC, represents a loss for the cold route contribution.
In contrast, the cold route contribution is enhanced by a larger ratio of MC/ACC transport, which controls the amount of particle entering through DP to be deviated north by a relatively more intense MC. These particles then travel north of the STF in the southern boundary of the subtropical gyre. Once north of the STF they can travel in the subtropical gyre and eventually reach 6.78S increasing the contribution from the cold route. The combined intensification of the ACC and MC leads to a net increase of the cold route contribution by carrying more particle from DP into the subtropical gyre while minimizing the exchanges through the STF. In summary, an increase in the AL does not necessarily imply an increase in the warm route contribution, if an increased MC/ACC ratio overcomes the AL enhancement. This competition is in contrast with previous studies indicating that coarse noneddying ocean models tend to overestimate the strength of AL (and hence potentially also the warm water route contribution) due to a too laminar and constant Indo-Atlantic exchange (Biastoch et al. 2008;van Sebille et al. 2009;Durgadoo et al. 2013).
The mechanisms outlined above explain the differences between partitions of the warm and cold route contributions from ocean state estimates at different resolution. This comparison reveals that the intensity of the South Atlantic main currents (or their transport) as well as the ratio among them are crucial factors controlling the routes partition.
The eddy-permitting spatial resolution at 1/68 from SOSE compared to the noneddy resolution of ECCO allows to also investigate the relative influence of the eddy flow compared to that of the time-mean flow on the partition.
The relative influence of the mean and eddy flows can be assessed by investigating the mean and eddy kinetic energies computed with both ECCO and SOSE surface fields (Fig. 7). MKE and EKE are computed as defined in section 2c(1) and we note that for the ECCO product the velocities are the sum of the Eulerian plus bolus velocities parameterizing the transport of tracers by unresolved eddies, which are used to advect virtual particles.
The MKE derived from ECCO and SOSE surface fields compares well with the MKE derived from satellite currents (AVISO, https://doi.org/10.48670/moi-00148) with maxima (.25 cm s 21 ) found along the strong currents: MC, NBC, AC and its retroflection and along the ACC. It is not surprising the kinetic energies are in good agreement since both state estimates are fitted to satellite data. SOSE represents the smaller-scale variability expressed by EKE, especially along the ACC. The satellite-derived EKE shows highest values in the Agulhas retroflection region (.25 cm s 21 ) and an important contribution in the MC zone (;15-20 cm s 21 ). The ECCO dataset fails to represent these patterns: the EKE spatial distribution is uniform in the entire South Atlantic with a relatively low maxima found in the Weddell Gyre (;10 cm s 21 ). In contrast, the EKE derived from SOSE surface fields represents well the high eddy energy in the Agulhas retroflection and MC areas but tends to overestimate the EKE in the vicinity of DP and south of the Agulhas retroflection with values reaching 25 cm s 21 while the satellite EKE is estimated around 12-13 cm s 21 . It is noteworthy that AVISO based EKE includes mesoscale variability of the geostrophic velocities only while the EKE from both ocean state estimates also contains ageostrophic components of the flow, which contributes to part of the differences.
The kinetic energy analysis clearly shows that the ECCO fields underestimate the eddy energy consequently favoring, and probably overestimating, the mean flow as a major driver of the cold and warm route partition. On the other hand, although SOSE fields give a better representation of the eddy surface flow very few connections are distinguishable between 6.78S and the AC and DP sections on the surface EKE distribution. On the contrary, pathways are clearly traceable between the key sections and 6.78S on the MKE maps thus suggesting the mean flow mainly drives the routes partition in both ocean state estimates. Another way to evaluate the influence of mesoscale processes on the partition is to estimate the eddy diffusivity affecting Lagrangian particle trajectories. Since SOSE fields better represents the eddy flow, we compute horizontal maps of the eddy diffusivity to identify the impact of the eddy diffusivity on the cold versus warm route contribution. Figure 8 displays horizontal maps of lateral eddy diffusivity vertically averaged in different s 2 layers representative of the surface (29.5-34 kg m 23 ), middle (34-35.5 kg m 23 ), and deepest (35.5-36.6 kg m 23 ) circulation of the upper branch of the AMOC. The density discretization is done on the initial position of each particle at 6.78S independently of their density along their trajectory. The density classes are chosen wide enough so that most of the particles travel almost exclusively within the same layer between entry and exit sections despite the property modifications experienced along trajectories.
Figure 8 shows both the symmetric part of the Davis diffusivity tensor k davis p2 [left panels; Eq. ( 4)] and the total diffusivity tensor K [right panels; Eq. ( 3)] superimposed with the total Lagrangian streamfunction computed with SOSE (black contours). The spatial patterns and magnitude of the K estimate are similar to that of the k davis p2 tensor estimate for each density layer. However, the K estimate is more horizontally spread due to the dispersion tensor [k disp jk ; Eq. ( 5)]. Overall, the diffusivity horizontal distribution remains comparable with increasing density (i.e., deepening) but decreases in intensity: maxima are about 22 3 10 3 m 2 s 21 at the surface and around 10 3 10 3 m 2 s 21 in the deepest density layer.
The highest diffusivity estimates (k davis p2 and K) are found in high kinetic energy regions: the western part of the AC system southwest of South Africa, the MC region from DP to 408S and within the narrow NBC along the Brazilian coast. The Agulhas rings entering the South Atlantic induce relatively intense diffusivity estimates ranging from 5 to 15 3 10 3 m 2 s 21 .
A similar spatial distribution in the AC region was already noted in Rühs et al. (2018) with comparable diffusivity values (between 8 and 16 3 10 3 m 2 s 21 ) obtained both with observations from drifter data and Lagrangian particles at 15-m depth. Zhurbas and Oh (2004) also found, in the South Atlantic, similar patterns of diffusivity estimates derived from surface drifters but with higher magnitudes: the maximum values are located in the AC system and MC region and amount to 22-24 3 10 3 m 2 s 21 at the surface. Considering that diffusivity decreases with depth the values computed here are consistent with Zhurbas and Oh (2004) estimates.
The lowest diffusivities (,500 m 2 s 21 ) occur within the tropical and subtropical gyres because of the low EKE values simulated by the model (and observed by Aviso) in the open ocean. A surface and subsurface band of lower diffusivity values (;1 3 10 3 m 2 s 21 ) is visible along 458S from 508 to 108W. A similar band corresponding to the circulation of the South Atlantic Current (SAC) is identified by Zhurbas and Oh (2004) between 308 and 408S with higher diffusivity values (about 5 3 10 3 m 2 s 21 ). In our study this band is located south of the SOSE Lagrangian streamlines associated with the SAC circulation. Considering simultaneously the position and the low values of diffusivities within this band it is unlikely that the diffusivity induces large exchanges between the subtropical gyre interior and the SAC boundary along this band. No conclusions as for the diffusivity in the Southern Ocean can be drawn from this experiment since very few or no particle FIG. 8. Spatial pattern of lateral eddy diffusivity estimates (color bar; m 2 s 21 ) combined with Lagrangian streamfunction (black contours of 0.5 Sv from 212 to 0 Sv) computed from particle trajectories advected with SOSE 1/68 velocity fields. The eddy diffusivity estimates from (left) the minor principal component of the symmetric part of the Davis diffusivity tensor k davis p2 and (right) the combined lateral eddy diffusivity estimate K, are computed from the particle trajectories whose initial position is located within the (top) 29.5-34, (middle) 34-35.5, and (bottom) 35.5-36.6 s 2 layers. The pale violet refers to diffusivity estimates between 1 and 500 m 2 s 21 .
(white grid cells on Fig. 8) circulates south of 608S. Overall the values of diffusivity estimated from SOSE in most of the South Atlantic are similar to the typical values ranging from 100 to 1000 used in ECCO in this region (Forget et al. 2015).
The SOSE diffusivity maps suggest that the dispersion is increased in regions of high energy in the South Atlantic such as the southern part of the NBC (between 258 and 408S), the Malvinas and Agulhas retroflections. As already depicted in section 4, these regions are of crucial importance in the routes partition due to their enhanced transport. To quantitatively evaluate the influence of eddy diffusion versus the mean flow advection in these regions we compute the Péclet number. Figure 9 shows the horizontal distribution of the Péclet number in logarithmic scale (base 10). The South Atlantic is clearly dominated by advection as indicated by the large values of the Péclet number: mean value of 10 5 and the minimum value is 3.3 at a single point. The lowest values of the Péclet number are found in the NBC, in the Agulhas, and Malvinas confluence zones and at the southern subtropical gyre boundaries especially along the STF suggesting these are the places where diffusion plays a more important role. However, the lowest Péclet values amount to 100, which implies that advection dominates even in these regions. In summary, in this study the mean flow, as measured by the Lagrangian streamfunction, dominates over the eddies, as measured by the Lagrangian diffusivity, in the cold and warm route partition. This is the case even where the diffusivity is highest, that is, in the crucial bifurcation regions of the Malvinas and Agulhas confluence zones, because the mean flow is also maximum there.
Our study agrees with previous Lagrangian estimates identifying the warm route as the major source (88%) for the upper limb transport of the AMOC. Our results confirm a relatively small direct contribution (12%) from the cold and fresh waters entering through DP. However, the indirect contribution, that is, the route from DP to the Indian Ocean and back to the South Atlantic through AC, is not quantifiable from this Lagrangian experiment. Indeed, the Lagrangian domain does not extend east enough to capture the indirect pathways and the signature of cold and fresh waters is not clearly detectable on the u-S diagrams since the waters experienced substantial changes in the Indian Ocean. As a consequence, the total (direct 1 indirect) contribution from the cold route cannot be assessed here. Previous studies agree that the warm route prevails over the total cold route but there is still no consensus on the total cold route contribution to the upper limb: Speich et al. (2001) suggest the total cold route amounts to 44%, Speich et al. (2007) estimate the contribution to 43%, whereas Rousselet et al. (2020) found a much lower contribution of 15%. Moreover, Rühs et al. (2019) indicated that the ratio of the two sources is subject to temporal variability. Using 6-yr-long fields repeated over 90 years might introduce a bias in the partition by overestimating or underestimating one or the other route: R ühs et al. ( 2019) obtained significantly different results when performing Lagrangian analysis that cycle different periods of time (e.g., the cold water route contribution changes from around 40% if cycling velocity data over the whole period between 1958 and 2009, to 34% and 48% if cycling only over the 2000s and 1960s, respectively).
The comparison between SOSE and ECCO mean flows suggests that an increase in the resolution leads to an increase in the major current mean transport. The AC and AL increase does not necessarily induce an increase in the warm route contribution. Rather the increase of the MC/ACC ratio overcomes the AL increase leading to an enhancement of the cold route contribution when resolution increases: MC/ACC ECCO 5 0.16 # MC/ACC SOSE 5 0.26. The MC has already been suggested to play an important role for the upper limb of the AMOC since all waters entering through DP travel in the MC before reaching the Atlantic equator (Friocourt et al. 2005). In particular our study shows that by creating a sharper and impassable STF, a stronger MC/ACC system pumps more waters in the Malvinas confluence zone and in the subtropical South Atlantic Gyre thus increasing the direct contribution of cold Pacific waters to the upper limb of the AMOC.
Maps of mean and eddy kinetic energies reveal that although ECCO clearly underestimates the eddy flow, the mean flow is the main driver of the connections between 6.78S and the Indian and Pacific oceans. Lateral eddy diffusivity estimated in three different density layers also shows that both AC and MC systems experience equivalent high diffusivities. We believe the eddy-diffusivity estimates presented here are robust enough since the SOSE outputs result from data assimilation and are well enough resolved in time (5 day) to sufficiently capture the cumulative effect of eddies on particle trajectories (R ühs et al. 2018). Despite some enhanced eddydiffusivity values near boundary currents, advection dominates over diffusion throughout the South Atlantic. Indeed, the Péclet number is large also in intense eddy regions, because the mean flow dominates over the eddy-induced diffusivity. Taken together, these results indicate that the eddy-induced flow does not play a significant role in the different ratio estimated for both experiments. However, we cannot completely rule out the role of eddies in the partition for the following reasons: 1) SOSE is not eddy-resolving: a higher resolution would be needed but it is not yet available for an ocean state estimate although improvements are implemented to provide a 1/128 SOSE iteration. 2) SOSE uses a telescoping grid and is eddy-permitting
(1/68) only south of 308S (Mazloff et al. 2010). A large part of the warm route is located between 6.78 and 308S. The increased resolution in this latitude range could change the warm versus cold route balance.
While several surface and subsurface observations estimated a fairly significant contribution from the cold route (Rodrigues et al. 2010;Drouin and Lozier 2019), the numerical Lagrangian-based study of R ühs et al. ( 2019) is the only one finding a substantially higher contribution from the direct cold route with 40% of the upper limb of the AMOC originating from DP (see Table 1). It is also the only one performed at eddy-resolving resolution (1/208). However, most of the previous studies, including a recent one performed by Xu et al. (2022) using 1/128 fields from HYCOM, agree with our partition: ;90% and 10% for the warm and cold routes, respectively. In the following we review the potential factors explaining the different estimate from R ühs et al. ( 2019). The INALT20 model provides quantitatively different major current ratios: the AC is more intense (86.3 6 32.6 Sv) while the ACC is clearly less intense and probably underestimated (116.2 6 7.5 Sv). The MC transport ranges from 37 to 48 Sv, which is close to the value in the SOSE estimate. Their estimate of the AL is weaker (12.9 Sv), and the AR is more intense (42 Sv; for more details see Schwarzkopf et al. 2019). The discrepancies between the high-resolution mean flow from INALT20 and the mean flow in SOSE can explain the different contributions from the cold and the warm routes: [also compared to a recent estimate from Daher et al. (2020;;21.3 Sv)]. This underestimation combined with a larger AR can substantially enhance the cold route contribution.
We can also add a third hypothesis explaining the discrepancies between both estimates: the diffusivity. Although our study indicates eddy diffusivity should not play an important role in the partition, we cannot completely eliminate this assumption especially because SOSE may underestimate diffusivities in the ACC region. On the other hand, it is difficult to draw a conclusion from INALT20 experiment since we do not have access to its diffusivity values. It is possible that INALT20 produces higher diffusivity values and lower advection/diffusion ratio since diffusivity tends to increase with model resolution (R ühs et al. 2018). However, it is not clear what is the effect of data assimilation on the advection/diffusion ratio. Last, both SOSE and INALT20 Lagrangian experiments have limitations: while SOSE assimilates data, it is only available for 6 years, whereas INALT20 offers a 5-decade simulation at 1/208 but does not assimilate data. Ideally, an eddy-resolving ocean state estimate would overcome some of the limitations noted above and could confirm/refute the warm route prevalence.
The results and comparisons with previous estimates presented in this study suggest that the mean flow characteristics are the main drivers of the cold route versus warm route ratio. In particular, more attention should be drawn to the MC/ACC ratio, which seems to parallel the cold route contribution (MC/ACC ECCO # MC/ACC SOSE # MC/ACC INALT20 ). Our results highlight the importance of faithfully representing the main currents of the South Atlantic such as the ACC, the Agulhas and the Malvinas systems as well as the eddy-induced transport when using Lagrangian particle diagnostics. Because ). The transports are estimated across each section defined in Fig. 6.
the AMOC contribution in the South Atlantic is largely through the mean flow, it is critical to obtain a good representation of time-mean transport of the major currents, whereas the impact of horizontal resolution (beyond representing mesoscale eddies) may not be as critical as one expected. The use of high-resolution (in space and time) state estimates assimilating observations is well suited to this kind of study, but estimates at higher-resolution and longer in time will be necessary to improve the evaluation of the warm/cold routes partition and its variability.
JANUARY 2023
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