We investigate the advection of the two LSW masses previously defined by Chomiak et al. (2022), LSW_1987-1994 and LSW_2000-2003, tracked along the neutral density (γ _n, kg/m³) isopycnal planes of γ _n = 27.99 and γ _n = 27.90, respectively. The scale in the anomaly of the convective imprint along each isopycnal level is nearly identical when looking in both temperature and salinity space (Chomiak et al., 2022) and thus redundant. Therefore, only salinity anomalies are explored here. We use EN.4.2.2 monthly gridded salinity profiles from 1990-2021 for the North Atlantic (Gouretski and Reseghetti, 2010; Good et al., 2013 bias corrections applied). The salinity fields are annually averaged and interpolated along the two characteristic neutral density surfaces. Annual salinity anomaly planes are generated by subtracting the climatological mean values from the annual averages. The climatological mean is calculated over the years 2003-2021, representing the period within the EN4 dataset that has ≥50% observational coverage over the domain. The annual salinity anomalies are then detrended and normalized by the standard deviation.

Mediterranean Overflow Water (MOW) occupies a similar density range as LSW but is slightly warmer and more saline (van Aken, 2000). The interaction of these two water masses is not well understood. Previous studies have estimated MOW contribution to western North Atlantic waters of about 20% (van Sebille et al., 2011), and removal of the discrete water mass signal from datasets resulted in an enhanced LSW convective signal (Chomiak et al., 2022). In this study, since the region occupied by MOW is included within the studied domain, we do not remove the MOW influence from the isopycnal layers of interest to be able to observe the natural modification of these water masses. We anticipate that modification of LSW will be detectable in the salinity anomalies, due in part to the interaction with MOW during its equatorward spread, but we do not quantify these interactions in this study, however.

The EN4-derived salinity anomalies depict the spatial extent of LSW along the defined constant isopycnal surfaces. In addition to the optimally interpolated EN4 data, we also use full-depth GO-SHIP Repeat Hydrographic data for the North Atlantic basin to observe the extent of LSW. Meridional GO-SHIP A16, A20, and A22 sections and the zonal A03 occupations ranging from years 1993-2023 are used ( Figure 1 ). The summertime AR07W occupations in the Labrador Sea from 1994 and 2001 show cross-sectional views of each LSW class development. Normalized salinity anomalies for each occupation and at each pressure level are computed by subtracting the horizontal mean and dividing by the standard deviation.

We perform a Complex Empirical Orthogonal Function (CEOF) analysis on the annual EN4-derived salinity anomalies along both isopycnal planes to reduce the dimensionality of the dataset and extract the most influential modes of variability (Navarra and Simoncini, 2010). The main advantage of CEOF analysis over the conventional EOF analysis is the ability to detect propagating signals and return their spatial and temporal amplitude and phase information (Navarra and Simoncini, 2010). This allows investigation of the spatial and temporal propagation of LSW salinity anomalies spreading out of the Labrador Sea across the 31-year dataset. The CEOF analysis of salinity anomalies was performed at the γ _n = 27.99 isopycnal plane for the 1990-2021 time interval and γ _n = 27.90 isopycnal plane for the 2000-2021 time interval. The different time intervals were used to reduce biasing from the LSW_1987-1994 convective imprint on the upper isopycnal plane (γ _n = 27.90). The spatial and temporal patterns are referred to here as CEOFs and complex principal components (CPCs), respectively. Only the leading CEOF_1/CPC₁ mode explaining about 30% of the salinity variance is used. The time–space progression of the reconstructed CEOF₁ mode is obtained by (i) multiplying CPC₁(t) by a rotation matrix whose argument varies between 0 and 360° at 45° intervals and (ii) regressing the normalized salinity anomaly planes onto the rotated CPC₁. The reconstructed CEOF₁ for the two isopycnal surfaces considered reflect the temporal evolution of the annual normalized salinity anomalies over a complete cycle.

The CPC₁ time series of the two isopycnal surfaces are compared to the wintertime December-March (DJFM) North Atlantic Oscillation (NAO) index (Hurrell et al., 2003). A cross correlation is computed between the CPC₁ and NAO time series, where the maximum correlation is used to determine lag time between each series in years.

We utilize adjusted geostrophic velocities derived from Argo and altimetry measurements (Schmid, 2014) interpolated onto the γ _n = 27.99 and γ _n = 27.90 isopycnal planes to assess LSW advective pathways. The original Schmid (2014) dataset is expanded to cover years 1993-2021. These velocities were derived by using Argo dynamic height profiles and sea surface heights from altimetry to calculate synthetic dynamic height profiles, which are then used to derive the horizontal geostrophic velocity, followed by a barotropic adjustment (see Schmid, 2014 for a detailed description of this method). At locations along the isopycnal plane exceeding 2000 m, velocity data is substituted with the deepest velocity for that grid point (2000 m, due to Argo constraint).

The time evolutions of the salinity anomalies for both of the convectively-generated LSW classes are shown in Figure 2 . AR07W hydrographic transect occupations in 1994 and 2001 showcase the initial structure of both LSW masses in the Labrador Sea. The annual spatial planes along the corresponding neutral densities illuminate the unique spreading patterns of salinity anomalies characteristic to these two LSW classes as they radiate out of the Labrador Sea. The specific neutral density planes are selected based on LSW formation in the Labrador Sea, where the LSW class of the early 1990s reached a core density of γ _n= 27.99 and then advected out of the Labrador Sea along that constant plane (Chomiak et al., 2022). Similarly, the LSW class of the early 2000s reached a core density of γ _n= 27.90 and advected out of the Labrador Sea along that constant plane. While showcasing the entire North Atlantic domain when visualizing the salinity anomalies along both constant neutral density planes it is possible that other water masses, not associated with LSW, are also present in the domain. For example, negative salinity anomalies (freshening) present in the eastern subpolar region, outside of the Mediterranean Sea, and in the South Atlantic in the respective LSW class formation years of 1994 and 2001 ( Figure 2 ) are unlikely to be associated with the observed LSW classes. In this study, we assume that salinity anomalies found elsewhere of the Labrador Sea at the time of LSW formation (ex., 1994 and 2001) are not associated with the specific LSW class. We focus only on tracking the anomalies that propagate out of the Labrador Sea along the defined neutral density planes, which we attribute to the two classes of LSW discussed in the next sections in more detail.

We perform a CEOF analysis to better illustrate the spatial and temporal patterns of the propagating large-scale salinity anomalies associated with LSW along the defined neutral density planes. While the CEOF analysis yields purely statistical modes, the leading CEOF mode appears to be representative for the spread of LSW out of the Labrador Sea along the two specific LSW density planes. The CEOF₁ spatial and CPC₁ temporal patterns highlight what was observed in Chomiak et al. (2022) using hydrographic transects along the DWBC (assessing the advection and timescales of the salinity anomalies associated with LSW at specific densities from the Labrador Sea to 26.5°N). Furthermore, by expanding the analysis over the entire North Atlantic rather than just along the boundary, other LSW propagation and advective pathways supported in past and current literature (ex. Spall, 1996; Bower and Hunt, 2000a; Bower and Hunt, 2000b; Bower et al., 2009; Bower et al., 2011; Biló and Johns, 2019; Bower et al., 2019; Chomiak et al., 2022; Lozier et al., 2022; Petit et al., 2023) are reinforced with these CEOF analyses. The CEOF₁ explains approximately 30% of the salinity variance in both isopycnals, which is a relatively large number considering that it relates to the entire North Atlantic domain; the other modes explain significantly less variance and are not used in the analysis.

Displayed in Figures 3A and 4A are the time evolutions of the spatial patterns of the LSW_1987-1994 and LSW_2000-2003 salinity anomalies, respectively, reconstructed with CEOF₁ for one full cycle (0-360°) at 45° phase intervals to visualize spatial propagation throughout the complete cycle of the first mode. The CPC₁ time series ( Figures 3B , 4B ) illustrate how CEOF₁ spatial pattern has changed over time, with the real and imaginary parts being associated with CEOF₁ at 0° and 90° phase, respectively. Positive [negative] tendencies in CPC₁ mean increasing [decreasing] salinities in the regions of positive CEOF₁ anomalies and decreasing [increasing] salinities in the regions of negative CEOF₁ anomalies (compare panels a and b in Figures 3 , 4 ).

The reconstructed CEOF₁ along the γ _n = 27.99 isopycnal shows the LSW_1987-1994 salinity anomaly (blue shading, Figure 3A ) to propagate out from the western subpolar region and down the western boundary while also spreading to the eastern subpolar and Atlantic interior, congruent with the observable anomalies. The temporal evolution of the CEOF₁ mode (CPC₁, Figure 3B ) matches the timescale of signal propagation observed in the annual anomalies of LSW_1987-1994. The western subpolar freshening observed at the 0° phase ( Figure 3A ) peaks in the late 1990s-early 2000s ( Figure 3B ) following formation and initial propagation of the LSW class. Freshening of the eastern subpolar gyre, western boundary, and Atlantic interior regions (90° phase in Figure 3A ) occur in the early to late 2000s shown by the peak in the imaginary component of the CPC₁ (dashed line in Figure 3B ) as the anomaly associated with LSW_1987-1994 propagates out of the Labrador Sea. The spatial and temporal propagation of this anomaly is consistent with the previous 10-year advective time scale estimated for 26.5°N, where the deep LSW_1987-1994 convective signal was shown by van Sebille et al. (2011) and Chomiak et al. (2022) to reach this subtropical latitude in the mid 2000s. The temporal phase of CEOF₁/CPC₁ (blue dots in Figure 3B ) highlights the completion of almost two cycles approximately 16 years in duration each along the γ _n = 27.99 isopycnal plane. A steady positive shift in the phase indicates that this signal is propagating with time.

Due to the lighter and shallower isopycnal that LSW_2000-2003 occupies, possible mixing and competing with warmer and saltier Mediterranean and Subtropical water masses results in a reduced coherence of the original convective signal as aforementioned. Therefore, a CEOF analysis along the γ _n = 27.90 isopycnal results in a relatively noisy spatial pattern when compared to the deeper γ _n = 27.99 isopycnal. Despite reduced signal coherence, the reconstructed CEOF₁ for γ _n = 27.90 ( Figure 4A ) highlights the propagation of LSW_2000-2003 out of the Labrador Sea to the eastern subpolar region, equatorward along the western boundary, and via the Atlantic interior. The temporal evolution of the CEOF₁ mode ( Figure 4B ) captures the western subpolar freshening in the early 2000s associated with the LSW_2000-2003 class (0° phase in Figure 4A and real component of CPC₁ in Figure 4B ) and the presence of LSW_2000-2003 in the western subtropical North Atlantic 5-10 years later (90° phase in Figure 4A and the imaginary component of CPC₁ in Figure 4B ). The temporal phase of CPC₁ (blue dots in Figure 4B ) highlights the completion of approximately 1.5 cycles, with one cycle lasting about 15 years in duration. The subtle shift in the phase through the years 2006-2015 indicates that this signal was not effectively propagating with time, compared to the steady positive shift observed along the deeper γ _n = 27.99 isopycnal plane. This likely suggests that LSW_2000-2003 may have lingered within the interior domain during this period rather than propagating through.

To investigate any connection to large-scale climate drivers that may influence these pathways, we compare the temporal evolutions of both CEOF spatial patterns to wintertime North Atlantic Oscillation (NAO) indices ( Figures 3B , 4B ). The NAO is a dominant mode of climate variability in the North Atlantic (Hurrell et al., 2003), representing the variations of sea-level pressure difference between the Subtropical High and Subpolar Low. Positive wintertime NAO phases have been linked to enhanced convection in the Labrador Sea with subsequent LSW formation (Curry and McCartney, 1996; Yashayaev et al., 2007). It has also been shown that positive [negative] NAO index is associated with easterly [westerly] winds over the Strait of Gibraltar, which probably favors greater [lesser] Mediterranean outflow (e.g. MOW) congruent with a lower [higher] Mediterranean sea level (Volkov and Landerer, 2015; Volkov et al., 2019). The discrete relationship between the spreading of LSW and MOW and the NAO is not well explored, but Lozier and Stewart (2008) observed a NAO influence on the shallow layers of LSW and MOW in the eastern subpolar Atlantic, suggesting there may be a possibility for the wintertime NAO to influence these waters elsewhere in the North Atlantic.

The real components of the CEOF₁ and CPC₁ of both LSW classes ( Figures 3 , 4 ) highlight freshening in the western subpolar North Atlantic associated with LSW formation following the positive phases of the wintertime NAO and salinification following the negative phases of the wintertime NAO. Cross-correlations of the real components of CPC₁ against the wintertime December-March (DJFM) NAO index show that salinity anomalies along both isopycnal planes associated with the two LSW classes lag the NAO each by 4 years with a maximum correlation of 0.7. Given the very short time series (i.e. only 1-2 complete cycles) this correlation is insignificant. Nevertheless, the link between the NAO and salinity anomalies in the subpolar North Atlantic associated with the formation of the two LSW classes appears to be robust and congruent with earlier studies (Curry and McCartney, 1996; Yashayaev et al., 2007). The likely modulation of the spread of MOW by the NAO in the subtropical North Atlantic may permit or hinder the eastward spread of LSW along the same isopycnal level (e.g., Lozier and Stewart, 2008; Volkov and Landerer, 2015; Volkov et al., 2019). Continued observation of LSW and MOW across the North Atlantic is required to better understand the spread and interaction of the two water masses and their relationship with the NAO and other modes of climate variability.

Several meridional and zonal GO-SHIP hydrographic transects in the North Atlantic are analyzed to further validate the interior presence of LSW along its spreading pathway at the two characteristic isopycnal levels ( Figure 5 ). Normalized salinity anomalies from the 1993 and 2005 zonal A03 GO-SHIP trans-Atlantic hydrographic transects along 36°N ( Figure 5B ) illuminate the prominent LSW plume extending from the western boundary to 55°W and 40°W in the interior, countered by the evident Mediterranean Overflow Water (MOW) plume of higher salinity along the same isopycnal extending from the eastern boundary. Meridional GO-SHIP cross-sections along the western North Atlantic (A20 along 52°W and A22 along 66°W; Figures 5C, D ) showcase the salinity anomalies characteristic of both LSW classes extending from the North American continental shelf (40°N, DWBC throughflow) to 35°N and in some cases, as far as 32°N. This north/south extent of the LSW plume is suggestive of the injected interior route stemming from the subpolar gyre since the anomalies are observed outside of the western boundary. More interestingly, it could be a hint of the alternative interior recirculation that stems from the western boundary. Looking closely at the meridional A22 sections, a small core of LSW within and extending slightly above and below the defined isopycnal cores is evident at 32°N. This feature likely corresponds to the returning westward-flowing recirculation band that rejoins the western boundary passing Bermuda at 32°N in the process ( Figure 1 ), as was suggested by advective timescales in Chomiak et al. (2022). South of the LSW plume, the strong MOW saline signal is observed, congruent with its east-west propagation across the North Atlantic interior (van Aken, 2000).

Salinity anomalies along the eastern North Atlantic (A16 along 29/20°W; Figure 5E ) highlight the southward extent of LSW to about 40°N. The intersection of GO-SHIP lines A03 and A16 at 36°N and 20°W show little evidence of LSW, rather a strong presence of MOW. This suggests that LSW i) does not spread further south of this latitude in the eastern North Atlantic, and/or ii) LSW flows westward towards the interior just north of this transect intersection at 40°N, likely hugging the Mid Atlantic Ridge based on the observations along the A03 transect east of the ridge at 25°W. There is likely a strong LSW/MOW interaction in this eastern North Atlantic region due to the isopycnal similarities and pronounced fresh/saline signatures, respectively, and this relationship remains to be investigated. The combination of the zonal A03 and meridional A22/A20/A16 sections visualizes a three-dimensional spatial pattern based solely on the convective salinity anomalies observed with western boundary recirculations extending to 55°W and 40°W zonally and 32°N meridionally, and direct injections of LSW to the interior from the central and eastern subpolar regions.

To further understand LSW advection pathways along the two isopycnal planes analyzed herein, we use adjusted geostrophic velocities derived from Argo and altimetry measurements (Schmid, 2014) interpolated along the γ _n = 27.99 and γ _n = 27.90 isopycnal planes. The climatological mean (averaged over years 2003-2021) of the annually-averaged density-interpolated velocity fields are showcased in Figure 6B . The depth of the neutral density planes of both LSW classes examined in this study across the North Atlantic are shown in Figure 6A for reference. Velocity vectors along both isopycnal planes illuminate the three spreading pathways previously discussed. Most importantly, we show that LSW is not only bound to the DWBC, but spreads all over the North Atlantic. Based on the direction and magnitude of the observed fields, export via the DWBC and a direct injection to the Atlantic interior (stemming from DWBC recirculations near Flemish Cap/Grand Banks) seem to be the favorable pathways. Eastward advection opposite of the Greenland Current ( Figure 1 ) is apparent in both velocity fields near the northern limit of the subpolar gyre, with LSW entering both the Irminger and the Iceland basins. In agreement with our findings, Petit et al. (2023) recently showed using Lagrangian floats that upper North Atlantic Deep Water (most closely related in density space to the LSW_2000-2003 defined herein) can travel from the Labrador Sea to the Irminger Basin outside of the Greenland Current. Yashayaev et al. (2007) also showed that LSW signatures reach the Irminger Basin, separate from any local Irminger convective influence. Continued investigation of LSW volume transports and Lagrangian-based advective studies are necessary, however, to determine the leading advective pathways. The Eulerian flow patterns from the adjusted geostrophic velocity fields provide further evidence for an interior recirculation pathway that branches from the DWBC off Cape Hatteras at 36°N, with anti-cyclonic flow extending as far east as 50°W and rejoining the continental slope at approximately 30°N, passing Bermuda (32°N) in the process. Absolute velocities along the shallower γ _n = 27.90 ( Figure 6 ) isopycnal plane are larger than those of the deeper γ _n = 27.99 plane. Given nearly identical vector (direction) fields between the two planes, this suggests that despite the increased velocities along these pathways, LSW_2000-2003 was likely entrained within the interior recirculation or was subject to multiple pathways given the longer advective timescales observed both in this study and previously in Chomiak et al. (2022).