Western boundary circulation and coastal sea-level variability in northern hemisphere oceans

. The northwest basins of the Atlantic and Paciﬁc oceans are regions of intense Western Boundary Currents (WBC), the Gulf Stream and the Kuroshio. The variability of these poleward currents and their extension in the open ocean is of major importance to the climate system. It is largely dominated by in-phase meridional shifts downstream of the points where they separate from the coast. Tide gauges on the adjacent coastlines have measured the inshore sea level for many decades and provide a unique window on the past of the oceanic circulation. The relationship between coastal sea level and the variability 5 of the western boundary currents has been previously studied in each basin separately but comparison between the two basins is missing. Here we show for each basin, that the inshore sea level upstream the separation points is in sustained agreement with the meridional shifts of the western boundary current extension over the period studied, i.e. the past seven (ﬁve) decades in the Atlantic (Paciﬁc). Decomposition of the coastal sea level into principal components allows us to discriminate this variability in the upstream sea level from other sources of variability such as the inﬂuence of large meanders in the Paciﬁc. This result 10 suggests that prediction of inshore sea-level changes could be improved by the inclusion of meridional shifts of the western boundary current extensions as predictors. Conversely, long duration tide gauges, such as Key West, Fernandina appropriately. KE are derived the EN4 controlled ocean temperature 2010 objectively mean gauge data sea-level 650


Introduction
Western boundary currents (WBCs) are a major feature of global ocean circulation and play an important role in global climate 15 by redistributing warm salty waters from the tropics to higher latitudes. The role of WBCs in the redistribution of heat and salt in the Atlantic is an integral part of the Atlantic Meridional Overturning Circulation (AMOC), resulting in heat transported towards the equator in the South Atlantic and the largest heat transport of any ocean northwards in the North Atlantic (Bryden and Imawaki, 2001). WBCs also interact strongly with the atmosphere, influencing regional and global climate variability (Imawaki et al., 2013;Kwon et al., 2010;Czaja et al., 2019) and impact the sea level of the coastlines they are adjacent to 20 Sasaki et al., 2014;Woodworth et al., 2019;Collins et al., 2019). (b) indicate the angle used to rotate the wind stress in an alongshore/across-shore coordinate system for the removal of sea-level variability driven by local atmospheric effect (See Supplementary Table S1 and Supplementary Table S2). Shadings in (a) and (b) indicate bathymetry.
In the Pacific, north of 30°N, the Kuroshio flows northeastwards along the coast of mainland Japan before leaving the coast at approximately 35°N and becoming a separated boundary current known as the Kuroshio Extension (KE, Figure 1 (a)). The Kuroshio and KE have variable flow regimes including decadal timescale variability, with the KE following either a stable and northern path, or an unstable and southern path (Qiu et al., 2014;Imawaki et al., 2013;Kawabe, 1985). This variability 25 is driven by the wind stress curl over the central North Pacific which generates Sea Surface Height (SSH) anomalies. These anomalies progress westward as jet-trapped waves, shifting meridionally the KE before reaching the Kuroshio -Oyashio confluence (Sugimoto and Hanawa, 2009;Sasaki et al., 2013;Sasaki and Schneider, 2011a;Ceballos et al., 2009). Southeast of Japan, negative (positive) SSH anomalies ultimately displace the Kuroshio southward (northward) above the shallower (deeper) region of the Izu-Ogasawara Ridge (IOR). Interaction of the Kuroshio with the bathymetry when it is shifted above where ζ is the sea-level anomaly, evaluated at the coast (x W ) and at the frontier between the boundary layer and the ocean 125 interior (x I ), and β is the meridional gradient of the Coriolis frequency f . In the real ocean, the mass input into the western boundary region is more accurately described by the jet-trapped Rossby wave framework than by the direct westward propagation of linear long Rossby waves (Sasaki et al., 2013;Sasaki and Schneider, 2011a;Taguchi et al., 2007). Therefore, pairing the jet-trapped theory with Minobe et al. (2017) framework is expected to better estimate the sea level on the coast of western boundaries. In accordance with this idea, the coastal sea level south of Japan is known to be in agreement with the Kuroshio 130 location above the Izu-Ogasawara Ridge (Kuroda et al., 2010), the KE meridional shifts during the satellite era (Sasaki et al., 2014) and the regime shifts in North Pacific mid-latitude (Senjyu et al., 1999). Simply put, the mechanism is that jet-trapped long waves, originating from the east and responsible for the meridional shifts of the WBC extension, break, when reaching the coastline, in coastally trapped waves that propagate equatorward (Sasaki et al., 2014). Globally, the mean sea level has shown an increased rate of rise in the last decades Nerem et al.,   In this study, we analyse datasets of mean sea level along US and Japanese eastern coastlines, identify major spatial modes of variability, and interpret this in terms of ocean circulation variability. This paper is organized as follows. Section 2 presents the data used in this study and the derivation of indices for the WBC extensions. The results of the analysis of the gauge records and their relationship to upstream and downstream WBC variability are presented and discussed in Sect. 3 and Sect. 4.
A conclusion is presented in Sect. 5.

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2 Data and Methods

Tide gauge selection, treatment, and adjustment for surge variability
Tide gauge data were obtained from the Permanent Service for Mean Sea Level (Holgate et al., 2013, PSMSL, 2020 //www.psmsl.org/) on the 17 th August 2020. We selected tide gauge stations along the western boundary of the North Atlantic, on the coast of the United States and Canada; and along the western boundary of the North Pacific, on the coast of Japan.

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To retain only measurements of sufficient quality, length and completeness, historical series with more than 10% of missing monthly values as well as those flagged for quality issues are excluded. Consequently, the number of individual tide gauge records available is dependent of the chosen period. Summary of gauge details are given in Supplementary Table S1 and   Supplementary Table S2.
For the Atlantic, the period considered is January 1948 -December 2019 due to the availability of the atmospheric reanalysis 155 used to correct for surge effects. The island station on Key West is located onshore of the Gulf Stream and features a signal coherent with the Florida tide gauges. It is therefore included, leaving a total number of 22 stations on the American east coast.
The Japanese tide gauge network is more recent, therefore the period considered for the Pacific is January 1968 -December To correct the records from the effect of local winds and pressure, monthly sea-level pressure and ten meters above sea level wind speeds were obtained from the NCEP/NCAR Reanalysis 1 (Kalnay et al., 1996, NOAA/OAR/ESRL PSL, https: //psl.noaa.gov/). They are available from 1948 to present-day. The grid has a resolution of 1.875°in longitude and ∼1.904°in latitude. The variables are detrended and deseasonalized, after the wind speed is converted to wind stress. The Japanese 55-
Results were similar to those obtained with the NCEP variables and are therefore not discussed. To assess and remove the local atmospheric contribution to changes in sea level, each monthly sea-level record is regressed against the atmospheric pressure and the wind stress interpolated at the gauge location, following the method of Dangendorf et al. (2013), Frederikse et al. (2017 and Piecuch et al. (2019). Details are given in the appendix (Sect. A), together with a brief analysis of the results. 175 We find that the local forcing of the atmosphere drives between 30% and 50% of the monthly sea-level variability at tide gauges located north of Cape Hatteras, the separation point of the Gulf Stream, and at tide gauges located north of 38°N on the eastern coast of Japan, whereas the atmospheric influence is reduced upstream of the separation points of the Kuroshio and Gulf Stream. The unexplained residual represents the sea level corrected for local atmospheric effects.
Finally, to focus on inter-annual and slower variations, a low-pass 19-months Tukey filter is applied. The filtering effectively 180 reduces the period analysed to November 1968 -January 2019 for the Japanese gauges, and November 1948 -January 2019 for the American gauges.

Additional datasets
Gridded monthly Sea Surface Height (SSH), Temperature (SST) and Velocities (SSV) derived from satellite altimetry are available from 1993 and were obtained from the Copernicus Marine Environment Monitoring Service (CMEMS) website 185 (https://marine.copernicus.eu). SSH and SST are obtained from the ARMOR3D product (Guinehut et al., 2012). SSV is retrieved from the REP L4 product and consists of the sum of geostrophic and modelled-derived Ekman components (Rio et al., 2014 The significance of correlations between two timeseries A and B is calculated using the non-parametric method of Ebisuzaki (1997), as was previously done in McCarthy et al. (2015). The method consists of evaluating the Fourier transform of A and generating a large number (here 5000 is used) of random timeseries with similar spectral properties. The modulus is 210 preserved while the phase is randomized. The randomly generated signals are then correlated against B. Significance for zero-lag correlation between A and B is given as the percentage of randomly generated correlations which are less than the correlation between A and B (using absolute values). When we report lagged correlations, we use a more stringent test of confidence, as McCarthy et al. (2015). In this case, the lead-lag correlation between each randomly generated signal and B is computed, and the maximum correlation is determined. The significance is given as the percentage of randomly generated 215 maximum correlations which are inferior to the maximum correlation between A and B (within the limit of a lead, or lag, of a fourth of A or B length).

Meridional motions of the Western Boundary Current Extensions
At interannual to multidecadal scale, the Gulf Stream Extension and the Kuroshio Extension are quite similarly characterized by strong lateral movements. The displacements are of about half a degree in the Atlantic (Joyce et al., 2000) and about one 220 degree in the Pacific (Sasaki et al., 2013), with an increase in the meridional extent of the shifts toward the east.
For each ocean, the methods used to quantify such oscillations have evolved differently. In the North Atlantic, the Gulf Stream North Wall (GSNW) is defined as the leading mode of the temperature anomaly at the climatological position of the jet, or, more traditionally, its northern front (the 'North Wall'). Indeed, because the WBC extensions separate cold water to the north from warm water to the south, warming (cooling) at the climatological jet position reflects a northern (southern) shift of 225 the jet. In the Pacific, recent work has used SSH estimates averaged in the 31°N -36°N and 140°E -165°E box as proxy to infer the past Kuroshio Extension meridional location (Qiu et al., 2014(Qiu et al., , 2016. This area corresponds to the Kuroshio Southern Recirculation Gyre (KSRG) of which the strength is a good indicator not only of the Kuroshio Extension latitudinal location, but also of its stability and intensity (Qiu et al., 2014).
To produce consistent indices for both oceans, we made use of the subsurface sparse temperature observations to derive construction of an along-jet temperature matrix. The search radius acts as a spatial low-pass filter and was purposely set well above the Rossby deformation radius, to minimize the meso-scale meandering variability in the gridded temperature anomaly.
The leading mode of variability is extracted for each basin by performing an Empirical Orthogonal Function (EOF) decomposition based on correlation (rather than covariance) on the detrended temperature anomaly. Figure 2 present the associated amplitude in both oceans varies in-phase all along the climatological jet axis. In the remainder of this paper, we refer to the principal components as GSNW and KE Index (KEI), and specify "this study/our GSNW" or "this study/our KEI" whenever precision is needed.
To contextualize the temporal variations of our GSNW and KEI with existing indices, we retrieved the GSNW estimate (Temperature/Salinity) data (Qiu et al., 2016). The wind-based index is obtained by forcing a 1½-layer reduced-gravity model with historical wind stress merged from ERA-20C and Interim reanalysis sets. Although such model has limited skills in reproducing the westward narrowing of the meridional jet oscillations (see Sasaki et al., 2013;Sasaki and Schneider, 2011a), 250 it is able to correctly reproduce the timing of the meridional shift of the KE (Taguchi et al., 2007). The three indices are presented alongside the GSNW (this study) and KEI (this study) in Figure 2 (c) and (d), after detrending is applied. They are yearly averaged for comparison with our GSNW and KEI. Correlations between both Qiu et al. (2016) indices and our KEI are high, with greater value obtained with the T/S index, (r = 0.75, significance is above 99%), than with the wind-based index (r = 0.67, significance is 99%). Similar correlation is found between Joyce et al. (2000) GSNW and this study GSNW over 255 their overlapping period, 0.71 (significance >99%).

Results
In this section, we propose a scrutiny of the inshore sea level measured by tide gauges using cross-correlation and moving correlation analysis, as well as Empirical Orthogonal Function (EOF) analysis. We relate the obtained spatial and temporal patterns to ocean circulation. Senjyu et al. (1999); Valle-Levinson et al. (2017) and Sasaki et al. (2014) used EOF decomposition 260 on the Pacific and the Atlantic tide gauges, and hence our analysis can be seen as building on their work. which we argue is the fingerprint of ocean circulation on coastal sea level.

Cross-correlation analysis
We expand the analysis to tide gauges along the Japanese Coast. Three tide gauge groupings are apparent on Figure 3 (a), based on the cross-correlation between Japanese records. West of the Kii peninsula, the correlation between gauges is on average 0.85. From the Kii peninsula to the Bōsō peninsula, region that we refer to as Tōkai for simplicity, another highly correlated group exists. The mean of the correlations within that group is 0.74, with the tide gauge of Owase showing slightly 270 lower agreement. These two groups south of Japan were identified by the early work of Moriyasu (1958). The gauges on In the Atlantic, Thompson and Mitchum (2014), Frankcombe and Dijkstra (2009), as well as Häkkinen (2000)  Hatteras. While we do find a few significant correlation at the 95% level across Cape Hatteras, indicated by bold outlines in Figure 3, the distinct drop in correlation is more prominent. We therefore investigate the evolution of the correlation patterns and (d)). The large deviations between individual correlations within the Oyashio group underline the overall lower agreement between the gauges there (panel (e)). As will be discussed further below, the sea level south of Tōkai is largely affected by the appearance of large meanders, which is a phenomenon unique to the Pacific. Thus, to compare southern and northern 300 variability as was done for the Atlantic in Figure 4 (b), we plotted the changing correlations between the group west of Kii and the Oyashio group in Figure 4 (a). The correlations are relatively low over the whole period, with the correlation median exceeding r = 0.35 only at three occasions, 1978 -1982, 1991 -1993 and 2011 -2012 (not shown), and the moving correlation between the two grouping averages rarely significant except in the early 1990s. More importantly, the moving correlations do not show an abrupt change, in contrast with the situation in the Atlantic.

Empirical orthogonal function analysis
We employ Empirical Orthogonal Function (EOF) analysis to objectively reduce the sea-level anomalies in an ensemble of modes, each composed of a time-varying coefficient α, the Principal Component (PC), and associated spatial-varying coefficients φ, the Empirical Orthogonal Vector or Function (EOF). Covariance-based EOF decomposition is performed on tide gauge sea-level anomalies interpolated on a regular grid. This prevents the sea-level variability in better sampled region from 310 being favored in the analysis. Details of the interpolation on a regular grid, including handling of estuarine stations, are given in Appendix B. The regular grid points are referred to as virtual stations.
The EOF analysis is computed separately on both Atlantic and Pacific gridded sea-level anomalies. Together, the two leading modes explain 85% (77%) of the variability of the Atlantic (Pacific) dataset. To demonstrate the link between the gauge records and the ocean dynamics, we computed two composites using the monthly surface velocity magnitude since the beginning of that record in 1993 (Rio et al., 2014). The surface velocity magnitudes are averaged over periods of strongly positive α 1 (greater than two third its standard deviation, i.e., α 2 > 2/3) to form a 330 first composite, and similar procedure is done over periods of strongly negative α 1 (lower than minus two third its standard deviation, i.e., α 1 < −2/3). The treshold of ±2/3 is arbitrary, but taking any other tresholds within 0 -1 lead to similar patterns. Colour shadings on Figure 5   velocities are above the deep channel located north of 34°N (deeper than 1500m) whereas negative velocities are spread above the shallower part of the ridge to the south (shallower than 1500m). The Kuroshio was hence found northward (southward) during periods of positive (negative) α 1 . Moreover, it is obvious that the positive velocity pattern (associated with high α 1 ) 345 resembles the nearshore NLM (see Figure 1), whereas the negative velocity pattern (associated with low α 1 ) resembles the offshore NLM. In the Atlantic, the negative velocity pattern is inshore of the positive velocity pattern upstream of Cape

Atlantic and Pacific first modes
Hatteras, indicating that during periods of positive (negative) α 1 , the upstream Gulf Stream was offshore (inshore). Joyce et al., 2000) described in Sect. 2. The principal components are correlated against the indices, after they were yearly or quarterly averaged (when necessary). There is moderate but significant correlation between the Pacific α 1 and the various that the agreement at low-frequency is significant. For example, we took up again the EOF analysis, after the 19-months filter applied to the sea-level anomalies was substituted by a 73 months (∼6 years) filter. The obtained EOF φ 1 is not greatly changed (Suppl. Fig. S2 (a)). The correlation between the obtained α 1 and Joyce et al. (2000) (our) GSNW, similarly filtered, equals 0.61 (0.78) when α 1 leads by one and a quarter of a year (one year) which is significant at 92% (99%).
We can conclude that the link between coastal sea-level upstream the separation point and the latitude of the jet extension 370 downstream, which was highlighted in the Pacific by Sasaki et al. (2014) and Kuroda et al. (2010) is actually a feature of both basins, and extend before the satellite era.

Atlantic and Pacific second modes
While similar patterns emerge in both the Atlantic and Pacific leading modes, the same is not true for the second modes. The second EOFs φ 2 's of the Pacific and Atlantic tide gauges are presented on Figure 6   In the Pacific, a second group west of Kii varies in antiphase with the Tōkai gauges, with amplitudes on average of −1.2 cm.
In the Atlantic, amplitudes south of Cape Hatteras are on average −0.8 cm (Figure 6 (a)). In both cases, the magnitudes of these negative variations are more than 2 times smaller than to the magnitude of the positive variations (north of Cape Hatteras 385 and south of Tōkai).
In the Pacific, large amplitude in the EOF φ 2 are confined upstream the Kuroshio separation point, whereas the Atlantic mode is dominated by the variability passed the separation point, to the north. Furthermore, the velocity composite difference based on α 2 and obtained in similar manner to the procedure aforementioned, present very different patterns from one basin to another (colour shadings, Figure 6 (a) and (b)), which we return to in more detail below. As the two modes are different, we 390 discuss them separately.

The second mode in the Pacific
The section. The relationship between the tLM periods and the sea-level difference between those two stations is known since the early work of Moriyasu (1958Moriyasu ( , 1961 and was investigated by Kawabe (1985Kawabe ( , 1995Kawabe ( , 2005, among others. The inset on  Figure 6 (c) (orange line, axis is inverted so that southern shift is a positive anomaly). Correlation with the principal component α 2 is strong and highly significant (r = 0.82, significance >99%), confirming that the mode is a footprint of the large meander. Note that the correlation is slightly higher with the principal component than with the difference between Kushimoto and Uragami (r = 0.78, significance >99%).

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The velocity composite, derived on high (>2/3) minus low (<−2/3) values of α 2 as was done for the leading modes, is shown in Figure 6  that is, the Kuroshio Extension, is found more to the north when the principal component is positive. The negative velocities are also more scattered than their positive counterparts, highlighting that the KE was more stable during period of positive α 2 (see also Sugimoto and Hanawa, 2012).

The second mode in the Atlantic
The principal component associated with the second EOF in the Atlantic increases from 1948 to the early 1970s, followed by a decrease until the mid-1990s, with interannual deviations from those long-term changes ( Figure 6 (d)). The mid-1990s mark an abrupt change, with the interannual variability increasing greatly in amplitude from then onwards. This is shown on Figure 7, which presents the moving standard deviation of α 2 obtained with a 15 year running window (solid blue line). very high, r = 0.88 (significant above 99%). As for the difference between Kushimoto and Uragami, substracting the sea level south of Cape Hatteras from north of Cape Hatteras (or reversely) minimizes the influence of the leading mode. Indeed, the difference between φ 1 's magnitude either side of Cape Hatteras is 1.3 cm on average, whereas the difference between the EOF φ 2 magnitude either side of Cape Hatteras is 2.5 cm.
The velocity composite exhibits two well-defined patterns of opposite sign off Cape Hatteras, indicating that the positive 440 (negative) phases of α 2 are concurrent with a southern (northern) shift of the Gulf Stream west of 69°W ( Fig. 6 (b)). The patterns bear some resemblance with the ones obtained with α 1 and presented on Figure 5 (b), but the amplitudes of the composite along the Gulf Stream Extension make a strong contrast. The positive and negative velocity patches are now maximum in the region west of 69°W, where they have greater across-shore width than the ones obtained with α 1 (Figure 5 (b)). There, because the −25 to 25 cm/s colour scale was retained for comparison with the other modes, the composite amplitudes are 445 largely clipped. They are in the range of (±) 40 -60 cm/s, larger than the magnitudes obtained with α 1 in the same region, which were in the range of (±) 10 -40 cm/s. On the other hand, composite amplitudes east of 69°W are smaller when obtained with α 2 than when obtained with α 1 . In this second region, the α 2 -based composite is also less consistent, with the negative velocities intruding southward and splitting the positive pattern in two at ∼68°W. Hence, the link between α 2 and the Gulf Stream Extension meridional shifts in this second region is not as clear as the one obtained with α 1 . Although the different starting and ending periods may play a role, we find that the dissimilarity mostly arises because of the correction we applied for surge-driven sea-level change (Appendix A). This result however, should not be interpreted as 460 a demonstration that the atmosphere plays a role in extending the southern variability northward. Rather, the surge correction reduces the variance north of Cape Hatteras, which better constrains the EOF analysis and reduces undesired compensation between modes.
When the EOF analysis is recalculated restricting the period to 1960 -1990, where greater coherence either side of Cape Hatteras is seen (Figure 4 (a)), the northward decrease in φ 1 is still apparent. This is an important result, because previous 465 studies had excluded the Gulf Stream and its extension as plausible drivers of the sea level on the western coast of the North Atlantic basin, on the basis that such drivers were not able to explain coherence across Cape Hatteras (Thompson and Mitchum, 2014;Valle-Levinson et al., 2017). On the contrary, we found that the Gulf Stream separation marks the point from where the mode's imprints of sea level diminishes, which re-qualifies the Gulf Stream presence as a plausible sea-level driver. In our view, the northward decrease of φ 1 is related to the orientation of the Gulf Stream Extension which gradually moves away The leading mode temporal amplitudes in both basin are in agreement with the location of the WBC extensions in both altimetry-derived sea surface velocities and in-situ subsurface temperature. In the Pacific, anomalous wind stress curl triggers 475 westward propagating baroclinic jet-trapped Rossby waves that shift the jet meridionally (Sasaki et al., 2013;Sugimoto and Hanawa, 2009;Ceballos et al., 2009). A similar mechanism has been proposed for the Atlantic (Sasaki and Schneider, 2011b). Sasaki et al. (2014) hypothesized that the incoming jet-trapped Rossby waves, which are responsible for the extensions' shifts, break on the western boundary and propagate equatorwards as Kelvin or other coastally trapped waves, linking the extension variability to coastal sea level. Because the long jet-trapped Rossby waves provide a mass input to the western boundary which 480 has a narrower meridional extent than traditional Rossby waves, the alongshore coastal sea level gradient is maximum near the WBC separation point (Equation 1). This leads to a 'shadow' coastal area north of the separation point which is less affected by the incoming jet-trapped wave, and an 'active' area which sees the progression of the coastal wave (Sasaki et al., 2014), explaining the EOF patterns of Figure 5. Hence, although Sasaki et al. (2014) focused on the KE and south Japan sea level, our results support that such a mechanism could explain the link between the coastal sea-level and the extension meridional 485 location observed in both oceans. It is true that we found that, in the Atlantic, the correlation between the GSNW and the leading principal component of the sea-level variability is maximum when the GSNW lags by about one year, but we must emphasize that we found significant correlation between the GSNW and the Atlantic α 1 at zero-lag, in agreement with a mechanism of coastal wave following the jet-undulation.
The state-of-the-art theory of Sasaki et al. (2014) is elegant, but there is some limitations that we believe are useful to point 490 out for future developments on the relationship between WBC extensions and upstream sea levels. First, the upstream bottom temperatures at the shelf break and on the shelf are known to covary with the upstream sea level (Kuroda et al., 2010). This limits the spectrum of possible coastally trapped waves to waves with non-zero cross-shore flow (e.g. topographic Rossby waves) which are able to drive warm water on and off the shelf. Secondly, the role played by the path variability upstream the separation point is unclear. In the Pacific, the upstream patterns of velocity in Figure 5 (a) feature the offshore and nearshore 495 NLM paths (Figure 1), which have not previously been understood as the propagation of SSH anomalies as coastally trapped waves. Furthermore, positive (negative) α 1 values were shown to be concurrent to inshore (offshore) paths south of Japan, whereas south of Cape Hatteras, the opposite was observed (positive α 1 associated with an offshore path). If coastally trapped waves indeed drive the upstream coastal sea level, it is conceivable that they also cause the concurrent offshore (inshore) shifts of the western boundary currents upstream of their separation point. Yet, it is unclear why they would drive opposite behaviour 500 in term of paths in the two basins, hence weakening the hypothesis. These issues underscore the difficulties to understand the causal relationship between the WBC extension and the upstream sea level.
The EOF analysis highlighted very different second modes in the two basins. The second EOF explained 30% of the variance in the Pacific gauges and 25% of the variability in the Atlantic gauges. In the Pacific, this second mode is the manifestation of the meandering of the Kuroshio upstream of its separation point, whereas the second EOF in the Atlantic is mainly associated 505 with variability north of Cape Hatteras, the separation point.
In the Pacific, the typical large meander influence on the sea level south of Tōkai was shown in our analysis, and is known since many decades (Moriyasu, 1958(Moriyasu, , 1961Kawabe, 1985Kawabe, , 1995Kawabe, , 2005. The elevated values of α 2 closely match the typical large meander periods (Fig. 6 (c) Fig. S4 (b)). SST and SSH averages over this period show that the intrusion of warm water south of Tōkai goes along with a rise of the SSH there, as do composites obtained over tLM periods (Suppl. Fig. S4 (c -515 f)). In fact, the major distinction from tLM period is that between 2000 and 2001, the Kuroshio veered northward east of the ridge (or on the ridge at 140°E). These types of pathway are sometimes called straddled large meander, because, in contrast with typical large meanders, the anticyclonic eddy straddles the Izu-Ogasawara Ridge at 140°E.
The common denominator to the tLM and such atypical paths is the presence of the westward flow identified by Sugimoto et al. (2019), which brings warm waters south of Tōkai. We hypothesize that the sea-level rise recorded by the gauges in the 520 region is forced by the intrusion of the Kuroshio warm water brought by such current (geostrophic tilting and/or steric rise). From a coastal sea-level perspective, there is no qualitative difference between the forcing of typical large meander and the forcing of atypical paths that straddle the ridge.
The second mode of variability of the Atlantic tide gauge is perhaps the most puzzling mode among the four discussed here. Our analysis based on sea surface velocity composites highlighted the agreement of α 2 with the Gulf Stream Extension meridional location west of 69°W, consistently with Andres et al. (2013). The relevance of the satellite measurements for interpretation of ocean dynamics prior to ∼1990 is however questionable. The sharp increase in the variance of the mode around ∼1990 arises the issue whether this mode represents the pursuance of the same physical phenomenon throughout 545 the whole period 1948 -2019, or if a mechanism supplanted another around ∼1990. We find that α 2 has a non-stationary relationship with this study GSNW index (Figure 7 (b), solid blue line). The correlation between the GSNW and α 2 is of −0.45 (significant above 99%) over the full period 1948 -2019, quite similar to the correlation between the GSNW and α 1 , but this agreement is due to the period after ∼1990, where correlation is r = −0.63 (>99%) while the correlation between 1948 and 1989 is −0.17 (61%). Hence, the relationship with the location of the Gulf Stream is largely limited to the recent 550 era, which complicates understanding of the forcing prior to α 2 variance change around 1990. Note that here we use 1990 as change point for simplicity, but similar results are obtained when using 1987 (Kenigson et al., 2018;Boon, 2012) or 1994, which corresponds to the first strong negative α 2 dip after more than 40 years.

As was indicated by
One mechanism in particular has been hypothesized to tie the Gulf Stream location west of 69°W and the Nova Scotia to   Andres et al. (2013) hypothesized that the shelf transport is triggered by the alongshore wind forcing over the shelf, and eventually drives the movements of the Gulf Stream to the south, rather than the opposite. A strong negative correlation between the coastal sea level north of Cape Hatteras and the alongshore wind stress over the northern part of the shelf supported the hypothesis. Kenigson et al. (2018) highlighted that the year 1987 marked an abrupt change of the wind orientation above the US northeast coast and Canadian east coast. If this hypothesis is indeed correct, it is intriguing that such sea-level variability 565 appears in our analysis, given that the tide gauge records have been corrected for instantaneous wind forcing, especially as the sea-level response to the atmospheric forcing that was removed from the record (Appendix A) is quite different from α 2 (Supplementary Figure S8 (b)). To investigate the question, we repeated the procedure of Andres et al. (2013)  shelf remains negligible everywhere. Hence, the variability of α 2 is not due to the alongshore wind stress above the shelf, and we can say that the latter has been successfully removed from the tide gauge records by our correction for local atmospheric forcing. Furthermore, the role of remote wind stress in the Gulf of Saint Lawrence or east of Newfoundland is uncertain as well, because at these latitudes the NAO is a confounding variable. When corrected for the NAO, the correlation between the alongshore wind stress and α 2 is not significant anywhere on sea ( Figure Supplementary S5 (d)). This does not necessarily 580 exclude alongshore wind stress in the Gulf of Saint Lawrence or east of Newfoundland as a possible driver of the variability of α 2 since 1990, but indicates that any other forcing strongly correlated with the NAO is an as likely driver.
Alternatively, density anomalies formed in the Labrador Sea propagating southward along the western boundary, either as coastally trapped waves or advected within the deep western boundary current, have been proposed as driver of the sea-level variability north of Cape Hatteras (Frederikse et al., 2017). However, existing indices of the AMOC and DWBC do not show 585 the same variability as α 2 (Caesar et al., 2018;Thornalley et al., 2018). Finally, we have not considered the role of salt (or lack of) and water-volume input to the shelf caused by both river discharges and eddies detaching from the Gulf Stream, which are an additional potential driver of the sea-level on the shelf (Piecuch et al., 2018).
EOF analysis can help to understand the major distinctions observed in the alongshore sea-level coherence between the two basins. Upstream of the separation point in the Pacific, the cross-correlation analysis highlighted two distinct groupings either 590 side of the Kii peninsula. This is the point at which the Kuroshio path either follows the large meander or stays close to the coast on a non-large meander path (Fig. 1). The EOF analysis revealed that the sea level in the region east of Kii is the sum of the two leading mode, whereas in the region west of Kii the sea level is well approximated by the first mode only, where the first mode is associated with the Kuroshio Extension meridional motions, and the following mode with meandering south of Japan. Hence the second grouping of co-variability south of Japan is due to the emergence of (a)typical large meanders, which 595 are an additional forcing for the sea level east of Kii. This forcing has no equivalent in the Atlantic, and therefore there is only one distinct grouping of variability south of Cape Hatteras.
In the Atlantic, the moving correlation analysis showed that the agreement between gauges south and north of Cape Hatteras changed strongly around ∼1990. This is an additional distinction between the Atlantic and Pacific, as no coherence change of such magnitude was observed between the Oyashio and West of Kii groupings in the Pacific.

Conclusion
This study presents a consistent analysis of the two western boundary regions of northern Atlantic and northern Pacific. The agreement between the upstream sea level and the WBC extensions' meridional shifts was highlighted in the two basins conjointly. This agreement supports the mechanism of Sasaki et al. (2014) of trapped Rossby waves propagating within the western boundary current extensions, shifting them meridionally en route and progressing into coastally trapped waves at arrival sea level with other plausible drivers, including the ocean temperature within the western boundary current vicinity (Kuroda et al., 2010;Domingues et al., 2018) and the subtropical gyre interior sea surface height (Woodworth et al., 2014;Thompson and Mitchum, 2014;Volkov et al., 2019). It would be interesting to know what are the statistical and causal relationships between these proposed drivers of the sea level and the shifts of the extensions of the western boundary currents. In the 615 absence of such information, the mechanism proposed by Sasaki et al. (2014) is, so far, the only linking the upstream sea-level and the WBC extensions' meridional shifts. While this hypothesis is an important conceptual development, quantitative studies are for now missing. Hence, further work is required on the matter.
We showed that dissimilarities between Japanese and American inshore sea level emerge in the second mode of variability.
In the Pacific this relates to upstream meso-scale dynamics (Kuroshio large meander), whereas in the Atlantic, the second mode 620 is mainly associated with changes north of Cape Hatteras, the separation point of the Gulf Stream, although weak antivariations exist to the south. In the Pacific and in comparison with existing studies, we noted that the sea level south of Tōkai was affected by the presence of large meanders in a broader sense, including atypical meanderings that straddle the Izu-Ogasawara Ridge.
In the Atlantic, we found that the variability of the second mode drives the coherence across Cape Hatteras. We showed that the strong link of this mode with the shifts of the Gulf Stream Extension west of 69°W is relatively recent and does not extend 625 prior to ∼1990. We also showed that the local alongshore wind was an unlikely driver of this mode variability. Hence, whether this Atlantic second mode represents the pursuance of the same physical phenomenon, or if a mechanism supplanted another around ∼1990 is still an open question.
Because the tide gauge networks in both oceans extend further back in time than the period analysed in this study, inshore sea level has potential for reconstruction of the variability of the ocean circulation mode of variability. Although the causal 630 link between the upstream sea level and the meridional shifts of WBC extensions is not yet completely understood, our results suggest that upstream inshore tide gauges, such as Key West (available from 1913 in the PSMSL revised local reference (RLR) database), Fernandina Beach (1897) or Hosojima (1930) could be used as proxies for the extension meridional shifts and, by extension, the forcing responsible for such meridional shifts. In the Pacific, tide gauges in the region west of Kii, where the sea level is less affected during large meander periods, should be preferred.  1953 -1955 and 1959 -1963 as large meander periods, similar to Moriyasu (1958Moriyasu ( , 1961 640 and Kawabe (1985Kawabe ( , 1995Kawabe ( , 2005 Underlying datasets for α1 and α2 include (1) the original monthly tide gauge data available from the Permanent Service for Mean Sea Level (PSMSL, https://www.psmsl.org/), (2) sea-level pressure and ten meters above sea level wind speeds from the NCEP/NCAR Reanalysis 1 (Kalnay et al., 1996), distributed by the NOAA/OAR/ESRL PSL, and (3)  (τ ) and across-shore (τ ⊥ ) wind stress anomalies interpolated at each tide gauge location as predictors. The angles used for 655 the rotation in across-shore/alongshore coordinates are presented in Supplementary Table S1 and Supplementary Table S2.
The quality of a regression is primarily depending of the correlation between the explanatory variables and of the period width. Here, the pressure and winds are not independent. Hence, for each tide gauge, an all possible regression procedure was designed. This means that, the model with the three regressors is tested (equation A1), alongside all the possible models where first, second and (or) third term of that equations are (is) ruled out. In total, 2 3 − 1 = 7 combinations of possible regression are 660 tested at each tide gauge.
The regressions returns the regression coefficients β 1 , β 2 , and β 3 , that describe the relationship between pressure, alongshore and across-shore winds and the gauge record. O(t) represents the unexplained residual. Y-intercepts are estimated to improve the computation, but are not removed to form the residual O(t). Note that the inverse barometer effect is not proportional to 665 the local pressure alone but to the difference between the local pressure and the global sea-level pressure p(t) averaged over the oceans. Also, β 1 is preceded by a minus (−) because rise of local atmospheric pressure makes sea level fall and vice versa.
To determine the best model for each tide gauge, 95% confidence intervals are computed for each regression coefficient within the Matlab built-in function. The regression models that feature one (or several) coefficient confidence interval(s) crossing zero are excluded. Then, the best regression is defined as the one with the highest adjusted coefficient of determination 670 R 2 Adj , which is the proportion of the variance in the gauge record that is predictable from the atmospheric predictors, adjusted for their number (see equation A2).
where m is the number of timestep, n r is the number of regressors for that particular model (n r ∈ [1, 2, 3]), and Y the sum of the obtained atmospheric contributions.  (12) are, in contrast, much less affected, because they are located at the mouth of the estuaries. The best regression does not feature the across-shore wind north of Cape Cod (TG 20 -22). The obtained alongshore coefficients show less deviations from the average of −7.9 m 3 /N, yet the maximums are also found in the estuaries region. Finally, it is to note that, north of Cape Cod (TG 14 to 23), we obtain values for β 2 an order of magnitude greater than reported by Piecuch et al. (2019). For most of the Japanese gauges, 690 the best regression does not feature either the across-shore or the alongshore component of the wind stress, as using all of the explanatory variables does not explain more variability in the tide gauge records. However a consistent effect of the alongshore winds for the southern tide gauges (TG 1 -2 and 4 -19) is revealed by the regression.
Supplementary Figure S7 present the adjusted coefficient of determination R 2 Adj (Eq. A2). It depicts better the effect of the atmosphere on the sea level than the regression coefficients alone, as even a weak β i coefficient could affect greatly the sea 695 level if the corresponding regressor variability is important at the tide gauge location. Consistently with Piecuch and Ponte (2015), we find that the atmospheric effect on sea level explains an important part of the gauge variability north of Cape Hatteras (Supplementary Figure S7 Figure S7 (b)) show high R 2 Adj , whereas tide gauges south of Japan (TG 1 to 24) are not at all explained by the atmospheric forcing. The drop in the variability explained by the atmosphere is, in both regions, located at the separation point of the western boundary current (Cape Hatteras and the Bōsō Peninsula respectively). This does not necessarily means that there is no atmosphere-related sea level change south of the separation 705 points but rather that they are dwarfed by other sources of variability.
Supplementary Figures S8 (a) and (b) present the mean of ζ Atm north of the Bōsō Peninsula and Cape Hatteras respectively, where ζ Atm is the sea-level driven by the atmosphere and regroups the three first terms of equation A1 (ζ = ζ Atm + O(t)). It is apparent that, while most of the variability is intra-annual, there is also interannual variations.
In the paper, we consider the residual O(t) (Eq. A1), which represents the sea-level variability unexplained by the atmo-710 spheric variables, as the sea-level 'corrected' from the local atmospheric forcing, and refer to it as ζ for simplicity.

Appendix B: Empirical Orthogonal Function Analysis
Here we provide further insights on the Empirical Orthogonal Function (EOF) analysis used to objectively reduce the sea-level anomalies in an ensemble of modes.
EOF decomposition using covariance matrix is performed on tide gauge records after they are interpolated on a regular grid 715 to prevent variability in better sampled region from being favored in the analysis. First, tide gauges located in the Chesapeake Bay, the Inland Sea (west and east separately) are averaged and associated with a virtual location at the mouth of, respectively, the Chesapeake Bay, the Bungo Channel and the Kii Channel. Then, in the Pacific (Atlantic), the 20 (18) remaining gauge records plus the two (one) aggregated estuary records are interpolated onto a regular, alongshore grid with 150 km spacing.
The modes are composed of a time-varying coefficient α, the Principal Component (PC), and an associated spatial-varying 720 coefficients φ, the Empirical Orthogonal Vector or Function (EOF): where i = 1, 2, 3, ... represents the modes, which are ordered by decreasing percentages of total variability explained, n is the total number of spatial grid points and x and t are, respectively, space (alongshore) and time.
Note that the spatial amplitudes φ's that are discussed within the text are relative to periods when their associated principal 725 component α's are equal to standard deviation, that is, α i = 1. For example, it is shown that the amplitude of the leading mode south of Japan, φ 1 , is on average 2.3 cm ( Fig. 5 (a)). The peak-to-peak amplitude of the associated temporal amplitude α 1 , defined as the difference between the maxima of late 2004 and the minimum of 1985, is roughly equal to 5 (Fig. 5 (c)). Hence, between 1985 and 2004, the sea-level rise associated with this mode is of ∼ 12 cm south of Japan. Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. Samuel Diabaté would like to thank his colleagues of the A4 team as well as Benoit Meyssignac, Simon Michel,