In this section, we propose 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 on the Pacific and the Atlantic tide gauges, and hence our analysis can be seen as building on their work.

3.1 Cross-correlation analysis

Correlation analysis has been performed extensively for tide gauges on the US east coast from Woodworth et al. (2014), McCarthy et al. (2015), Piecuch et al. (2016) and Calafat et al. (2018), among others. The resultant correlation patterns suggest groupings of tide gauges across geographic regions, with boundaries defined by changing oceanographic circulation regimes, which we argue are the fingerprints of ocean circulation on coastal sea level.

We expand the analysis to tide gauges along the Japanese coast. Three tide gauge groupings are apparent in Fig. 3a 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, which 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 (tide gauge 18) showing slightly lower agreement. These two groups south of Japan were identified by the early work of Moriyasu (1958). The gauges on the eastern coastline of Honshū and Hokkaidō, including the tide gauge of Katsuura (TG 24) east of the Bōsō peninsula, show lower correlation with each other and are referred to as the Oyashio group. The limits of the correlation groupings match two oceanographic boundaries: the Kii peninsula, where the Kuroshio detaches during large meander periods, and the region of the Bōsō peninsula, where the Kuroshio leaves the coast to become the Kuroshio Extension (see Fig. 1).

Figure 3(a) Pacific and (b) Atlantic tide gauge cross-correlation at zero lag. Each circular marker gives the correlation r_ij between gauge i and gauge j. Tide gauges are numbered in ascending order from south to north, following the coastline (a list is given in Tables S1 and S2 in the Supplement). The bolder circular contour indicates that the correlation is above a significance level of 95 %.

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In the Atlantic, the pattern of correlation previously highlighted by McCarthy et al. (2015) and Woodworth et al. (2014) of a drop in correlation between tide gauges north and south of Cape Hatteras – the point at which the Gulf Stream leaves the coastline – is also seen in our analysis, with a distinct change in correlation patterns noted either side of Cape Hatteras (Fig. 3b). All gauges south of Cape Hatteras display almost identical behaviour, with a correlation average within that group equal to 0.78. All the gauges north of Cape Hatteras display high correlations as well: on average 0.72. The correlation of the three gauges located north of Cape Cod with the others north of Cape Hatteras is lower (on average r=0.64, including the tide gauge of Boston, TG 20, and r=0.58 without). This indicates that another boundary exists at Cape Cod, although the transition is not as abrupt as across Cape Hatteras. Despite the tide gauges being instruments locked at the coast, the obtained correlation patterns are representative of the two-dimensional sea-level coherence above the shelf. Indeed, similar groupings are visible in SSH data, extending from the coast to the shelf edge and featuring similar boundaries between one another (Cape Hatteras and Cape Cod; see Fig. 2 in Ezer, 2019).

In the Atlantic, Thompson and Mitchum (2014), Frankcombe and Dijkstra (2009), and Häkkinen (2000) noted high correlation of sea-level variations from Nova Scotia (Canada) to the Caribbean. This, of course, implies correlation across Cape Hatteras. While we do find a few significant correlations at the 95 % level across Cape Hatteras, indicated by bold outlines in Fig. 3, the distinct drop in correlation is more prominent. We therefore investigate the evolution of the correlation patterns through time in Figs. 4 and S1 in the Supplement. Within the groups (a) south and (b) north of Cape Hatteras, the individual correlations (Fig. S1a and b in the Supplement, thin grey lines) are high and show little time dependency, with the median never dropping below 0.54 south of Cape Hatteras and below 0.65 north (solid red lines). Figure 4b shows the changing correlations between gauges located on either side of Cape Hatteras (thin grey line) and the moving correlation between the two grouping averages. The correlations are high and the moving correlation between the two grouping averages is significant most of the time from roughly the 1950s to the late 1980s, when the correlations drop abruptly. From the 1990s onwards, there is no correlation between the two regions, with the exception of the most recent era from approximately 2010, when the correlation is negative. This change in behaviour was also noted by Kenigson et al. (2018) (see their Supplement).

Figure 4Moving correlation analysis between tide gauge records with a running window of 15 years. Each individual grey line renders the moving correlation between two records. The x axis represents the centre of the moving window. (a) Cross-correlation between the Oyashio group and west of the Kii group (grey lines). (b) Cross-correlation between gauges on either side of Cape Hatteras, the separation point of the Gulf Stream (again, grey lines). In each panel, the solid blue line is the moving correlation between the group average of sea-level anomalies. Significant correlations above the 95% level are indicated by a thicker blue line.

In the Pacific, the correlations within the two southern groupings feature little temporal variation (Fig. S1c and d in the Supplement). 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 variability as was done for the Atlantic in Fig. 4b, we plotted the changing correlations between the group west of Kii and the Oyashio group in Fig. 4a. The correlations are relatively low over the whole period, with the correlation median exceeding r=0.35 only on three occasions: 1978–1982, 1991–1993 and 2011–2012 (not shown). The moving correlation between the two grouping averages is rarely significant except in the early 1990s. More importantly, the moving correlations do not show an abrupt change, in contrast to the situation in the Atlantic.

3.2 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 regions from being favoured 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.

3.2.1 Atlantic and Pacific first modes

The leading mode of the Pacific dataset explains 47 % of the overall variance. The associated EOF, ϕ₁, features a common region of coherence west of the Bōsō peninsula, south of Japan, where the Kuroshio separates from the coast (Fig. 5a, circular markers). The Atlantic leading mode explains 60 % of the variance, and, in a similar way, ϕ₁ features greater amplitudes south of the separation point at Cape Hatteras, decreasing northward from there (Fig. 5b).

Figure 5The leading EOF (ϕ₁) of the gridded tide-gauge-based sea-level anomaly (circular markers) from the Pacific (a) and the Atlantic (b). The associated principal components α₁ are shown as thick dark blue lines for the Pacific (c) and Atlantic (d), together with indices of the WBC extension meridional location: this study (thick light blue line), Qiu et al. (2016) T $/$ S-based (thin orange line) and wind-based (thin dot-dashed red line) KEIs, and Joyce et al. (2000) GSNW (thin red dot-dashed). All time series in (c) and (d) are normalized. For each basin, colour shading in (a) and (b) is the sea surface velocity magnitude composite difference based on the principal component α₁ (period of ${\mathit{\alpha }}_{\mathrm{1}}>+\mathrm{2}/\mathrm{3}$ minus period of ${\mathit{\alpha }}_{\mathrm{1}}<-\mathrm{2}/\mathrm{3}$). The arbitrary threshold of $\pm \mathrm{2}/\mathrm{3}$ was used, but taking any number between 0 and 1 leads to similar patterns. The inset in (a) presents the regression coefficient obtained when the principal component is regressed on the original tide gauges, with a zoom-in on the Kii peninsula.

On the southern coastline of Japan (130–141^∘ E), the amplitude is on average 2.3 cm (excluding the easternmost virtual station located on the Bōsō peninsula; ϕ₁=0.7 cm). Towards the north, east of Honshū and Hokkaidō, the mode amplitude is reduced by a factor of 3 and equals 0.7 cm on average (this time including the virtual station on the Bōsō peninsula). The mode temporal variations α₁ are presented in Fig. 5c. There is a decrease from the late 1970s to 1985, followed by an increase until 1990. From there onwards, the principal component exhibits marked fluctuations with a 4–7-year period. In the Atlantic, the transition from the south of Cape Hatteras, where ϕ₁ is on average 2.6 cm, to the north where it is on average 1.3 cm is not as pronounced as with the Pacific gauges. The associated time-varying amplitude α₁ was maximum in the mid-1970s, the mid-1980s and the early 1990s, and it was particularly low in the mid-1960s, the early 1980s and the 2000s (Fig. 5d).

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 (Mulet et al., 2012). The surface velocity magnitudes are averaged over periods of strongly positive α₁ (greater than two-thirds its standard deviation, i.e. ${\mathit{\alpha }}_{\mathrm{2}}>\mathrm{2}/\mathrm{3}$) to form a first composite, and a similar procedure is done over periods of strongly negative α₁ (lower than minus two-thirds its standard deviation, i.e. ${\mathit{\alpha }}_{\mathrm{1}}<-\mathrm{2}/\mathrm{3}$). The threshold of $\pm \mathrm{2}/\mathrm{3}$ is arbitrary, but taking any other thresholds within 0–1 leads to similar patterns. For each basin, colour shading in Fig. 5a–b represent the difference between sea surface velocity composites based on each mode temporal amplitude.

Similar patterns are seen in both basins downstream of the separation points. In the Pacific, the positive velocities east of the ridge (>140^∘ E) are located farther north than the negative velocities, indicating that the Kuroshio Extension is found more to the north during the period of positive α₁. The surface velocity composite in the Atlantic presented alongside the EOF in Fig. 5b highlights an analogous situation, with the Gulf Stream Extension drifting to the north (positive velocity pattern) during periods of strong positive α₁ (early 1990s, mid-2010s) and to the south (negative velocity pattern) during periods of strong negative α₁ (2000s).

Different patterns are found upstream of the separation point. South of Japan and east of 136^∘ E, a region of positive velocity exists close to the coast, to the north of negative velocities. In particular, in the Izu–Ogasawara Ridge region (140^∘ E), positive velocities are above the deep channel located north of 34^∘ N (deeper than 1500 m), whereas negative velocities are spread above the shallower part of the ridge to the south (shallower than 1500 m). The Kuroshio south of Tōkai was hence found northward (southward) during periods of positive (negative) α₁. Moreover, it is obvious that the positive velocity pattern (associated with high α₁) resembles the nearshore NLM (see Fig. 1), whereas the negative velocity pattern (associated with low α₁) resembles the offshore NLM, which is a finding consistent with Kawabe (1989). In the Atlantic, the negative velocity pattern is inshore of the positive velocity pattern upstream of Cape Hatteras, indicating that during periods of positive (negative) α₁, the upstream Gulf Stream was offshore (inshore).

To extend the analysis of the relationship between the two principal components and the extension location prior to the satellite era, we make use of the Kuroshio Extension indices and Gulf Stream North Wall indices (this study; Qiu et al., 2016; 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 α₁ and the various KE indices. The maximum correlation with our KEI (Fig. 5c, solid green curve) is r=0.52 (significance is 99 %) and is found at zero lag. Similarly, we obtain moderate correlation between α₁ and the two Qiu et al. (2016) indices. There is better agreement with the index based on temperature and salinity (Fig. 5c, orange line), with r=0.52 when α₁ leads by 1 month (significance is 99 %; note that r=0.52 for leads between 0 and 2 months, with similar significance), than with the wind-based index (dot-dashed red line), for which the correlation maximum is found when α₁ lags by 7 months and is r=0.41 (61 %). The correlation is not stationary through time, however. The 1990s are a period of lesser agreement, as the sea-level features a bump which is not seen in KEIs. In contrast, the signals co-vary from 2000 onwards. Likewise, they all feature the strong shift of the late 1970s to mid-1980s.

Correspondingly, the Atlantic principal component α₁ is in agreement with our GSNW index at no lag, with r=0.46 (99 %), although greater correlation is obtained when α₁ leads by 1 year (r=0.52, significance is 99 %). The agreement with the Joyce et al. (2000) GSNW is more tenuous, with r=0.30 at no lag (90 %). The correlation maximum is 0.34 (68 %) and is found when α₁ leads by 2 years, although correlations above 0.27 are obtained in a lag range of minus 3 to plus 1 year (negative sign indicates α₁ leads). The values obtained with the Joyce et al. (2000) GSNW are not significant above the 95 % level, but we argue that the agreement at low frequency is significant. For example, we took up the EOF analysis again after the 19-month filter applied to the sea-level anomalies was substituted by a 73-month (∼6-year) filter. The obtained EOF ϕ₁ is not greatly changed (Fig. S2a in the Supplement). The correlation between the obtained α₁ and the Joyce et al. (2000) (our) GSNW, similarly filtered, equals 0.61 (0.78) when α₁ leads by 1.25 years (1 year), which is significant at 92 % (99 %).

We can conclude that the link between coastal sea-level upstream of the separation point and the latitude of the jet extension 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.

3.2.2  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 ϕ₂ of the Pacific and Atlantic tide gauges are presented in Fig. 6a and b, respectively. The EOF of the Pacific dataset is dominated by the tide gauges on the shores of the Tōkai district. This pattern corresponds to the group of correlation from Uragami (TG 17) to Yokosuka (TG 23) presented in Fig. 3a. The averaged amplitude of the mode in the region is 2.5 cm, but it rises to 3.0 cm when only the two virtual stations east of the Kii peninsula are considered. This indicates that, in the region south of Tōkai, the second mode is larger in magnitude than the leading mode. The second EOF of the Atlantic is dominated by the tide gauges north of Cape Hatteras, with an amplitude of 1.7 cm on average north of 35^∘ N. There is little deviation from the value of 1.7 cm, but, because the leading mode diminishes northward (Fig. 5b), the second mode dominates north of Cape Cod, whereas the two modes have similar magnitude in the Mid-Atlantic Bight.

Figure 6The second EOF (ϕ₂) of the gridded tide-gauge-based sea-level anomaly (circular markers) from the Pacific (a) and the Atlantic (b). The associated principal components α₂ are shown as thick dark blue lines for the Pacific (c) and Atlantic (d). Also in (c), the Kuroshio southernmost latitude south of Tōkai is represented by the solid orange line (positive values indicate Kuroshio further to the south); the difference between sea level at Uragami and Kushimoto is represented by the dot-dashed red line, and grey shading represents periods of typical large meander (JMA, 2018). In (d), the dashed yellow line is the sea-level difference between the averages of northern and southern groupings of tide gauges, as in McCarthy et al. (2015). All time series in (c) and (d) are normalized. For each basin, colour shading in (a) and (b) is the sea surface velocity magnitude composite difference based on the principal component α₂ (period of ${\mathit{\alpha }}_{\mathrm{2}}>+\mathrm{2}/\mathrm{3}$ minus period of ${\mathit{\alpha }}_{\mathrm{2}}<-\mathrm{2}/\mathrm{3}$). The arbitrary threshold of $\pm \mathrm{2}/\mathrm{3}$ was used, but taking any number between 0 and 1 leads to similar patterns. The inset in (a) presents the regression coefficient obtained when the principal component is regressed on the original tide gauges, with a zoom-in on the Kii peninsula.

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In the Pacific, a second group west of Kii varies in antiphase with the Tōkai gauges, with ϕ₂ on average equal to −1.2 cm. In the Atlantic, ϕ₂ south of Cape Hatteras is on average −0.8 cm (Fig. 6a). In both cases, the magnitudes of these negative variations are more than 2 times smaller than the magnitude of the positive variations (north of Cape Hatteras and south of Tōkai).

In the Pacific, large amplitudes in the EOF ϕ₂ are confined upstream of the Kuroshio separation point, whereas the Atlantic mode is dominated by the variability past the separation point to the north. Furthermore, the velocity composite difference based on α₂ and obtained in a similar manner presents very different patterns from one basin to another (colour shadings, Fig. 6a and b), which we return to in more detail below. As the two modes are different, we discuss them separately.

3.2.3 The second mode in the Pacific

The principal component α₂ obtained with the Pacific gauges is closely linked with the typical large meander of the Kuroshio. Negative values coincide with known periods when the Kuroshio took the tLM pathway (as acknowledged by the Japan Meteorological Agency – JMA, 2018: August 1975 to March 1980, November 1981 to May 1984, December 1986 to July 1988, December 1989 to December 1990, July 2004 to August 2005, August 2017–2020; see shading in Fig. 6c), whereas the Kuroshio took one of the NLM pathways the rest of the time or, less often, an atypical path.

The principal component is extremely close (r=0.83, significance well above 99 %) to the difference in sea level between Kushimoto and Uragami (thin dot-dashed red line in Fig. 6c), two stations located either side of Cape Shiono-Misaki on the Kii peninsula, which is the point of separation between the two groups of coherent variability highlighted in the previous section. The relationship between the tLM periods and the sea-level difference between those two stations has been known since the early work of Moriyasu (1958, 1961) and was investigated by Kawabe (1985, 1995, 2005), among others. The inset in Fig. 6a presents the regression coefficient obtained when the principal component is regressed on the original tide gauge records, with a zoom-in on the Kii peninsula. Despite geographical proximity (less than 20 km), the stations of Kushimoto and Uragami (indicated by a K and a U in the inset) are affected very differently by the second mode. The amplitude at Uragami is negative and is positive at Kushimoto. On the other hand, as was discussed previously, the leading EOF is of same sign and relatively similar magnitude on all of the southern coast of Japan (see the inset of Fig. 5a for the amplitude of the leading mode at Kushimoto and Uragami), and the other modes have negligible amplitudes in the region. From there, subtracting the Kushimoto time series from the ones from Uragami essentially gets rid of the influence of the leading EOF and reveals the underlying variability south of Tōkai.

The Japan Meteorological Agency estimate of the southernmost latitude of the Kuroshio axis south of Tōkai (136–140^∘ E) is shown in Fig. 6c (orange line, axis is inverted so that southern shift is a positive anomaly). Correlation with the principal component α₂ 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 %).

The velocity composite, derived on high ($>\mathrm{2}/\mathrm{3}$) minus low ($<-\mathrm{2}/\mathrm{3}$) values of α₂ as was done for the leading modes, is shown in Fig. 6a. When the principal component is strongly positive, i.e. when the Tōkai coastal sea level is high, the Kuroshio south of Tōkai (135–141^∘ E) is found farther south than when the principal component is negative, in which case it is found much closer to the coast. The positive velocity patch intersects the negative velocity patch so that the Kuroshio path east of the Bōsō peninsula is closer to the coast during the positive α₂ periods and flows northeastward, whereas during the negative period, the Kuroshio essentially flows eastward. Simply put, the negative velocity pattern represents the non-large meander paths, and the positive velocity pattern represents the large meander paths (see Fig. 1). The situation east of the ridge (>140^∘ E) is roughly similar to Fig. 5a; 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 the fact that the KE was more stable during the period of positive α₂ (see also Sugimoto and Hanawa, 2012).

3.2.4  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 inter-annual deviations from those long-term changes (Fig. 6d). The mid-1990s mark an abrupt change, with the inter-annual variability increasing greatly in amplitude from then onwards. This is shown in Fig. 7a, which presents the moving standard deviation of α₂ obtained with a 15-year running window (solid blue line).

Figure 7(a) Moving standard deviation of α₂ with a 15-year running window (solid blue line) and moving correlation with the same windowing between the northern and southern Atlantic gauge grouping averages (orange dashed line). The latter is the same as the blue line in Fig. 4a. (b) Moving correlation with a 15-year running window between the second principal component α₂ and our GSNW index (solid blue line) and between α₂ and our GSNW index computed on 75–69^∘ W (dot-dashed red line).

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As noted by Valle-Levinson et al. (2017), the variability of this mode has already been shown in the past by the difference in the sea level either side of Cape Hatteras (McCarthy et al., 2015; Woodworth et al., 2017). The yellow dashed line in Fig. 6d shows the difference between the averages of northern and southern gauge groupings. In comparison with the mean sea-level difference indices of McCarthy et al. (2015) and Woodworth et al. (2017), the time series are flipped, as we computed the difference as north minus south rather than the other way around. The agreement between the sea-level difference and α₂ is very high, r=0.88 (significant above 99 %). As for the difference between Kushimoto and Uragami, subtracting 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 ϕ₁ magnitude either side of Cape Hatteras is 1.3 cm on average, whereas the difference between the EOF ϕ₂ 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 (negative) phases of α₂ are concurrent with a southern (northern) shift of the Gulf Stream west of 69^∘ W (Fig. 6b). The patterns bear some resemblance to the ones obtained with α₁ presented in Fig. 5b, 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 α₁ (Fig. 5b). There, because the −25 to 25 cm s⁻¹ colour scale was retained for comparison with the other modes, the composite amplitudes are largely clipped. They are in the range of (±)40–60 cm s⁻¹, larger than the magnitudes obtained with α₁ in the same region, which were in the range of (±)10–40 cm s⁻¹. On the other hand, composite amplitudes east of 69^∘ W are smaller when obtained with α₂ than when obtained with α₁. In this second region, the α₂-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 α₂ and the Gulf Stream Extension meridional shifts in this second region is not as clear as the one obtained with α₁.

EOF analysis showed similar features of the leading mode of the two basins. The leading mode explained 47 % of the variance in the Pacific gauges and 60 % of the variability in the Atlantic gauges. Their spatial patterns were similar, having a greater amplitude south of the separation points than to the north (Fig. 5). In both basins, the temporal amplitudes of these similar modes were shown to co-vary with the meridional shifts of the western boundary current extension.

An important dissimilarity, however, is that the amplitude of the leading EOF in the Atlantic decreases gently north of the separation point, while the transition is abrupt in the Pacific. This result contrasts with the findings of Valle-Levinson et al. (2017), who obtained a leading EOF of the Atlantic gauge records with a less marked northward decrease in amplitude. Although the different starting and ending periods may play a role, we find that this discrepancy mostly arises because of the correction we applied for surge-driven sea-level change (Appendix A). This result, however, should not be interpreted as 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, when greater coherence either side of Cape Hatteras is seen (Fig. 4b), the northward decrease in ϕ₁ is still apparent. This is an important result because previous 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 which the mode's imprint of sea level diminishes, suggesting that the Gulf Stream presence is a plausible sea-level driver – in line with other studies (e.g. Ezer, 2015; Ezer et al., 2013; Ezer, 2019). In our view, the northward decrease in ϕ₁ is related to the orientation of the Gulf Stream Extension, which gradually moves away from the shoreline north of 35^∘ N. Following the same idea, the difference between the abrupt decrease in the EOF amplitude in the Pacific and the gradual decrease in the Atlantic arises from the different WBC extension orientations, with the Gulf Stream Extension flowing northeastward and the Kuroshio Extension eastward.

The leading mode temporal amplitudes in both basins 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 westward-propagating baroclinic jet-trapped Rossby waves that shift the jet meridionally (Sasaki et al., 2013; Sasaki and Schneider, 2011a; Sugimoto and Hanawa, 2009; Ceballos et al., 2009). A similar mechanism has been proposed for the Atlantic (Sasaki and Schneider, 2011b; Sirven et al., 2015). 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 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 in Fig. 5. Hence, although Sasaki et al. (2014) focused on the KE and southern Japan sea level, our results support the idea that such a mechanism could explain the link between the coastal sea level and the extension meridional 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 1 year, but we must emphasize that we found significant correlation between the GSNW and the Atlantic α₁ at zero lag, in agreement with a mechanism of coastal waves following the jet undulation.

The SSV analysis showed difference between the two basins in the upstream velocity patterns associated with α₁. The upstream Kuroshio was displaced on-shoreward south of Tōkai, but the Gulf Stream south of Cape Hatteras moved off-shoreward during the positive phase of α₁ (Fig. 5a and b). The two situations are not necessarily opposing, as off-shoreward motion is also seen southeast of Kyūshū in the Pacific (around 30^∘ N, 132^∘ E; see Fig. 5a). So, when α₁ is positive, the Kuroshio shifts off-shoreward south of Tōkai, but moves in-shoreward southeast of Kyūshū. Nonetheless, the patterns in the two basins are visually quite different. These patterns may suggest that some mechanisms more involved than a pure Kelvin wave (Sasaki et al., 2014) are at work. The velocity patterns seen south of Japan relate to the alternation of offshore NLM and nearshore NLM paths. Unfortunately, with the data at our disposal we cannot assess whether the upstream velocity patterns associated with α₁ extend before the satellite era as we did for the downstream variability with the GSNW and KEI indices – although it should be noted that Kawabe (1989) showed the same agreement between the sea level south of Japan and alternation of offshore NLM and nearshore NLM for the period 1964 to 1975. Interestingly, transition from one of these paths to the other is related to the Kuroshio transport but the established paths are not (Kawabe, 1989, 1990), meaning that differences in coastal sea level between oNLM and nNLM seen in α₁ are not due to geostrophic adjustment. The proximity (remoteness) of the warm water of the Kuroshio during nNLM (oNLM) might be responsible for the sea-level rise (drop) through thermosteric adjustment (Kuroda et al., 2010; Kawabe, 1989). A mechanism linking the upstream sea level to the water temperature in the vicinity of the Gulf Stream has also been proposed (Domingues et al., 2018), although this does not explain why the Gulf Stream was shifted in-shoreward when the Kuroshio was shifted off-shoreward.

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 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 has been known for many decades (Moriyasu, 1958, 1961; Kawabe, 1985, 1995, 2005). The elevated values of α₂ closely match the typical large meander periods (Fig. 6c), with the exception of April 2000–April 2001 when α₂ was high despite the Kuroshio not being in a tLM phase. Sugimoto et al. (2019) highlighted the fact that, during tLM phases, the strengthening of the anticyclonic circulation accelerates a westward coastal current in the 137–140^∘ E region, which allows the intrusion of warm Kuroshio water south of Tōkai. Between 2000 and 2001, this westward flow, which closes the anticyclonic circulation south of Tōkai, can also be observed. It is clearly apparent in monthly snapshots (Fig. S3 in the Supplement) and in the mean velocity between April 2000 and April 2001, although to a lesser extent (Fig. S4b in the Supplement). 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 (Fig. S4c–f in the Supplement). In fact, the major distinction from the 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 pathways are sometimes called straddling large meanders because, in contrast to 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 region is forced by the intrusion of the Kuroshio warm water brought by such currents (geostrophic tilting and/or steric rise). From a coastal sea-level perspective, there is no qualitative difference between the forcing of a 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 modes discussed here. As was indicated by Valle-Levinson et al. (2017), differentiating north minus south of Cape Hatteras sea level approximates this mode well (McCarthy et al., 2015; Woodworth et al., 2017). However, the EOF ϕ₂ has a much greater absolute magnitude north of Cape Hatteras than south, in contrast to Valle-Levinson et al. (2017). This indicates that simultaneous anti-variations south of Cape Hatteras are weak. Again, this difference arises because of the correction we applied to remove local atmospherically driven variability. It suggests that, at first order and for the period 1948–2019, differentiating the sea level across Cape Hatteras removes the influence of the leading mode on the sea-level variability north of Cape Hatteras. In this region, ϕ₁ and ϕ₂ have comparable amplitudes, despite the northward decrease in the strength of the leading mode.

Our results indicate a clear change in the variance of α₂ occurring around ∼1990 (Fig. 7a). Previous studies showed an increase in the agreement between the North Atlantic Oscillation and the sea-level variations north of Cape Hatteras occurring around the same time (Andres et al., 2013; Kenigson et al., 2018). Studies that focused on the low-frequency (7-year filtered) mean sea-level difference across Cape Hatteras (McCarthy et al., 2015; Woodworth et al., 2017) noted greater agreement with the NAO since the second half of the 20th century than before. For example, Woodworth et al. (2017) report a correlation of −0.62 for the period 1950–2014 between the difference of New York minus Key West and the NAO, as well as a lower correlation of 0.21 for the period 1913–1949. It is reasonable to believe that the strong agreement since ∼1990 contributes to the overall low-frequency agreement since 1950, in conjunction with anticorrelated multidecadal variability: sea-level rise north of Cape Hatteras (NAO decline) between 1948 and ∼1970 as well as between ∼1990 and ∼2010 and sea-level drop (NAO increase) between ∼1970 and ∼1990.

Our analysis based on sea surface velocity composites highlighted the agreement of α₂ with the Gulf Stream Extension meridional location west of 69^∘ W, consistent with Andres et al. (2013). The relevance of satellite measurements for interpretation of ocean dynamics prior to ∼1990 is, however, questionable. The sharp increase in the variance of the mode around ∼1990 raises the issue of whether this mode represents the pursuance of the same physical phenomenon throughout the whole period of 1948–2019 or if a mechanism supplanted another around ∼1990. We find that α₂ has a non-stationary relationship with the GSNW index in this study (Fig. 7b, solid blue line). The correlation between the GSNW and α₂ is −0.45 (significant above 99 %) over the full period of 1948–2019, quite similar to the correlation between the GSNW and α₁, but this agreement is due to the period after ∼1990 when correlation is $r=-\mathrm{0.63}$ (>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 era, which complicates understanding of the forcing prior to α₂ variance change around 1990. Note that here we use 1990 as a 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 α₂ dip after more than 40 years.

One mechanism in particular is hypothesized to have tied the Gulf Stream location west of 69^∘ W and the Nova Scotia to Cape Hatteras sea level together since ∼1990: Andres et al. (2013) argued that the coastal sea level is proportional to the geostrophic southward shelf transport, which interacts with the Gulf Stream at the separation point at which the shelf transport and the Gulf Stream meet. The use of the inshore sea level alone to diagnose the shelf transport is supported by a variance minimum in SSH anomaly located on the shelf break. Whether the Gulf Stream dictates the shelf sea level – and hence the shelf southward transport – or the other way around is an open debate (Andres et al., 2013; Ezer et al., 2013; Peña-Molino and Joyce, 2008).

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 the fact that the year 1987 marked an abrupt change in 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 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 α₂ (Fig. S8b in the Supplement). To investigate the question, we repeated the procedure of Andres et al. (2013) and correlated the principal component against the detrended NCEP wind stress fields projected onto a 20^∘ from zonal angle, roughly corresponding to the orientation of the shelf. A 19-month filter was applied to the wind stress for compatibility with the principal component. Figure S5a in the Supplement presents the correlation over the full period of 1948–2019 between α₂ and the along-20^∘ wind stress. The correlation above the shelf does not exceed 0.23. When the correlation is computed reducing the period to 1990 onwards, the patterns are greatly changed (Fig. S5c in the Supplement), as noted by Andres et al. (2013) and Kenigson et al. (2018). In contrast to Andres et al. (2013), however, the negative correlation pattern in Fig. S5c is shifted towards the Gulf of Saint Lawrence and east of Newfoundland so that the agreement with the alongshore wind on the shelf remains negligible everywhere. Hence, the variability of α₂ 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 α₂ is not significant anywhere on sea (Fig. S5d in the Supplement). This does not necessarily exclude alongshore wind stress in the Gulf of Saint Lawrence or east of Newfoundland as a possible driver of the variability of α₂ since 1990, but it indicates that any other forcing strongly correlated with the NAO is as likely to be a 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 drivers of the sea-level variability north of Cape Hatteras (Frederikse et al., 2017). However, existing indices of the AMOC and DWBC do not show the same variability as α₂ (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 us 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 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 modes, whereas in the region west of Kii the sea level is well approximated by the first mode only; 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 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 $\sim \mathrm{1990}.$ 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. Figure 7a presents the moving correlation between the southern and northern gauge averages (dashed orange line) alongside the standard deviation of the principal component α₂ computed with a moving 15-year window (solid blue line). It is apparent that the change in variance of α₂ is concurrent with the shift in correlation between north and south of Cape Hatteras seen in the moving correlation analysis. The EOF analysis hence leads us to interpret the change in coherence across Cape Hatteras as due to an increase in the variability north of Cape Hatteras appearing in the second mode. Clearly, this is a realistic possibility, but a caveat should also be stated. As previously mentioned, we were not able to link this second mode to a continuous physical mechanism, with agreement of α₂ with both the Gulf Stream position and with the winds seen only after the increase in the mode variance (Figs. 7b and S5 in the Supplement). It is thus possible that this EOF–PC couple is solely statistical and cannot be understood as a continuous physical mode. If a physical process replaced another around 1990, for example under the background influence of Gulf Stream transport changes or AMOC changes, it is possible that EOF analysis would not distinguish between the two mechanisms and mix them into a single statistical mode. That is because EOF analysis is not designed to deal with physical mechanisms whose spatial footprints are non-stationary in time (such as disappearing or emerging modes).

GSNW and KE indices from this study are available online, as are the principal components α₁ and α₂. They can be downloaded in “.csv” spreadsheet format at https://doi.org/10.5281/zenodo.4659318 (Diabaté et al., 2021). When using these time series, please cite the present study appropriately. The GSNW and KE indices are derived from the EN4 quality-controlled ocean temperature profiles (Good et al., 2013, EN4.2.1) available at https://www.metoffice.gov.uk/hadobs/en4/ (last access: 2 June 2021) and from the 1981–2010 objectively analysed mean temperature of the World Ocean Atlas 2018 (Locarnini et al., 2018, WOA18) available at https://www.nodc.noaa.gov/OC5/woa18/ (last access: 28 September 2021). 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/, last access: 18 October 2021), (2) sea-level pressure and 10 $\mathrm{m}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ wind speeds from the NCEP/NCAR Reanalysis 1 (Kalnay et al., 1996) distributed by the NOAA/OAR/ESRL PSL, and (3) gridded monthly SSH from the ARMOR3D product (Guinehut et al., 2012) available from the Copernicus Marine Environment Monitoring Service (CMEMS, https://marine.copernicus.eu, last access: 18 October 2021).

The supplement related to this article is available online at: https://doi.org/10.5194/os-17-1449-2021-supplement.

STD set up the methodology and carried out the investigation and the analysis. GDM and DS supervised the research and conceptualized research goals. STD, IDH and GDM implemented the computer code for analysis and visualization. STD and GDM prepared the paper with contributions from all co-authors.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Gerard D. McCarthy and Samuel Tiéfolo Diabaté work as part of the A4 Project (Aigéin, Aeráid, agus Athrú Atlantaigh – Oceans, Climate, and Atlantic Change; grant-aid agreement no. PBA/CC/18/01), which is carried out with the support of the Irish Marine Institute under the Marine Research Programme funded by the Irish Government, co-financed by the European Regional Development Fund. Gerard D. McCarthy is further supported by the ROADMAP project (grant-aid agreement no. PBA/CC/20/01) supported by the Marine Institute and funded by the Irish Government under the 2019 JPI Climate and JPI Oceans Joint Call. Didier Swingedouw received support from the Blue-Action (European Union's Horizon 2020 research and innovation programme, grant number: 727852) and EUCP (European Union's Horizon 2020 research and innovation programme under grant agreement no. 776613) projects. Joël Jean-Marie Hirschi acknowledges funding from the Newton Fund CSSP China project DYVA and from the NERC project ACSIS (NE/N018044/1).

This paper was edited by Katsuro Katsumata and reviewed by Tal Ezer and one anonymous referee.