Western boundary circulation and coastal sea-level variability in Northern Hemisphere oceans

TLDR: In this paper, the relationship between coastal sea level and the variability of the western boundary currents has been previously studied in each basin separately, but comparison between the two basins is missing.

Abstract: . The northwest basins of the Atlantic and Pacific oceans are regions of intense western boundary currents (WBCs): the Gulf Stream and the Kuroshio. The variability of these poleward currents and their extensions 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 at which 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 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 of 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 7 (5) 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. Our result extends previous findings limited to the altimetry era and 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. Long-duration tide gauges, such as Key West, Fernandina Beach or Hosojima, could be used as proxies for the past meridional shifts of the western boundary current extensions.

Figures

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

Figure 1. (a) Kuroshio region circulation: The three Kuroshio paths — the typical Large Meander (tLM), the near-shore Non-Large Meander (nNLM) and the offshore Non-Large Meander (oNLM) are indicated upstream of the Izu-Ogasawara Ridge. The mean location of the KE is indicated offshore of this point showing the location of the quasi-stationary meanders. The Oyashio current is shown in blue. On land, K indicates Kyūshū, Hon stands for Honshū and Ho indicates Hokkaidō. (b) Gulf Stream region circulation from the Florida Current to the Gulf Stream Extension. The Northern Recirculation Gyre is also indicated. On land, M.-A. B. stands for Mid-Atlantic Bight and N.S. indicates Nova Scotia. Markers in (a) and (b) indicate the location of the tide gauges used in this study. The colour and shape of the markers in (a) and (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.

Figure 2. (a) GS climatological position (solid line) and GS climatological position plus GSNW spatial amplitude based on EOF analysis of the along-jet temperature anomalies (dashed line). Conversion ratio from normalized temperature to latitude is arbitrarily set for visualisation, but is the same at every grid point. (c) GSNW time series obtained from EOF analysis (thick light blue), with also the GSNW index of Joyce et al. (2000) shown in red. (b) and (d) As for (a) and (c), but obtained for the Kuroshio Extension, and with the KE indices of Qiu et al. (2016) replacing Joyce et al. (2000). The solid orange line in (d) corresponds to the temperature and salinity based index, and the dashed thin red line corresponds to the wind-based index. All timeseries in (c) and (d) are normalized.

Figure 5. (a) and (b) present the leading EOF (φ1) of the gridded, tide gauge obtained, sea-level anomaly (circular markers). (c) and (d) present, for the Pacific and Atlantic respectively, the associated principal components α1’s (solid blue lines), together with indices of extension meridional location: this study and Qiu et al. (2016) T/S-based and wind-based KEIs (on (c), thick light blue line, orange solid line and dot-dashed red line respectively); and this study and Joyce et al. (2000) GSNWs (on (d), thick light blue line and dot-dashed red line, respectively) . All quantities on (c) and (d) are normalized. Colour shadings on (a) and (b) are, for each basin, the sea surface velocity magnitude composites difference based on the principal component α1 (period of α1 >+2/3 minus period of α1 <−2/3). The arbitrary threshold of ±2/3 was used, but taking any number between zero and one leads to akin patterns. The inset on (a) present the regression coefficient obtained when the principal component is regressed on the original tide gauges, with a zoom in on the Kii peninsula.

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 (red dashed line). The latter is the same as the blue line on Figure 4 (a). (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°W – 69°W (dot-dashed red line).

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

Full text

Western boundary circulation and coastal sea-level variability in
northern hemisphere oceans
Samuel Tiéfolo Diabaté
1
, Didier Swingedouw
2
, Joël Jean-Marie Hirschi
3
, Aurélie Duchez
3
, Philip
J. Leadbitter
4
, Ivan D. Haigh
5
, and Gerard D. McCarthy
1
1
ICARUS, Department of Geography, Maynooth University, Maynooth, Co. Kildare, Ireland
2
Environnements et Paleoenvironnements Oceaniques et Continentaux (EPOC), UMR CNRS 5805 EPOC-OASU-Universite
de Bordeaux, Allée Geoffroy Saint-Hilaire, Pessac 33615, France
3
National Oceanography Centre, Southampton, UK
4
University of East Anglia, Norwich, UK
5
University of Southampton, Southampton, UK
Correspondence: Samuel Tiéfolo Diabaté (samuel.diabate.2020@mumail.ie)
Abstract. 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 variability5
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 result10
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 Beach or
Hosojima could be used as proxies for the past meridional shifts of the western boundary current extensions.
1 Introduction
Western boundary currents (WBCs) are a major feature of global ocean circulation and play an important role in global climate15
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 to20
(Little et al., 2019; Sasaki et al., 2014; Woodworth et al., 2019; Collins et al., 2019).
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Figure 1. (a) Kuroshio region circulation: The three Kuroshio paths — the typical Large Meander (tLM), the near-shore Non-Large Meander
(nNLM) and the offshore Non-Large Meander (oNLM) are indicated upstream of the Izu-Ogasawara Ridge. The mean location of the KE
is indicated offshore of this point showing the location of the quasi-stationary meanders. The Oyashio current is shown in blue. On land, K
indicates Ky
¯
ush
¯
u, Hon stands for Honsh
¯
u and Ho indicates Hokkaid
¯
o. (b) Gulf Stream region circulation from the Florida Current to the Gulf
Stream Extension. The Northern Recirculation Gyre is also indicated. On land, M.-A. B. stands for Mid-Atlantic Bight and N.S. indicates
Nova Scotia. Markers in (a) and (b) indicate the location of the tide gauges used in this study. The colour and shape of the markers in (a) and
(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 variability25
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 above30
the shallower region of the IOR is possibly the cause of an unstable Kuroshio Extension (Sugimoto and Hanawa, 2012). In any
case, when the KE is unstable, it has a more southern mean position, and the Kuroshio follows the offshore Non-Large Meander
(oNLM) path (see Fig. 1 (a)). When unstable the Kuroshio has a lower overall transport (Sugimoto and Hanawa, 2012), which
has an impact on the associated ocean heat transport. When the KE is stable, it exhibits a quasi-stationary meanders and a
more northern mean position, and the Kuroshio south of Japan tends to follow either the typical Large Meander (tLM) or the35
near-shore Non-Large Meander (nNLM) (Sugimoto and Hanawa, 2012; Qiu et al., 2014; Usui et al., 2013).
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Among the typical paths that the Kuroshio can take south of Japan (Fig. 1), the typical large meander is without doubt
the most remarkable, and is a major driver of the regional sea level (Kawabe, 2005, 1995, 1985) and atmospheric variability
(Sugimoto et al., 2019). Large meanders (LM) occur when two stationary eddies strengthen south of Japan. One is located
southeast of Ky
¯
ush
¯
u and associated with an anticyclonic circulation; and the other one is located south of T
¯
okai and associated40
with a cyclonic circulation. The front bounded by the two eddies becomes the Kuroshio large meander, and thus the cyclonic
anomaly is inshore between the Kuroshio path and the southern coasts of T
¯
okai.
In the Atlantic, the Gulf Stream has its origins in the eponymous Gulf of Mexico, flowing past the Florida coastline as the
Florida Current before leaving the boundary at Cape Hatteras near 35°N. From here it flows eastward as a meandering, eddying,
free current in the Gulf Stream Extension, and eventually the North Atlantic Current. From the American coast to 60°W – 55°W,45
northward or southward lateral motions of the Gulf Stream Extension dominate its interannual and seasonal variability. This
notable intrinsic variability follows closely the main mode of Atlantic atmospheric variability: the North Atlantic Oscillation
(NAO) (Joyce et al., 2000; McCarthy et al., 2018). The abrupt transition from warm subtropical waters to cold subpolar waters
marks a ‘North Wall’ of the Gulf Stream (Fuglister, 1955). This Gulf Stream North Wall (GSNW) is a convenient marker of
the lateral motions of the Gulf Stream Extension (Frankignoul et al., 2001; Joyce et al., 2000; Sasaki and Schneider, 2011b).50
The horizontal circulation of separated western boundary current interact closely with the vertical circulation. The vertical
circulation in this region is part of the AMOC which can be simplified as northward flowing Gulf Stream waters and southward
flowing deep waters as part of the Deep Western Boundary Current (DWBC). One paradigm of the interaction of vertical
and horizontal circulation in the region is that an enhanced DWBC, enhanced AMOC, ‘pushes’ the GSNW to the south, and
expands the Northern Recirculation Gyre (NRG). However, diverse behavior has been found in models, with some supporting55
this paradigm (Zhang and Vallis, 2007; Zhang, 2008; Sanchez-Franks and Zhang, 2015) and some finding the opposite: an
enhanced AMOC, northward shifted GSNW (De Coetlogon et al., 2006; Kwon and Frankignoul, 2014). Alternatively, as in
the Pacific with the KE, the Gulf Stream Extension has been linked to the mechanism of remote wind stress curl forcing the
westward propagation of large-scale jet undulations (Sasaki and Schneider, 2011b). Finally, Andres et al. (2013) highligted that
the coastal sea level on the large shelf north of Cape Hatteras was in agreement with the location of the Gulf Stream Extension60
west of 69 °W and suggested that the shelf transport ‘pushes’ the Gulf Stream, whereas Ezer et al. (2013) hypothesized that a
more inertial Gulf Stream south of the separation point may ‘overshoot’ to the north when leaving the coastline at 35°N and
control, at least to some extent, the location of the extension.
While the Gulf Stream and Kuroshio are western boundary currents driven by the closure of the Sverdrup balance (Stommel,
1948; Munk, 1950), even the brief introduction presented here highlights both differences and similarities between the currents.65
Upstream of separation point, the currents behave quite differently. The Kuroshio takes a number of distinct paths, whereas
the Gulf Stream hugs the coast tightly. The separation point at the B
¯
os
¯
o peninsula and Cape Hatteras has a remarkably similar
latitude both at 35°N. Downstream, the Gulf Stream Extension flows northeastward, whereas the Kuroshio Extension is mainly
flowing eastward. The meandering of the Kuroshio in its extension region is much more defined than that of the Gulf Stream
Extension, with no named quasi-stationary meanders in the Gulf Stream Extension (until farther downstream at the Mann70
eddy). The north – south shifts of the extensions are remarkable features of both basins and account for an important part the
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extensions’ variability. It is well established that these lateral shifts are caused by the propagation of long jet-trapped waves
forced by downstream wind in the Pacific, whereas the mechanisms driving the GSNW are not completely clear, with plausible
role of a similar mechanism of wind-forced jet undulation. These jet-trapped waves are possible thanks to the sharp background
velocity gradient induced by WBC Extensions, comparable or greater to the meridional gradient of planetary vorticity within75
the mid-latitude band. Hence, the jet-trapped waves are essentially Rossby waves, but they propagate in the waveguide formed
by the WBC extension, which allow their meridional narrowing as they progress westward, and their southwestward flow in
the Atlantic (Sasaki et al., 2013; Sasaki and Schneider, 2011a, b). It is however important to note that, in the Atlantic, the
lateral shifts of the Gulf Stream Extension have been more often linked with the DWBC and the NRG. In the Pacific, southern
(northern) shifts of the Kuroshio Extension are known to be concurrent with periods of instability (stability), whereas, until80
recent years (prior to ∼2000), the Gulf Stream Extension has been much more stable (Andres, 2016; Gangopadhyay et al.,
2019). The interaction with the cold currents to the north is also quite different. The continent north of the Gulf Stream to
Newfoundland lends to a topographical constraint on the gyre circulation, whereas the Oyashio is much less constrained by
land. Conversely, the upstream Kuroshio is much more constrained than the upstream Gulf Stream, due to the presence of the
Izu-Ogasawara Ridge. Additionally, there is no Pacific equivalent to the coastal circulation on the prominent shelf north of Cape85
Hatteras (Peña-Molino and Joyce, 2008). The AMOC is a notably Atlantic-specific feature but there is not a distinct feature of
the horizontal circulation that identifies clearly with the presence of the AMOC in the Atlantic basin that is not present in the
Pacific basin. While a decline in the AMOC is robust in climate projections, WBCs are also expected to change. WBCs have
been observed to be shifting polewards (Wu et al., 2012; Stocker et al., 2013) and becoming more unstable (Andres, 2016; Beal
and Elipot, 2016; Gangopadhyay et al., 2019).90
Tide gauges estimate relative sea level at the coast and have done so since the 18
th
century in certain locations (e.g. Amster-
dam, Stockholm, Kronstadt, Liverpool, Brest). Tide gauges have long been used to investigate ocean circulation in regions such
as the Gulf Stream where the impact of strong ocean circulation on coastal sea level is apparent (Montgomery, 1938). However,
ocean circulation is far from the only impact on sea level at the coast. The effects of land motion (including glacial isostatic
adjustment), thermosteric expansion, terrestrial freshwater changes (including river runoff and ice melt), and gravitational fin-95
gerprints all feature in sea level variations at the coast (Meyssignac et al., 2017). In addition, the local forcing of the atmosphere
drives an important part of the coastal sea-level variability, particularly in shelf environments. Variations in wind stress can
force water to travel toward (or away from) the coastline, consequently raising (lowering) the sea level at tide gauge locations.
Both across-shore and alongshore wind stresses can impact sea level as can variations in the local air pressure through the
Inverse Barometer (IB) effect. On the American northeast coast, the inverted barometer greatly influences interannual change100
in the mean sea level, dominates most extreme interannual changes, and is not negligible on multidecadal timescales (Piecuch
and Ponte, 2015), while the alongshore wind is also believed to play a role (Andres et al., 2013; Woodworth et al., 2014;
Piecuch et al., 2019). This contribution of the atmosphere to the mean sea level is particularly challenging to disentangle from
the contribution of ocean dynamics, because the two share similar range of timescales. Hence great care is needed to interpret
coastal sea level fluctuations, as measured by tide gauges, as representative of ocean circulation patterns.105
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A number of approaches have been developed to investigate ocean circulation using tide gauge data. The cross-stream
gradient of sea level can be estimated by using an onshore tide gauge and an offshore island tide gauge (Montgomery, 1938;
Kawabe, 1988; Ezer, 2015; Marsh et al., 2017) providing a direct estimate of a boundary current flowing between the gauges
via the geostrophic relationship. This type of estimate is restricted to locations where suitable offshore island tide gauges exist.
Apart from the limited number of such locations, the offshore estimate is located in the eddy-filled ocean interior which can110
experience sea level fluctuations driven by the ocean mesoscale (Sturges and Hong, 1995; Firing et al., 2004) that are not
representative of the large-scale ocean circulation. In the Atlantic, a number of studies (e.g. Bingham and Hughes, 2009; Ezer,
2013; McCarthy et al., 2015) have used long tide gauge records to estimate the strength of the AMOC, which has only been
continuously observed since 2004 (Cunningham et al., 2007). In the Pacific, the difference between the sea level either side
of the Kii peninsula (Fig. 1) has been extensively used to diagnose past occurrence of the typical large meander (Moriyasu,115
1958, 1961; Kawabe, 1985, 1995, 2005), despite the causal relationship not being fully understood.
Recent advances have been made on the theoretical underpinning of the relationship between sea level at the western bound-
aries of ocean and the offshore processes that influence sea level fluctuations (Minobe et al., 2017; Wise et al., 2018). The rule
of thumb of Minobe et al. (2017) for a western boundary of the northern hemisphere is as follows: the sea level at a point on
the coastline is influenced by (1) long Rossby waves (or any other mass input from the east) incident on that point and (2)120
coastally trapped waves, transmitting equatorward the sea level signal from points farther to the north which, equally, can be
influenced by incidental long Rossby waves. It follows that the alongshore gradient of the coastal sea level at a given latitude
is proportional to the sea level input from the east at the same latitude (Minobe et al., 2017),
∂
∂y

ζ
f






x
W
= −

β
f
2
ζ






x
I
, (1)
where ζ is the sea-level anomaly, evaluated at the coast (x
W
) and at the frontier between the boundary layer and the ocean125
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 propa-
gation 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 Kuroshio130
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 (Dangendorf et al., 2019; Nerem et al.,135
2018) induced by anthropogenic emission of greenhouse gases in the atmosphere, which is a major issue for coastal communi-
ties and environments. Understanding the relationship between sea level and ocean circulation is a component of understand-
ing coastal vulnerability to changing sea levels. Many densely populated regions border WBCs and large changes in WBCs
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Frequently asked questions

Q1. What have the authors contributed in "Western boundary circulation and coastal sea-level variability in northern hemisphere oceans" ?

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 the authors 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 ). 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. 

Q2. What are the future works in "Western boundary circulation and coastal sea-level variability in northern hemisphere oceans" ?

Hence, further work is required on the matter. The authors showed that dissimilarities between Japanese and American inshore sea level emerge in the second mode of variability. 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 causal630 link between the upstream sea level and the meridional shifts of WBC extensions is not yet completely understood, their 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. 

Q3. What is the potential for reconstruction of the ocean circulation mode of variability?

Because the tide gauge networks in both oceans extend further back in time than the period analysed in this study, inshoresea level has potential for reconstruction of the variability of the ocean circulation mode of variability. 

Q4. What is the effect of the surge correction on the EOF analysis?

the surge correction reduces the variance north of Cape Hatteras, which better constrains the EOF analysis and reduces undesired compensation between modes. 

Q5. What is the effect of wind stress on sea level?

Both across-shore and alongshore wind stresses can impact sea level as can variations in the local air pressure through theInverse Barometer (IB) effect. 

Q6. What is the role of the western boundary current in the redistribution of heat and salt?

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). 

Q7. What is the significance of the correlation between A and B?

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). 

Q8. How was the inverse distance weighting technique used?

For each year up to 2019, the available sparse subsurface temperature observations were interpolated at the climatological position of the Gulf Stream and KuroshioExtensions using an inverse distance weighting technique with power parameter p= 2 and a search radius of 400 km, allowing235construction of an along-jet temperature matrix. 

Q9. What is the main effect of the local forcing of the atmosphere on sea level?

In addition, the local forcing of the atmosphere drives an important part of the coastal sea-level variability, particularly in shelf environments. 

Q10. What are the indices used to determine the variability of the two WBC extensions?

The authors make use of the GSNW index from Joyce et al. (2000) and of the Kuroshio Extension indices from Qiu et al. (2016), and also derive in Sect. 2.3 indices for the variability of the two WBC extensions. 

Q11. What is the mechanism proposed by Sasaki et al.?

In the615absence 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.