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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.
Ocean Sci., 17, 1449–1471, 2021
https://doi.org/10.5194/os-17-1449-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
Western boundary circulation and coastal sea-level
variability in Northern Hemisphere oceans
Samuel Tiéfolo Diabaté1, Didier Swingedouw2, Joël Jean-Marie Hirschi3, Aurélie Duchez3, Philip J. Leadbitter4,
Ivan D. Haigh5, and Gerard D. McCarthy1
1ICARUS, Department of Geography, Maynooth University, Maynooth, Co. Kildare, Ireland
2Environnements et Paleoenvironnements Oceaniques et Continentaux (EPOC), UMR CNRS 5805 EPOC-OASU-Universite
de Bordeaux, Allée Geoffroy Saint-Hilaire, Pessac 33615, France
3National Oceanography Centre, Southampton, UK
4University of East Anglia, Norwich, UK
5University of Southampton, Southampton, UK
Correspondence: Samuel Tiéfolo Diabaté (samuel.diabate.2020@mumail.ie)
Received: 15 March 2021 – Discussion started: 6 April 2021
Revised: 14 September 2021 – Accepted: 21 September 2021 – Published: 22 October 2021
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 variabil-
ity 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 down-
stream of the points at which they separate from the coast.
Tide gauges on the adjacent coastlines have measured the in-
shore sea level for many decades and provide a unique win-
dow 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 miss-
ing. 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 Pa-
cific. Our result extends previous findings limited to the al-
timetry 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 predic-
tors. Long-duration tide gauges, such as Key West, Fernand-
ina 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
climate 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 At-
lantic Meridional Overturning Circulation (AMOC), result-
ing in heat transported towards the Equator in the South At-
lantic 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 re-
gional 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 (Little et al., 2019;
Sasaki et al., 2014; Woodworth et al., 2019; Collins et al.,
2019).
In the Pacific north of 30N, the Kuroshio flows north-
eastwards along the coast of mainland Japan before leaving
the coast at approximately 35N and becoming a separated
boundary current known as the Kuroshio Extension (KE,
Fig. 1a). The Kuroshio and KE have variable flow regimes in-
cluding decadal timescale variability, with the KE following
Published by Copernicus Publications on behalf of the European Geosciences Union.
1450 S. T. Diabaté et al.: Western boundary currents and coastal sea level
either a stable and northern path or an unstable and south-
ern path (Qiu et al., 2014; Imawaki et al., 2013; Kawabe,
1985). This variability 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 the KE meridionally before reaching
the Kuroshio–Oyashio confluence (Sugimoto and Hanawa,
2009; Sasaki et al., 2013; Sasaki and Schneider, 2011a; Ce-
ballos 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) (Qiu and Chen, 2005). Interaction
of the Kuroshio with the bathymetry when it is shifted above
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 south-
ern mean position, and the Kuroshio follows the offshore
non-large meander (oNLM) path (see Fig. 1a). When un-
stable, 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 quasi-
stationary meanders and a more northern mean position, and
the Kuroshio south of Japan tends to follow either the typi-
cal large meander (tLM) or the nearshore non-large meander
(nNLM) (Sugimoto and Hanawa, 2012; Qiu et al., 2014; Usui
et al., 2013).
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 vari-
ability (Sugimoto et al., 2019). Large meanders (LMs) occur
when two stationary eddies strengthen south of Japan. One
is located southeast of Ky¯
ush¯
u and associated with an anti-
cyclonic circulation; the other one is located south of T¯
okai
and associated 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 coast-
line as the Florida Current before leaving the boundary at
Cape Hatteras near 35N. From here it flows eastward as
a meandering, eddying, free current in the Gulf Stream Ex-
tension and eventually the North Atlantic Current. From
the American coast to 60–55W, northward or southward
lateral motions of the Gulf Stream Extension dominate its
inter-annual and seasonal variability. This notable intrinsic
variability closely follows the main mode of Atlantic at-
mospheric variability: the North Atlantic Oscillation (NAO)
(Joyce et al., 2000; McCarthy et al., 2018). The abrupt tran-
sition from warm subtropical waters to cold subpolar wa-
ters marks a “North Wall” of the Gulf Stream (Fuglister,
1955). This Gulf Stream North Wall (GSNW) is a conve-
nient marker of the lateral motions of the Gulf Stream Ex-
tension (Frankignoul et al., 2001; Joyce et al., 2000; Sasaki
and Schneider, 2011b). The horizontal circulation of the sep-
arated western boundary current interacts 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 cir-
culation in the region is that an enhanced DWBC and en-
hanced AMOC “push” the GSNW to the south and expand
the Northern Recirculation Gyre (NRG). However, diverse
behaviours have been found in models, with some support-
ing this paradigm (Zhang and Vallis, 2007; Zhang, 2008;
Sanchez-Franks and Zhang, 2015) and some finding the op-
posite: an enhanced AMOC and 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; Sirven et al.,
2015). Finally, Andres et al. (2013) highlighted the fact that
the coastal sea level on the large shelf north of Cape Hatteras
was in agreement with the location of the Gulf Stream Ex-
tension west of 69W and suggested that the shelf transport
pushes the Gulf Stream, whereas Ezer et al. (2013) hypothe-
sized that a more inertial Gulf Stream south of the separation
point may “overshoot” to the north when leaving the coast-
line at 35N and control, at least to some extent, the location
of the extension.
The diversity of proposed driving mechanisms of the Gulf
Stream Extension meridional shifts may be explained by
the great spatial differences over short distances along the
Gulf Stream Extension. Indeed, some factors induce incon-
gruity in the along-jet variability of the Gulf Stream Exten-
sion. This is the case of the time-dependent flanking cells of
the Gulf Stream, which are recirculations located immedi-
ately downstream of Cape Hatteras and which induce along-
stream decorrelation in the Gulf Stream Extension surface
transport (Andres et al., 2020). This indicates that different
mechanisms are acting on the position of the Gulf Stream
Extension. The aforementioned hypotheses for meridional
shifts of the Gulf Stream Extension are hence not necessarily
mutually exclusive and may co-exist at different downstream
distances from Cape Hatteras.
While the Gulf Stream and Kuroshio are western bound-
ary 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. Upstream of the separation points, the
currents behave quite differently. The Kuroshio takes a num-
ber of distinct paths, whereas the Gulf Stream hugs the coast
tightly. The separation points at the B¯
os¯
o peninsula and Cape
Hatteras both have a remarkably similar latitude at 35N.
Downstream, the Gulf Stream Extension flows northeast-
ward, whereas the Kuroshio Extension mainly flows east-
ward. The meandering of the Kuroshio in its extension re-
Ocean Sci., 17, 1449–1471, 2021 https://doi.org/10.5194/os-17-1449-2021
S. T. Diabaté et al.: Western boundary currents and coastal sea level 1451
Figure 1. (a) Kuroshio region circulation: the three Kuroshio paths – the typical large meander (tLM), the nearshore 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 dashed pink. 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, MAB stands for Mid-Atlantic Bight and NS 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 and across-shore coordinate system for the removal of sea-level
variability driven by local atmospheric effects (see Tables S1 and S2 in the Supplement). Shading in (a) and (b) indicates bathymetry.
gion 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 Mann
eddy). The north–south shifts of the extensions are remark-
able features of both basins and account for an important
part the 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 com-
pletely clear, with a plausible role of a similar mechanism of
wind-forced jet undulation. These jet-trapped waves are pos-
sible thanks to the sharp gradient of relative vorticity induced
by WBC extensions comparable to or greater than the merid-
ional gradient of planetary vorticity within 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 propagation
in the Atlantic (Sasaki et al., 2013; Sasaki and Schneider,
2011a, b; Sirven et al., 2015). 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 peri-
ods of instability (stability), whereas, until recent years (prior
to 2000), the Gulf Stream Extension has been much more
stable (Andres, 2016; Gangopadhyay et al., 2019). The in-
teraction with the cold currents to the north is also quite
different. The continent north of the Gulf Stream to New-
foundland 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 pres-
ence of the Izu–Ogasawara Ridge. Additionally, there is no
Pacific equivalent to the coastal circulation on the promi-
nent shelf north of Cape 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
clearly identifies with the presence of the AMOC in the At-
lantic basin that is not present in the Pacific basin. While a
decline in the AMOC is robust in climate projections and will
weaken the Gulf Stream (Chen et al., 2019), WBCs are also
expected to change. The Kuroshio is expected to strengthen
because of sea surface warming (Chen et al., 2019). 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).
Tide gauges (TGs) estimate relative sea level at the coast
and have done so since the 18th century in certain locations
(e.g. Amsterdam, Stockholm, Kronstadt, Liverpool, Brest).
Tide gauges have long been used to investigate ocean cir-
culation in regions such as the Gulf Stream where the im-
pact of strong ocean circulation on coastal sea level is appar-
ent (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), ther-
mosteric expansion, terrestrial freshwater changes (including
river runoff and ice melt) and gravitational fingerprints all
https://doi.org/10.5194/os-17-1449-2021 Ocean Sci., 17, 1449–1471, 2021
1452 S. T. Diabaté et al.: Western boundary currents and coastal sea level
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, partic-
ularly 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 pres-
sure through the inverse barometer (IB) effect. On the Ameri-
can northeast coast, the inverted barometer greatly influences
inter-annual change in the mean sea level, dominates most
extreme inter-annual changes and is not negligible on mul-
tidecadal 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 par-
ticularly challenging to disentangle from the contribution of
ocean dynamics because the two share a similar range of
timescales. Hence, great care is needed to interpret coastal
sea-level fluctuations measured by tide gauges as representa-
tive of ocean circulation patterns.
A number of approaches have been developed to inves-
tigate 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 (Mont-
gomery, 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 suit-
able 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 can 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; Mc-
Carthy et al., 2015) have used long tide gauge records to es-
timate the strength of the AMOC, which has only been con-
tinuously 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 diag-
nose past occurrence of the typical large meander (Moriyasu,
1958, 1961; Kawabe, 1985, 1995, 2005), despite the causal
relationship not being fully understood.
Recent advances have been made on the theoretical under-
pinning of the relationship between sea level at the western
boundaries of the ocean and the offshore processes that influ-
ence sea-level fluctuations (Minobe et al., 2017; Wise et al.,
2018). The rule of thumb of Minobe et al. (2017) for a west-
ern 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) inci-
dent on that point and (2) coastally trapped waves transmit-
ting the sea-level signal equatorward from points farther to
the north, which can equally 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
fxW
= β
f2ζxI
,(1)
where ζis the sea-level anomaly evaluated at the coast (xW)
and at the frontier between the boundary layer and the ocean
interior (xI), and βis the meridional gradient of the Cori-
olis 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 the Mi-
nobe et al. (2017) framework is expected to better estimate
the sea level on the coast of western boundaries. In accor-
dance with this idea, the coastal sea level south of Japan is
known to be in agreement with the Kuroshio 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 reach-
ing the coastline into coastally trapped waves that propagate
equatorward (Sasaki et al., 2014). Similarly, two very re-
cent studies pointed towards an agreement between the Gulf
Stream Extension variability and the sea-level change south
of Cape Hatteras (Dangendorf et al., 2021; Ezer, 2019). This
link is not yet well known or understood in the Atlantic basin
and deserves to be furthermore explored.
Globally, the mean sea level has shown an increased rate
of rise in the last decades (Dangendorf et al., 2019; Nerem
et al., 2018) induced by anthropogenic emission of green-
house gases in the atmosphere, which is a major issue for
coastal communities and environments. Understanding the
relationship between sea level and ocean circulation is a com-
ponent of understanding coastal vulnerability to changing sea
levels. Many densely populated regions border WBCs, and
large changes in WBCs could have big sea-level impacts. In
the Northern Hemisphere, the Gulf Stream and Kuroshio bor-
der the US and Japanese eastern seaboards, two of the most
densely populated coastlines in the world.
Links between the coastal sea level of western boundaries
and the nearby ocean dynamics have rarely been compared
between basins. Chen et al. (2019) addressed projected sea-
level changes through the 21st century in both Kuroshio and
Gulf Stream regions in the context of global warming and
AMOC weakening. Ezer and Dangendorf (2021) focused on
the energy budget of the western boundary regions. Here, we
analyse datasets of mean sea level along US and Japanese
eastern coastlines, identify major spatial modes of variability,
Ocean Sci., 17, 1449–1471, 2021 https://doi.org/10.5194/os-17-1449-2021
S. T. Diabaté et al.: Western boundary currents and coastal sea level 1453
and interpret this in terms of ocean circulation variability. We
explore the statistical links between the sea-level changes and
the western boundary current extension variability. This pa-
per is organized as follows. Section 2 presents the data used
in this study and the derivation of indices for the WBC ex-
tensions. The results of the analysis of the gauge records and
their relationship to upstream and downstream WBC vari-
ability are presented and discussed in Sects. 3 and 4. A con-
clusion is presented in Sect. 5.
2 Data and methods
2.1 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,
https://www.psmsl.org/, last access: 18 October 2021) on
17 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. To retain only
measurements of sufficient quality, length and completeness,
historical series with more than 10 % of missing monthly val-
ues as well as those flagged for quality issues are excluded.
Consequently, the number of individual tide gauge records
available is dependent on the chosen period. A summary of
gauge details is given in Tables S1 and S2 in the Supplement.
For the Atlantic, the period considered is January 1948–
December 2019 due to the availability of the atmospheric
reanalysis used to correct for surge effects. The island sta-
tion 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 of 22 stations on the Amer-
ican east coast.
The Japanese tide gauge network is more recent; there-
fore, the period considered for the Pacific is January 1968–
December 2019. The records of most stations on the eastern
coast of Honsh¯
u feature important offset shift and/or drift af-
ter the March 2011 tsunami and cannot be used as such, leav-
ing a 700 km coastline strip depleted of any measurement.
To remedy the issue, we retained the three long records of
Onahama, Miyako II and Ayukawa and replaced existing or
missing data after February 2011 with the closest SSH mea-
surement with trend and offset adjustment. The total number
of tide gauges retained for the Pacific region is 30 after the
criterion of completeness is applied.
Missing values are linearly interpolated for both regions.
No adjustment for long-term processes affecting the sea
level is performed as the records are quadratically detrended.
Monthly anomalies are obtained by subtracting the climato-
logical monthly mean.
To correct the records for the effect of local winds and
pressure, monthly sea-level pressure and 10m a.s.l.wind
speeds were obtained from the NCEP/NCAR Reanalysis 1
(Kalnay et al., 1996, NOAA/OAR/ESRL PSL, https://psl.
noaa.gov/, last access: 18 October 2021). They are avail-
able from 1948 to the present day. The grid has a resolution
of 1.875in longitude and 1.904in latitude. The vari-
ables are detrended and deseasonalized after the wind speed
is converted to wind stress. The Japanese 55-year Reanal-
ysis (Kobayashi et al., 2015, JRA-55, https://jra.kishou.go.
jp/index.html, last access: 18 October 2021), available from
1958, was also retrieved. Results were similar to those ob-
tained with the NCEP variables and are therefore not dis-
cussed. To assess and remove the local atmospheric con-
tribution 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, 2014), Frederikse et al.
(2017) and Piecuch et al. (2019). Details are given in Ap-
pendix A, together with a brief analysis of the results. 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 38N
on the eastern coast of Japan, whereas the atmospheric in-
fluence is reduced upstream of the separation points of the
Kuroshio and Gulf Stream. The unexplained residual repre-
sents the sea level corrected for local atmospheric effects.
Finally, to focus on inter-annual and slower variations, a
low-pass 19-month Tukey filter is applied. The filtering ef-
fectively reduces the period analysed to November 1968–
January 2019 for the Japanese gauges and November 1948–
January 2019 for the American gauges.
2.2 Additional datasets
Gridded monthly sea surface height (SSH), temperature
(SST) and velocities (SSVs) derived from satellite altimetry
are available from 1993 and were obtained from the Coper-
nicus Marine Environment Monitoring Service (CMEMS)
website (https://marine.copernicus.eu, last access: 18 Octo-
ber 2021). They are obtained from the ARMOR3D product
(Guinehut et al., 2012; Mulet et al., 2012). The three datasets
have a regular grid of 0.25×0.25.
To examine the variability of the Gulf Stream exten-
sion and the Kuroshio extension, the EN4 quality-controlled
subsurface (200 m depth) ocean temperature profiles (Good
et al., 2013, EN4.2.1) are used. The 1981–2010 objectively
analysed mean temperature at 200 m depth field from the
World Ocean Atlas 2018 (Locarnini et al., 2018, WOA18) is
used to derive the climatological position of the Gulf Stream
and Kuroshio extensions between 75 and 55W and between
141 and 161E, respectively. The climatological extension
positions are defined as the whole-number isotherm roughly
corresponding to the surface velocity maximum, which is
17 C in the Atlantic and 16 C in the Pacific. The two
https://doi.org/10.5194/os-17-1449-2021 Ocean Sci., 17, 1449–1471, 2021
1454 S. T. Diabaté et al.: Western boundary currents and coastal sea level
datasets were downloaded on 8 September 2020. Derivation
of jet latitudinal position indices is detailed in Sect. 2.3
Finally, we retrieved additional indices that infer oceanic
and atmospheric variability. We make use of the GSNW
index from Joyce et al. (2000) and of the Kuroshio Extension
indices from Qiu et al. (2016), and we also derive indices
for the variability of the two WBC extensions in Sect. 2.3.
Additionally, the estimate of the southernmost latitude of
the Kuroshio axis south of T¯
okai (136–140E) produced
by the Japan Meteorological Agency (JMA) was retrieved
from their website (https://www.data.jma.go.jp/gmd/
kaiyou/data/shindan/b_2/kuroshio_stream/kuro_slat.txt,
last access: 18 October 2021). This index represents the
upstream meridional movements of the Kuroshio south
of Japan. We also retrieved the monthly North Atlantic
Oscillation (NAO) index from James Hurrell and the Na-
tional Center for Atmospheric Research Staff (Eds) NAO
web page (https://climatedataguide.ucar.edu/climate-data/
hurrell-north-atlantic-oscillation-nao-index-station-based,
last access: 18 October 2021).
As the tide gauge records and the reanalysis variables,
satellite observations are deseasonalized, detrended and fil-
tered with a 19-month Tukey filter, unless otherwise men-
tioned. All aforementioned indices are similarly deseason-
alized, detrended and filtered, with a couple of exceptions:
yearly indices cannot be filtered at such a high cut-off fre-
quency, and the indices of Qiu et al. (2016) feature no sea-
sonal variability and are therefore not deseasonalized.
The significance of correlations between two time series
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 trans-
form of A and generating a large number (here 5000 is used)
of random time series with similar spectral properties. The
modulus is 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 in McCarthy et al.
(2015). In this case, the lead–lag correlation between each
randomly generated signal and B is computed, and the max-
imum correlation is determined. The significance is given as
the percentage of randomly generated maximum correlations
which are lower than the maximum correlation between A
and B (within the limit of a lead or lag of a fourth of A or B
length).
2.3 Meridional motions of the western boundary
current extensions
At inter-annual to multidecadal scale, the Gulf Stream Exten-
sion and the Kuroshio Extension are quite similarly charac-
terized by strong lateral movements. The displacements are
of about half a degree in the Atlantic (Joyce et al., 2000) and
about 1in 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 oscilla-
tions 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 the jet. In the Pacific, recent work has used
SSH estimates averaged in the 31–36N and 140–165E box
as proxy to infer the past Kuroshio Extension meridional lo-
cation (Qiu et al., 2014, 2016). This area corresponds to the
Kuroshio Southern Recirculation Gyre (KSRG), the strength
of which is a good indicator not only of the Kuroshio Exten-
sion 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 up-to-date indices of the meridional location of the
Kuroshio Extension and Gulf Stream Extension, follow-
ing the GSNW calculation method of Sasaki and Schneider
(2011b) and Frankignoul et al. (2001). Given the data avail-
ability, the analysis period was restricted to 1960 and 1965
onwards for the Atlantic and Pacific, respectively. For each
year up to 2019, the available sparse subsurface tempera-
ture observations were interpolated at the climatological po-
sition of the Gulf Stream and Kuroshio extensions using an
inverse distance-weighting technique with power parameter
p=2 and a search radius of 400 km, allowing 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 mesoscale
meandering variability in the gridded temperature anomaly.
The leading mode of variability is extracted for each basin
by performing an empirical orthogonal function (EOF) de-
composition based on correlation (rather than covariance) on
the detrended temperature anomaly. Figure 2 presents the as-
sociated EOFs (a and b) and principal components (c and d,
light blue lines) for the Atlantic and the Pacific, respectively.
The EOF 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 the GSNW and KE in-
dex (KEI), and we 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 compared the GSNW esti-
mate of Joyce et al. (2000), available from 1955 to 2011, and
the two KEIs of Qiu et al. (2016). The KEIs of Qiu et al.
(2016) are derived from the KSRG strength as mentioned
above and were initially introduced by Qiu et al. (2014) us-
ing satellite altimetry and model output. They have recently
been made available from 1905 to 2015 (1945 to 2012) us-
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1455
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 visualization
but is the same at every grid point. (c) GSNW time series obtained from EOF analysis (thick light blue), with the GSNW index of Joyce
et al. (2000) also shown in red. Panels (b) and (d) are 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 time series in (c) and (d) are normalized.
ing wind (temperature /salinity) data (Qiu et al., 2016). The
wind-based index is obtained by forcing a 1.5-layer reduced-
gravity model with historical wind stress merged from the
ERA-20C and ERA-Interim reanalysis sets. Although such
a model has limited skills in reproducing the westward nar-
rowing of the meridional jet oscillations (see Sasaki et al.,
2013; Sasaki and Schneider, 2011a), it is able to correctly
match the timing of the KE meridional shift (Taguchi et al.,
2007). The three indices are presented alongside the GSNW
(this study) and KEI (this study) in Fig. 2c and d after de-
trending is applied. They are annually averaged for compar-
ison with our GSNW and KEI. Correlations between both
Qiu et al. (2016) indices and our KEI are high, with a greater
value obtained with the T / S index (r=0.75, significance is
above 99%) than with the wind-based index (r=0.67, sig-
nificance is 99 %). Similar correlation is found between the
Joyce et al. (2000) GSNW and the GSNW from this study
over their overlapping period: 0.71 (significance >99 %).
3 Results
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 tempo-
ral patterns to ocean circulation. Senjyu et al. (1999), Valle-
Levinson et al. (2017) and Sasaki et al. (2014) used EOF de-
composition 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 circula-
tion 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 B¯
os¯
o penin-
sula region, which we refer to as T¯
okai for simplicity, an-
other highly correlated group exists. The mean of the cor-
relations 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 coast-
line of Honsh¯
u and Hokkaid¯
o, including the tide gauge of
Katsuura (TG 24) east of the B¯
os¯
o peninsula, show lower
correlation with each other and are referred to as the Oy-
ashio group. The limits of the correlation groupings match
two oceanographic boundaries: the Kii peninsula, where the
Kuroshio detaches during large meander periods, and the re-
gion of the B¯
os¯
o peninsula, where the Kuroshio leaves the
coast to become the Kuroshio Extension (see Fig. 1).
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1456 S. T. Diabaté et al.: Western boundary currents and coastal sea level
Figure 3. (a) Pacific and (b) Atlantic tide gauge cross-correlation
at zero lag. Each circular marker gives the correlation rij between
gauge iand gauge j. Tide gauges are numbered in ascending or-
der 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%.
In the Atlantic, the pattern of correlation previously high-
lighted 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 dis-
tinct change in correlation patterns noted either side of Cape
Hatteras (Fig. 3b). All gauges south of Cape Hatteras dis-
play 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 av-
erage 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 in-
struments locked at the coast, the obtained correlation pat-
terns are representative of the two-dimensional sea-level co-
herence 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 Hat-
teras 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 correla-
tion 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 Sup-
plement. 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 de-
pendency, with the median never dropping below 0.54 south
of Cape Hatteras and below 0.65 north (solid red lines). Fig-
ure 4b shows the changing correlations between gauges lo-
cated 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 correla-
tion 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 Kenig-
son et al. (2018) (see their Supplement).
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 T¯
okai 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 cor-
relations are relatively low over the whole period, with the
correlation median exceeding r=0.35 only on three occa-
sions: 1978–1982, 1991–1993 and 2011–2012 (not shown).
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1457
Figure 4. Moving correlation analysis between tide gauge records
with a running window of 15 years. Each individual grey line ren-
ders the moving correlation between two records. The xaxis rep-
resents the centre of the moving window. (a) Cross-correlation be-
tween the Oyashio group and west of the Kii group (grey lines).
(b) Cross-correlation between gauges on either side of Cape Hat-
teras, 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.
The moving correlation between the two grouping averages
is rarely significant except in the early 1990s. More impor-
tantly, 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 in-
terpolation 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 com-
mon region of coherence west of the B¯
os¯
o 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, φ1features greater am-
plitudes south of the separation point at Cape Hatteras, de-
creasing northward from there (Fig. 5b).
On the southern coastline of Japan (130–141E), the am-
plitude is on average 2.3cm (excluding the easternmost vir-
tual station located on the B¯
os¯
o peninsula; φ1=0.7 cm). To-
wards the north, east of Honsh¯
u and Hokkaid¯
o, 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 B¯
os¯
o
peninsula). The mode temporal variations α1are 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 φ1is on average 2.6cm, to the north
where it is on average 1.3cm 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. α2>2/3)
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. α1<2/3). The threshold
of ±2/3 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 ve-
locity 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 (>140E) 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 along-
side the EOF in Fig. 5b highlights an analogous situation,
with the Gulf Stream Extension drifting to the north (pos-
itive 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 136E, a region of posi-
tive velocity exists close to the coast, to the north of negative
velocities. In particular, in the Izu–Ogasawara Ridge region
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1458 S. T. Diabaté et al.: Western boundary currents and coastal sea level
Figure 5. The 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 α1are 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 α1>+2/3 minus period of α1<2/3). The arbitrary threshold of ±2/3 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.
(140E), positive velocities are above the deep channel lo-
cated north of 34N (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
T¯
okai was hence found northward (southward) during peri-
ods 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 veloc-
ity 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, indicat-
ing 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 princi-
pal 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 mod-
erate correlation between α1and 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 α1leads by 1 month (significance is 99 %; note that
r=0.52 for leads between 0 and 2 months, with similar sig-
nificance), 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 α1is
in agreement with our GSNW index at no lag, with r=0.46
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1459
(99 %), although greater correlation is obtained when α1
leads by 1 year (r=0.52, significance is 99 %). The agree-
ment 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 α1leads by 2 years, although
correlations above 0.27 are obtained in a lag range of mi-
nus 3 to plus 1 year (negative sign indicates α1leads). The
values obtained with the Joyce et al. (2000) GSNW are not
significant above the 95% level, but we argue that the agree-
ment 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 φ1is not greatly changed
(Fig. S2a in the Supplement). The correlation between the
obtained α1and the Joyce et al. (2000) (our) GSNW, simi-
larly filtered, equals 0.61 (0.78) when α1leads 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 φ2of 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 T¯
okai 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 T¯
okai, 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 35N. 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.
In the Pacific, a second group west of Kii varies in an-
tiphase with the T¯
okai gauges, with φ2on average equal to
1.2 cm. In the Atlantic, φ2south of Cape Hatteras is on
average 0.8cm (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 Hat-
teras and south of T¯
okai).
In the Pacific, large amplitudes in the EOF φ2are con-
fined upstream of the Kuroshio separation point, whereas the
Atlantic mode is dominated by the variability past the sepa-
ration point to the north. Furthermore, the velocity compos-
ite difference based on α2and obtained in a similar man-
ner 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 α2obtained 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, Decem-
ber 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 path-
ways the rest of the time or, less often, an atypical path.
The principal component is extremely close (r=0.83, sig-
nificance well above 99%) to the difference in sea level be-
tween 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 separa-
tion between the two groups of coherent variability high-
lighted 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 regres-
sion coefficient obtained when the principal component is re-
gressed 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 negli-
gible amplitudes in the region. From there, subtracting the
Kushimoto time series from the ones from Uragami essen-
tially gets rid of the influence of the leading EOF and reveals
the underlying variability south of T¯
okai.
The Japan Meteorological Agency estimate of the south-
ernmost latitude of the Kuroshio axis south of T¯
okai (136–
140E) is shown in Fig. 6c (orange line, axis is inverted so
that southern shift is a positive anomaly). Correlation with
the principal component α2is 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, sig-
nificance >99 %).
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1460 S. T. Diabaté et al.: Western boundary currents and coastal sea level
Figure 6. The 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 α2are shown as thick dark blue lines for the Pacific (c) and Atlantic (d). Also in (c), the Kuroshio
southernmost latitude south of T¯
okai 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 α2>+2/3 minus period
of α2<2/3). The arbitrary threshold of ±2/3 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.
The velocity composite, derived on high (>2/3) minus
low (<2/3) values of α2as was done for the leading
modes, is shown in Fig. 6a. When the principal component
is strongly positive, i.e. when the T¯
okai coastal sea level is
high, the Kuroshio south of T¯
okai (135–141E) is found far-
ther south than when the principal component is negative, in
which case it is found much closer to the coast. The posi-
tive velocity patch intersects the negative velocity patch so
that the Kuroshio path east of the B¯
os¯
o peninsula is closer
to the coast during the positive α2periods and flows north-
eastward, whereas during the negative period, the Kuroshio
essentially flows eastward. Simply put, the negative velocity
pattern represents the non-large meander paths, and the pos-
itive velocity pattern represents the large meander paths (see
Fig. 1). The situation east of the ridge (>140E) 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 pos-
itive 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, fol-
lowed 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 variabil-
ity increasing greatly in amplitude from then onwards. This
is shown in Fig. 7a, which presents the moving standard de-
viation of α2obtained with a 15-year running window (solid
blue line).
As noted by Valle-Levinson et al. (2017), the variability
of this mode has already been shown in the past by the dif-
ference in the sea level either side of Cape Hatteras (Mc-
Carthy et al., 2015; Woodworth et al., 2017). The yellow
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1461
Figure 7. (a) Moving standard deviation of α2with a 15-year run-
ning 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 run-
ning window between the second principal component α2and our
GSNW index (solid blue line) and between α2and our GSNW in-
dex computed on 75–69W (dot-dashed red line).
dashed line in Fig. 6d shows the difference between the aver-
ages of northern and southern gauge groupings. In compari-
son 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 α2is very high, r=0.88 (signif-
icant 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 in-
fluence of the leading mode. Indeed, the difference between
φ1magnitude either side of Cape Hatteras is 1.3 cm on aver-
age, whereas the difference between the EOF φ2magnitude
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 posi-
tive (negative) phases of α2are concurrent with a southern
(northern) shift of the Gulf Stream west of 69W (Fig. 6b).
The patterns bear some resemblance to the ones obtained
with α1presented in Fig. 5b, but the amplitudes of the com-
posite along the Gulf Stream Extension make a strong con-
trast. The positive and negative velocity patches are now
maximum in the region west of 69W, where they have
greater across-shore width than the ones obtained with α1
(Fig. 5b). There, because the 25 to 25 cm s1colour scale
was retained for comparison with the other modes, the com-
posite amplitudes are largely clipped. They are in the range of
(±)40–60 cm s1, larger than the magnitudes obtained with
α1in the same region, which were in the range of (±)10–
40 cm s1. On the other hand, composite amplitudes east of
69W are smaller when obtained with α2than when obtained
with α1. In this second region, the α2-based composite is also
less consistent, with the negative velocities intruding south-
ward and splitting the positive pattern in two at 68W.
Hence, the link between α2and the Gulf Stream Extension
meridional shifts in this second region is not as clear as the
one obtained with α1.
4 Discussion
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, hav-
ing 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 merid-
ional shifts of the western boundary current extension.
An important dissimilarity, however, is that the ampli-
tude 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 de-
crease in amplitude. Although the different starting and end-
ing 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 at-
mosphere 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 anal-
ysis and reduces undesired compensation between modes.
When the EOF analysis is recalculated restricting the pe-
riod to 1960–1990, when greater coherence either side of
Cape Hatteras is seen (Fig. 4b), the northward decrease in
φ1is still apparent. This is an important result because pre-
vious 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 (Thomp-
son 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 φ1is related to the orientation of the Gulf Stream Exten-
sion, which gradually moves away from the shoreline north
of 35N. Following the same idea, the difference between
the abrupt decrease in the EOF amplitude in the Pacific and
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1462 S. T. Diabaté et al.: Western boundary currents and coastal sea level
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 subsur-
face 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 pro-
posed for the Atlantic (Sasaki and Schneider, 2011b; Sirven
et al., 2015). Sasaki et al. (2014) hypothesized that the in-
coming 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 merid-
ional extent than traditional Rossby waves, the alongshore
coastal sea-level gradient is maximum near the WBC separa-
tion point (Equation 1). This leads to a “shadow” coastal area
north of the separation point, which is less affected by the in-
coming jet-trapped wave, and an “active” area, which sees
the progression of the coastal wave (Sasaki et al., 2014), ex-
plaining 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 ex-
plain the link between the coastal sea level and the exten-
sion 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 cor-
relation between the GSNW and the Atlantic α1at 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 T¯
okai, 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 Ky¯
ush¯
u in the Pa-
cific (around 30N, 132E; see Fig. 5a). So, when α1is pos-
itive, the Kuroshio shifts off-shoreward south of T¯
okai, but
moves in-shoreward southeast of Ky¯
ush¯
u. 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 α1extend 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. Interest-
ingly, 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 α1are 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 mecha-
nism 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 T¯
okai 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 α2was
high despite the Kuroshio not being in a tLM phase. Sug-
imoto et al. (2019) highlighted the fact that, during tLM
phases, the strengthening of the anticyclonic circulation ac-
celerates a westward coastal current in the 137–140E re-
gion, which allows the intrusion of warm Kuroshio water
south of T¯
okai. Between 2000 and 2001, this westward flow,
which closes the anticyclonic circulation south of T¯
okai, can
also be observed. It is clearly apparent in monthly snapshots
(Fig. S3 in the Supplement) and in the mean velocity be-
tween 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
T¯
okai goes along with a rise of the SSH there, as do com-
posites obtained over tLM periods (Fig. S4c–f in the Supple-
ment). 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 140E). These types of
pathways are sometimes called straddling large meanders be-
cause, in contrast to typical large meanders, the anticyclonic
eddy straddles the Izu–Ogasawara Ridge at 140E.
The common denominator to the tLM and such atypical
paths is the presence of the westward flow identified by Sugi-
moto et al. (2019), which brings warm waters south of T¯
okai.
We hypothesize that the sea-level rise recorded by the gauges
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1463
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 φ2has a
much greater absolute magnitude north of Cape Hatteras than
south, in contrast to Valle-Levinson et al. (2017). This in-
dicates that simultaneous anti-variations south of Cape Hat-
teras 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, φ1and 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 Os-
cillation and the sea-level variations north of Cape Hatteras
occurring around the same time (Andres et al., 2013; Kenig-
son et al., 2018). Studies that focused on the low-frequency
(7-year filtered) mean sea-level difference across Cape Hat-
teras (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 α2with the Gulf Stream Ex-
tension meridional location west of 69W, consistent with
Andres et al. (2013). The relevance of satellite measurements
for interpretation of ocean dynamics prior to 1990 is, how-
ever, 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 mech-
anism 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 α2is 0.45 (significant above 99%) over
the full period of 1948–2019, quite similar to the correla-
tion between the GSNW and α1, but this agreement is due
to the period after 1990 when 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 era, which
complicates understanding of the forcing prior to α2variance
change around 1990. Note that here we use 1990 as a change
point for simplicity, but similar results are obtained when us-
ing 1987 (Kenigson et al., 2018; Boon, 2012) or 1994, which
corresponds to the first strong negative α2dip after more than
40 years.
One mechanism in particular is hypothesized to have tied
the Gulf Stream location west of 69W and the Nova Sco-
tia 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 in-
shore sea level alone to diagnose the shelf transport is sup-
ported 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 correla-
tion 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 instanta-
neous 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 Sup-
plement). To investigate the question, we repeated the pro-
cedure of Andres et al. (2013) and correlated the principal
component against the detrended NCEP wind stress fields
projected onto a 20from zonal angle, roughly correspond-
ing to the orientation of the shelf. A 19-month filter was ap-
plied to the wind stress for compatibility with the principal
component. Figure S5a in the Supplement presents the cor-
relation over the full period of 1948–2019 between α2and
the along-20wind stress. The correlation above the shelf
does not exceed 0.23. When the correlation is computed re-
ducing 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 An-
dres et al. (2013), however, the negative correlation pattern
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1464 S. T. Diabaté et al.: Western boundary currents and coastal sea level
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 α2is 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 cor-
rection 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
α2is not significant anywhere on sea (Fig. S5d in the Sup-
plement). 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 α2since 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, ei-
ther 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 consid-
ered the role of salt (or lack of) and water volume input to
the shelf caused by both river discharges and eddies detach-
ing 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 distinc-
tions observed in the alongshore sea-level coherence between
the two basins. Upstream of the separation point in the Pa-
cific, 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 emer-
gence of (a)typical large meanders, which are an additional
forcing for the sea level east of Kii. This forcing has no equiv-
alent 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 addi-
tional distinction between the Atlantic and Pacific, as no co-
herence 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 α2computed
with a moving 15-year window (solid blue line). It is appar-
ent that the change in variance of α2is 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 α2with 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 an-
other around 1990, for example under the background influ-
ence 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).
5 Conclusions
This study presents a consistent analysis of the two west-
ern boundary regions in the northern Atlantic and northern
Pacific. The agreement between the upstream sea-level vari-
ability and the WBC extensions’ meridional shifts was high-
lighted in the two basins conjointly. In both oceans, this re-
lationship was previously observed for the altimetry period
(Sasaki et al., 2014; Ezer, 2019), but here we show that it
holds for the longer periods of 1948–2019 for the Atlantic
and 1968–2019 for the Pacific. This agreement, shown for
both basins, 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
at the coast, consequently modifying the inshore sea level.
The state-of-the-art wave theory of Sasaki et al. (2014) is
elegant, but there are some limitations that we believe are
useful to point out for future developments in the relation-
ship between western boundary current extensions and up-
stream sea levels. First, the upstream sea level is known to
co-vary with the upstream bottom temperatures at the shelf
break and on the shelf (Kuroda et al., 2010), as well as
with temperature within the western boundary current vicin-
ity (Domingues et al., 2018). This weakens the Sasaki et al.
(2014) hypothesis or at least limits the spectrum of possible
coastally trapped waves to waves with non-zero cross-shore
flow, which are able to drive warm water on and off the shelf
(e.g. topographic Rossby waves). Secondly, the role played
by the path variability upstream of the separation point is
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S. T. Diabaté et al.: Western boundary currents and coastal sea level 1465
unclear. In the Pacific, the upstream patterns of velocity in
Fig. 5a feature the offshore and nearshore non-large meander
paths (Fig. 1), which have not previously been understood as
propagating coastally trapped waves. Furthermore, positive
(negative) α1values were shown to be concurrent to inshore
(offshore) paths south of Japan, whereas south of Cape Hat-
teras, the opposite was observed (positive α1associated 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 in term
of paths in the two basins. Finally, recent studies have also
linked the inshore upstream sea level with the subtropical
gyre interior sea surface height and/or temperature (Wood-
worth et al., 2014; Thompson and Mitchum, 2014; Volkov
et al., 2019; Ezer, 2019). These diverging views underscore
the difficulties of understanding the causal relationship be-
tween the WBC extension and the upstream sea level. In the
Atlantic, our finding that the upstream sea level is in agree-
ment with the Gulf Stream Extension’s position converges
with the very recent study of Dangendorf et al. (2021), which
showed that the stero-dynamic portion of the upstream tide
gauge variability was correlated with the steric height signal
in the Gulf Stream Extension. The results of the present study
and of the recent work of Dangendorf et al. (2021) and Ezer
(2019), all presenting linkages between the Gulf Stream Ex-
tension and the upstream sea-level variability, are hence im-
portant and novel contributions to the understanding of Gulf
Stream dynamics. Further work is required to precisely com-
prehend the mechanisms that link the upstream sea level and
the western boundary current extensions’ variability.
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 mesoscale
dynamics (Kuroshio large meander), whereas in the Atlantic,
the second mode is mainly associated with changes north of
Cape Hatteras, the separation point of the Gulf Stream, al-
though weak anti-variations exist to the south. In the Pacific
and in comparison with existing studies, we noted that the
sea level south of T¯
okai was affected by the presence of large
meanders in a broader sense, including atypical meanderings
that straddle the Izu–Ogasawara Ridge. In the Atlantic, EOF
analysis highlighted the fact that the variability of the second
mode drives the coherence across Cape Hatteras. However, it
is not clear whether a physical mechanism – well represented
by the second mode of EOF analysis and with increasing ef-
fects after 1990 – caused the disconnect north and south of
Cape Hatteras or if a new process appeared circa 1990, which
cannot be resolved by stationary EOF analysis. We showed
that the strong link of this statistical mode with the shifts
of the Gulf Stream Extension west of 69W is relatively re-
cent and does not extend 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 vari-
ability of the ocean circulation mode of variability. Re-
construction of past large meander events requires at least
two gauges either side of the Cape Shiono-Misaki on the
Kii peninsula; traditionally, the tide gauges of Uragami and
Kushimoto are used. The two stations are respectively avail-
able from 1965 and 1957 in the PSMSL revised local ref-
erence (RLR) catalogue. Using sea-level aggregates based
on the correlation groupings (Fig. 3) rather than the two in-
dividual tide gauge records, in a manner akin to McCarthy
et al. (2015), allows the extension of the analysis up to 1944
and characterizes 1953–1955 and 1959–1963 as large mean-
der periods, similar to Moriyasu (1958, 1961) and Kawabe
(1985, 1995, 2005). On the other hand, further understand-
ing of the forcing on sea level prior to 1990 is needed to
use the north of Cape Hatteras gauge records as a proxy for
ocean and/or atmosphere variability prior to that date.
Finally, although the causal link between the upstream sea
level and the meridional shifts of WBC extensions is not yet
completely understood, our results suggest that upstream in-
shore tide gauges, such as Key West (available from 1913
in the PSMSL 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. That tide gauges
can be used to infer past open-ocean dynamics is a result in
line with some recent studies which have reconstructed open-
ocean sea level (and hence ocean dynamics) using the global
tide gauge network and advanced statistical methods (Ezer
and Dangendorf, 2020; Dangendorf et al., 2019, 2021).
Appendix A: Adjustment of tide gauge records for
surge-driven variability
Following the work of Dangendorf et al. (2013, 2014), Fred-
erikse et al. (2017), and Piecuch et al. (2019), we compute the
inverse barometer and wind-surge contributions to sea level
using multiple linear regression, with pressure (p) as well
as alongshore (τk) and across-shore (τ) wind stress anoma-
lies interpolated at each tide gauge location as predictors.
The angles used for the rotation in across-shore and along-
shore coordinates are presented in Tables S1 and S2 in the
Supplement. The quality of a regression primarily depends
on the correlation between the explanatory variables and the
period width. Here, the pressure and winds are not indepen-
dent. Hence, for each tide gauge, an “all-possible” regression
procedure was designed. This means that the model with the
https://doi.org/10.5194/os-17-1449-2021 Ocean Sci., 17, 1449–1471, 2021
1466 S. T. Diabaté et al.: Western boundary currents and coastal sea level
three regressors is tested (Eq. A1), alongside all the possible
models for which the first, second and (or) third term of the
equation are (is) ruled out. In total, 231=7 combinations
of possible regressions are tested at each tide gauge.
ζ= −β1[p(t ) p(t)] + β2τk(t ) +β3τ(t) +O(t). (A1)
The regressions return the regression coefficients β1,β2and
β3that describe the relationship between pressure, along-
shore and across-shore winds, and the gauge record. O(t)
represents the unexplained residual. Yintercepts are esti-
mated to improve the computation, but are not removed to
form the residual O(t). Note that the inverse barometer ef-
fect is not proportional to 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, β1is preceded
by a minus () because a rise of local atmospheric pressure
makes sea-level fall and vice versa.
To determine the best model for each tide gauge, 95 % con-
fidence intervals are computed for each regression coefficient
within the MATLAB built-in function. The regression mod-
els that feature one (or several) coefficient confidence inter-
val(s) crossing zero are excluded. Then, the best regression
is defined as the one with the highest adjusted coefficient of
determination R2
Adj, which is the proportion of the variance
in the gauge record that is predictable from the atmospheric
predictors, adjusted for their number (see Eq. A2):
R2
Adj =1
m
P
i=1ζib
Yi2
m
P
i=1ζiζ2
m1
mnr1,(A2)
where mis the number of time steps, nris the number of
regressors for that particular model (nr∈ [1,2,3]) and b
Ythe
sum of the obtained atmospheric contributions.
Figure S6a and b in the Supplement respectively present
the regression coefficients β1,β2and β3as well as their
95 % confidence interval for the Atlantic and for the Pacific
gauges. For each gauge, only the output of the best regres-
sions is shown. Hence, the number of regressors is not always
three, in particular for the Japanese stations. The adjusted co-
efficients of determination R2
Adj (bottom) for each tide gauge
are shown in Fig. S7 in the Supplement.
We compute values for β1of 0.11 and 0.9 mm Pa1on av-
erage for American and Japanese gauges, respectively (see
the green line in Fig. S6a and b in the Supplement). In
both regions, the computed β1values are comparable to the
theoretical (ρg)10.10 mm Pa1expected for an inverse
barometer response (dashed green line). The pressure is al-
ways one of the explanatory variables of the best regression,
highlighting the importance of the inverse barometer effect
on sea level. Across-shore coefficients are high in locations
upstream of the estuaries of Delaware Bay and Chesapeake
Bay (TGs 7, 8, 9, 10 and 12: Washington DC, Solomons
Island, Annapolis, Baltimore and Philadelphia). There, the
wind setup is amplified by the funnelling effect of the estuar-
ies. The nearby stations of Sewells Point (TG 6) and Lewes
(12) are, in contrast, much less affected because they are lo-
cated 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 de-
viation from the average of 7.9 m3N1, yet the maximums
are also found in the estuary region. North of Cape Cod (TG
14 to 23), we obtain values for β2an order of magnitude
greater than reported by Piecuch et al. (2019). For most of the
Japanese gauges, 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 ex-
plain more variability in the tide gauge records. However, a
consistent effect of the alongshore winds for the southern tide
gauges (TGs 1–2 and 4–19) is revealed by the regression.
Figure S7 in the Supplement presents the adjusted coef-
ficient of determination R2
Adj (Eq. A2). It better depicts the
effect of the atmosphere on the sea level than the regression
coefficients alone, as even a weak βicoefficient could greatly
affect the sea level if the corresponding regressor variabil-
ity 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 variabil-
ity north of Cape Hatteras (Fig. S7a in the Supplement), with
R2
Adj on average higher than 40 %. This result is in agreement
with Piecuch et al. (2019), who reported a value of 39%, al-
though their analysis focussed on the period 2004–2017. In
contrast, only 20 % of the variability in the time series of the
southern gauges can be explained with the regression, with
some deviations from that mean. This is consistent with pre-
vious findings of Woodworth et al. (2014), and we observe a
similar pattern in the Pacific. The tide gauges located north of
the B¯
os¯
o peninsula (Fig. S7b in the Supplement) show high
R2
Adj, whereas tide gauges south of Japan (TGs 1 to 24) are
not at all explained by the atmospheric forcing. The drop in
the variability explained by the atmosphere is located at the
separation point of the western boundary current in both re-
gions (Cape Hatteras and the B¯
os¯
o peninsula). This does not
necessarily means that there is no atmosphere-related sea-
level change south of the separation points but rather that
they are dwarfed by other sources of variability.
Figure S8a and b in the Supplement present the mean ζAtm
north of the B¯
os¯
o peninsula and Cape Hatteras, respectively,
where ζAtm is the sea level driven by the atmosphere and re-
groups the first three terms of Eq. (A1) (ζ=ζAtm +O(t)). It
is apparent that, while most of the variability is intra-annual,
there is also inter-annual variation.
In the paper, we consider the residual O(t) (Eq. A1),
which represents the sea-level variability unexplained by the
atmospheric variables, to be the sea level “corrected” from
the local atmospheric forcing and refer to it as ζfor simplic-
ity.
Ocean Sci., 17, 1449–1471, 2021 https://doi.org/10.5194/os-17-1449-2021
S. T. Diabaté et al.: Western boundary currents and coastal sea level 1467
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 a covariance matrix is per-
formed on tide gauge records after they are interpolated on
a regular grid to prevent variability in better-sampled regions
from being favoured in the analysis. First, tide gauges located
in the Chesapeake Bay and the Inland Sea (west and east sep-
arately) are averaged and associated with a virtual location at
the mouth of the Chesapeake Bay, the Bungo Channel and the
Kii Channel, respectively. Then, in the Pacific (Atlantic), the
20 (18) remaining gauge records plus the two (one) aggre-
gated estuary records are interpolated onto a regular along-
shore grid with 150 km spacing.
The modes are composed of a time-varying coefficient
α, the principal component (PC) and an associated spatial-
varying coefficient φ, the empirical orthogonal vector or
function (EOF):
ζ (x, t ) =
n
X
i=1
αi(ti(x), (B1)
where i=1,2,3,...represents the modes, which are ordered
by decreasing percentages of total variability explained, nis
the total number of spatial grid points, and xand tare space
(alongshore) and time, respectively.
Note that the spatial amplitudes φthat are discussed within
the text are relative to periods when their associated princi-
pal components αare equal to the standard deviation: that
is, αi=1. For example, it is shown that the amplitude of
the leading mode south of Japan, φ1, is on average 2.3cm
(Fig. 5a). The peak-to-peak amplitude of the associated tem-
poral amplitude α1, defined as the difference between the
maxima of late 2004 and the minimum of 1985, is roughly
equal to 5 (Fig. 5c). Hence, between 1985 and 2004, the
sea-level rise associated with this mode is 12 cm south of
Japan.
Data availability. GSNW and KE indices from this study are
available online, as are the principal components α1and 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 appropri-
ately. 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 α1and 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 m a.s.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 (Guine-
hut et al., 2012) available from the Copernicus Marine Environ-
ment Monitoring Service (CMEMS, https://marine.copernicus.eu,
last access: 18 October 2021).
Supplement. The supplement related to this article is available on-
line at: https://doi.org/10.5194/os-17-1449-2021-supplement.
Author contributions. 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.
Competing interests. The authors declare that they have no conflict
of interest.
Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Acknowledgements. Samuel Tiéfolo Diabaté would like to thank
his colleagues of the A4 team as well as Benoit Meyssignac, Si-
mon Michel, Juliette Mignot and David Pugh their for valuable ad-
vice and suggestions. Norihisa Usui, Magdalena Andres, Christo-
pher Piecuch, Arnoldo Valle-Levinson, Dudley Chelton, Thomas
Frederikse, Karen Simon, Philip Woodworth and David Smeed are
also thanked for their mail correspondence, as is Jeanne Auboiron
for her preliminary work.
Financial support. Gerard D. McCarthy and Samuel Tiéfolo Dia-
baté 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 sup-
port of the Irish Marine Institute under the Marine Research Pro-
gramme funded by the Irish Government, co-financed by the Eu-
ropean Regional Development Fund. Gerard D. McCarthy is fur-
ther 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 inno-
vation 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 ac-
knowledges funding from the Newton Fund CSSP China project
DYVA and from the NERC project ACSIS (NE/N018044/1).
https://doi.org/10.5194/os-17-1449-2021 Ocean Sci., 17, 1449–1471, 2021
1468 S. T. Diabaté et al.: Western boundary currents and coastal sea level
Review statement. This paper was edited by Katsuro Katsumata
and reviewed by Tal Ezer and one anonymous referee.
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