Kaneko et al.
Progress in Earth and Planetary Science(2022) 9:53
https://doi.org/10.1186/s40645-022-00509-z

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open AccessSubinertial frequency variations in the axisof the Tsugaru Warm Current east of the Tsugaru
StraitHitoshi Kaneko1* , Takahiro Tanaka2, Hiroto Abe1,3, Masahide Wakita1, Ken’ichi Sasaki1, Yasumasa Miyazawa4,
Takeshi Okunishi2, Shuichi Watanabe1, Shoko Tatamisashi1 and Yoshiaki Sato1

Abstract
The eastern part of the Tsugaru Strait (located at ~ 41.5° N) is a remarkable region of the coastal flow system around
Japan due to the Tsugaru Warm Current (TgWC), an intensive eastward current that flows over its complex topography and exhibits marked tidal variation. The TgWC has a jetlike structure and demonstrates drastic seasonal changes
in its path and vertical current structure. Using a high-resolution dataset obtained from a high-frequency radar system(HFR) and a coastal data assimilation experiment (JCOPE-T DA), we focused on the frontal variation, which is shorter
than the seasonal timescale, along the axis of the TgWC in relation to the meanders of the jet. We found variations in
the axis with multiple timescales between 1 and 14 days, especially in summer and autumn. The ~ 14-day variation,a remarkable occurrence on the west side of the eastern Tsugaru Strait, was consistent with the tidal variation in thestrait. The zonal scale of the axis meander estimated by the HFR matched a scale several times larger than the internal
deformation radius, especially in summer and autumn. JCOPE-T DA outputs showed that the crest of such a meander at greater depths progresses in relation to that at the surface. The outputs also suggested instabilities, indicating
potential and kinetic energy conversion from the mean to the eddy field. The propagation speed of the several-day
variation in the axis estimated from the HFR data was consistent with that of the two-layer baroclinic instability. The
several-day variation also showed relatively high coherence with wind variation from summer to autumn, during
which time the seasonal wind over the strait switched from easterly to westerly. These variations with multiple timescales imply an effect on north–south water mass mixing in the eastern part of the strait, including rapid acidificationin the strait and intensification of stratification.
Keywords: Tsugaru Strait, Tsugaru Warm Current, High-frequency radar, Data assimilation, JCOPE, Frontal waves, Tide,
Downfront wind, Baroclinic instability
1 Introduction
Ocean currents do not simply flow in a straight path; they
are known to meander from time to time. These meanders are caused by a variety of factors, including winds,
tides, and complex topography. The Tsugaru Warm
*Correspondence: h_kaneko@jamstec.go.jp
1
Mutsu Institute for Oceanography, Research Institute for Global Change,
Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 690
Kitasekine, Sekine, Mutsu, Aomori 035‑0022, Japan
Full list of author information is available at the end of the article

Current (TgWC) flows eastward in the Tsugaru Strait
between the mainland of Japan and Hokkaido; it demonstrates remarkable tidal variation over the characteristic
topography of the strait (Fig. 1). The volume transport of
the TgWC is ~ 1.5 Sv (= ­106 ­m3 ­s−1; e.g., Ito et al. 2003;
Onishi and Ohtani 1997), and the maximum speed of theeastward velocity reaches 1 m ­s−1 near the surface in theeastern part of the strait during summer, showing a jetlike structure with intense vertical shear (e.g., Kaneko
et al. 2021, hereafter K21).

© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
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Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 2 of 22

Fig. 1 a Schematic diagram of the flows around Japan. b Locations of stations along the repeated observation lines in the Tsugaru Strait. c
Observation site of the present study and distribution of the temporal mean velocity at each grid point for 2017–2019. The contours in b denotebathymetry. The rectangle in c indicates the subregions (R1 to R20) used to calculate the zonal average of the zonal velocity

The TgWC has remarkable seasonal flow pattern variation; due to its horizontal and vertical structure, its pathdetaches from the coast at times. Recent studies based onhigh-frequency radar (HFR) observations have indicatedthat the axis of the TgWC in the eastern part of the strait
shifts southward and follows the coast in winter andspring but shifts northward in summer and autumn (Abeet al. 2020; K21; Yasui et al. 2022). This seasonal patternchange is consistent with the development of a large anticyclonic circulation outside the strait in the coastal offshore area of the Pacific, a circumstance referred to as thegyre mode (e.g., Conlon 1982; Rosa et al. 2007; Fig. 1a).
Following the theory proposed by Kubokawa (1991), K21
pointed out the impact of the potential vorticity distribution in the upper layer associated with the jet on the seasonal development of the gyre.
In addition to this seasonal variation, shorter-term
variations can cause the TgWC to meander in the eastern part of the strait. Tanno et al. (2005) reported that thesurface current varies over an ~ 14-day period in addition
to the diurnal tide near Cape Esan (Fig. 1b); this may be
the effect of the Mf tide and/or spring–neap tide for the­K1 and O­ 1 constituents or the “pseudo-Mf tide” due to thenonlinear interaction of dominant diurnal constituents­K1 and ­O1 (Matsuura and Isoda 2020). In addition to sucha tidal forcing, wind changes over several days can also
generate subinertial frequency variations in the TgWC
axis. K21 referred to the possibility that the strengthening of the downfront wind (i.e., westerly wind along theeastward TgWC) dominating in autumn could also generate frontal variations and subsequent instabilities, assuggested by previous studies (mixed layer instabilities;e.g., Boccaletti et al. 2007; Yoshikawa et al. 2012; Thomas
et al. 2013).
The meandering current and propagation of suchmeanders downstream along the current have beenreported in other regions, such as the Kuroshio (Kimura
and Sugimoto 1993; Itoh and Sugimoto 2008), the Kuroshio Extension (Kouketsu et al. 2005, 2007), and the Gulf
Stream (e.g., Brooks and Bane 1981; Lee and Atkinson1983). Such waves frequently increase in amplitude;
eventually, a tonguelike meander detaches from the mainstream of the current, entraining warm–lighter (cold–denser) water in the area south (north) of the front as an
anticyclonic (cyclonic) eddy (e.g., Yanagi et al. 1998). The
origin of the TgWC is thought to be the Kuroshio, which
combines with the flow from the Taiwan Strait in the
East China Sea (Isobe 1999). The TgWC and its origins

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

are closely connected through the bifurcated Tsushima
Warm Current (TsWC; Kawabe 1982a, b; Wagawa et al.
2020; Yabe et al. 2021) (Fig. 1a). In the eastern part ofthe strait, a water mass front in the north–south direction has been detected between the warm/saline waterof the TgWC and the cold/fresh Coastal Oyashio Water(e.g., Kono et al. 2004; Matsuura et al. 2007; Saitoh et al.
2008; Kuroda et al. 2012; K21). Therefore, if similar waves
occur in the strait, such perturbation and subsequent disturbance may influence water exchanges across the front,
while also developing stratification. However, observations with sufficient resolution for such frontal waves inthe strait are rare—although many repeat observations
from ships and moorings are made there—because of therapid flow velocity of the TgWC and frequent ship traffic
through the strait.
Therefore, in the present study, we employ an HFR,
which is an effective instrument for the investigation offrontal disturbances, including eddies (e.g., Schaeffer
et al. 2017), as in K21. In addition, we use model output
from a high-resolution assimilation system (2–3 km) that
assimilates various satellite and in situ observed data
without the above-mentioned HFR data (a downscaled
and assimilated version of the Japan Coastal Ocean
Predictability Experiment, tide enabled; JCOPE-T DA;
Miyazawa et al. 2021). Data obtained from these systems
allow us to determine the impacts of frontal disturbanceson shorter-than-seasonal timescales.
The remainder of this paper is organized as follows. In
the next section, we provide details of the data, including the HFR, numerical model, and shipboard observations. Estimation methods in relation to instabilities arealso described, including the potential vorticity, energy
conversion rate, and propagation speed of the baroclinic
instability, based on the theories provided by previous
studies (e.g., Pedlosky 1987; Vallis 2006). In Sect. 3, we
first demonstrate the seasonal variation in the strait bycomparing the results obtained from the observations
and the numerical model. Then, we investigate the variations in the subinertial frequency and horizontal characteristics of the meanders. Subsequently, the possibilityof instabilities is examined based on JCOPE-T DA outputs. These results are discussed further in Sect. 4 using
observational data, and our conclusions are provided in
Sect. 5.

2 Methods
2.1 Velocity from high‑frequency radar

To monitor the surface current in the eastern part of
the Tsugaru Strait, the Mutsu Institute for Oceanography (MIO), Japan Agency for Marine-Earth Science andTechnology (JAMSTEC), installed a monitoring systemusing an HFR (CODAR, SeaSonde, 13.9 MHz; Fig. 1bPage 3 of 22

and c; K21). The HFR provides data with a horizontal
resolution of ~ 3 km over an area from ~ 3 to 60 km fromeach antenna (Fig. 1c). The surface current distribution
is calculated approximately every 30 min by the system
and uploaded to the MIO Ocean Radar data Site for the
Eastern Tsugaru Strait (MORSETS; http://​www.​godac.​
jamst​ec.​go.​jp/​morse​ts/e/​top/). In the present study, we
employed data from 2017 to 2019 when all three antennas were operating normally (monitoring started in2014).
K21 reported that the accuracy of the zonal velocityof the HFR was 20 × ­10−2 m ­s−1 along the Shiriya–Esanline (SE line) via comparison with the acoustic Doppler
current profiler mounted on some ships (SADCP) velocity obtained from repeated shipboard observations along
the SE line (Fig. 1b). The same type of HFR (CODAR,
SeaSonde, 13.9 MHz) has been used for surface current
monitoring at the Tsushima Strait (Yoshikawa et al. 2006,2010) and at the Soya Strait (Ebuchi et al. 2009; Fig. 1a).
Yoshikawa et al. (2006) mentioned that the root-meansquare velocity difference between the HFR and SADCPs
calculated from principal component analysis was 6.62–
11.3 × ­10−2 m ­s−1 in the Tsushima Strait. Ebuchi et al.
(2009) reported that the current estimated from the HFR
agreed well with those derived from SADCPs with rootmean-square differences less than 25 × ­10−2 m ­s−1 in the
Soya Strait. We excluded grids with data acquisition ratesof < 75% over the duration of the analysis.
2.2 Data assimilation model

To compare the results obtained from the HFR, we also
used outputs calculated by the JCOPE-T DA data assimilation system (Miyazawa et al. 2021). The JCOPE-T DA
system provides hourly output of variables, including sea
level, temperature, salinity, and ocean current velocities,
at a horizontal resolution of 1/36° and 46 active sigma
coordinate levels in the vertical direction (Miyazawa
et al. 2021). We converted the vertical level of the data
(temperature, salinity, and velocities) to z-coordinates at
5-m intervals, focusing on the 41.0° N–42.5° N, 140.5°
E–142.5° E region from June 5, 2018, to December 31,
2019. The model included volume fluxes and sea levelanomalies for 11 tidal constituents (Q1, O1, P1, K1, N2,
M2, S2, K2, M4, MS4, and MN4) at the lateral boundaries. Moreover, the surface pressure gradient included theequilibrium gradient due to 25 potential tidal constituents (Q1, O1, M1, P1, K1, J1, OO1, 2N2, MU2, N2, NU2,
M2, L2, T2, S2, K2, M4, MS4, MN4, MM, MF, SSA, SA,
MTM, and MSQM). The atmospheric forcing data wereobtained from the National Centers for Environmental
Prediction global forecast system. More details about theKaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 4 of 22

analysis, we employed the hourly sea level data distributed by the Japan Meteorological Agency at MIO
for 2017–2019 (41.37° N, 141.23° E; https://​w ww.​data.​
jma.​go.​jp/​kaiyou/​db/​tide/​genbo/​index.​php). For comparison with the results from the JCOPE-T DA, we also
employed local wind data at Cape Shiriya, Esan, andŌma (Fig. 1b) obtained from the Japan Oceanographic
Data Center online archive (https://​jdoss1.​jodc.​go.​jp/​
vpage/​wave.​html) for 2017–2019. We used bathymetry estimated from ETOPO1 (National Oceanic andAtmospheric Administration (NOAA) National Geophysical Data Center. 2009: ETOPO1 1 Arc-Minute
Global Relief Model. NOAA National Centers for Environmental Information. Accessed on 23 June 2021;
Amante and Eakins 2009).

JCOPE-T DA configuration may be found in Miyazawa
et al. (2021).
2.3 Shipboard observations and other data

To validate the subsurface fields in the strait with thoseestimated from the JCOPE-T DA, we employed the seasonal mean estimated repeated shipboard observations
along the SE line. Observations were conducted along
the SE line (Fig. 1b, Table 1) in almost every season from2009 to 2019 by three ships: the training ship (T/S) UshioMaru and T/S Oshoro-Maru belonging to Hokkaido University and the research vessel (R/V) Wakataka-Marubelonging to the Japan Fisheries Research and Education
Agency (Table 2). Observations of temperature, salinity,and pressure were obtained as conductivity–temperature–depth (CTD) observations during the cruises using
an SBE 911 plus (Sea-Bird Scientific, Inc.).
Moreover, to estimate variations in some tidal components, such as Mf, K­ 1, and O­ 1, through harmonic

2.4 Analysis methods

First, for analysis of the HFR data, we defined 20 subregions aligned in the north–south direction (Fig. 1c;
R1–R20) and calculated the spatial means of zonal
velocity at each latitude in the east–west direction ineach subregion. We also calculated the 24-h runningmean of this time series at each latitude in each subregion. Then, the latitude of the maximum mean zonal
velocity along the north–south direction was defined as
the axis of the TgWC (the same detection method wasadapted for the JCOPE-T DA zonal velocity). The temporal mean and standard deviation of the axis latitudein each season were estimated from the HFR. In thisstudy, winter was defined as January–March, spring as
April–June, summer as July–September, and autumn as
October–December.

Table 1 Locations of the stations with repeated shipboard
observations
StationLatitude (°N)

Longitude (°E)

SE1

41.44

141.42SE2

41.48

141.40SE3

41.53

141.37SE4

41.58

141.35SE5

41.64

141.32SE6

41.68

141.30SE7

41.74

141.26SE8

41.79

141.25SE9

41.83

141.22

Table 2 Implementation record of hydrographic observations along the Shiriya–Esan (SE) line. U, O, and W represent the observations
made by T/S Ushio-Maru, T/S Oshoro-Maru, and R/V Wakataka-Maru, respectively
WinterYear

Jan

Spring
Feb

Mar

Apr

Summer
May

Jun

Jul

Autumn
Aug

Sep

2009
2010

U

2011

O

U

2012

U
U

2015

U

2016

U

U

U

U

U

U

U
U

2013
2014

U

U

U

U

U

U

U
U

2017
2019

Nov
U

U

2018

Oct

U
U

U

U
U

W
U

W

U

Dec

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

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The potential density and its anomaly, σθ, were calculated using the temperature, salinity, and pressure
values following Gill (1982). Then, the buoyancy frequency (N) was defined as follows:

N2 = −

g ∂σθ
,
ρ ∂z

(1)

where g and ρ are the gravitational acceleration(9.8 m ­s−2) and potential density, respectively. Then, theseasonal mean geostrophic velocity between adjacent stations was calculated using the isodepth mean obtained
from the shipboard observations for each season, following Pond and Pickard (1986).
We calculated the power spectrum of the axis variation, P(f), after a 24-h running mean at each subregion(R1–R20) for each season (90 days). Then, we calculated
the ratio of P(f) for each subperiod to sum P(f), that is, RP,
and RP(f1,f2) as follows:yr2

f2

RP (f 1,f 2) =

yr2

fe

P f �fyr1

f1

P f �f ,
yr1

ff

(2)

where yr1 and yr2 are 2017 and 2019, respectively. Here,ff and fe are the 1/90 cycle per day (cpd) and 1 cpd,
respectively. We calculated RP(f1,f2) for the three cases:
f1 = 1/15 cpd and f2 = 1/12 cpd; f1 = 1/10 cpd and f2 = 1/5
cps; and f1 = 1/5 cpd and f2 = 1/1 cpd.
To examine the perturbations that vary with timescalesof several days, likely due to wind over the strait, we applieda bandpass fourth-order Butterworth filter to the axis variation with cutoff timescales of 1.3 days and 3 days (see subsection 4.1 for this period selection). Then, we analyzed thelagged correlations of the time series data for some seasons(summer and autumn) using the bandpass-filtered data.
The lagged correlations were calculated for each subregion with respect to the reference subregion (Fig. 1c). The
timescale of the correlation peaks was regarded as the lagof perturbation arrival, and by using the distance between
the reference subregion and each subregion, the propagation speed of the perturbation was estimated in summer
and autumn of each year during 2017–2019.
To investigate whether the necessary conditions of
instabilities (Charney and Stern 1962; Pedlosky 1964)
could actually be satisfied, we calculated potential vorticity based on the JCOPE-T DA outputs as follows. First,
we estimated stream function, ψ, as an integral of temporal mean zonal velocity, U, from the south bank of
the strait to the north direction. Then, we calculated thepotential vorticity, Q, as follows:

Q=−

2
∂U
∂ f41.5◦ N ∂ψ
.
+
2
∂y
∂z N
∂z

(3)

Here, we assumed that β is 0 since the meridional
width of the eastern part of the Tsugaru Strait is narrow (~ 0.4° latitude around the SE line, although thenorth boundary is open east to 141.2° E; Fig. 1b), and weassumed that the zonal velocity component of relative
vorticity dominates the meridional component. Furthermore, f41.5°N is the inertial frequency at 41.5° N. Then, we
compared the distribution of the differential of Q in themeridional direction, Qy, with that of the vertical shearof the zonal velocity, Uz. We tested one case as an example during July 26–27, 2019, when a marked meandering
was shown.
Using the data obtained from the JCOPE-T DA, wealso estimated the energy conversion rates between theeddy and mean fields for each season as follows (e.g.,
Brooks and Niiler 1977; Dewar and Baine 1989; Kang andCurchitser 2015):
MKE to EKE : Ck′ = −u′ u′



∂u
∂v
∂u ∂v
− u′ v′− v′ v′ ,
+
∂x
∂x
∂y
∂y

(4)

 
 
∂ρ  ∂ρ −1∂ρ  ∂ρ −1gg
MPE to EPE : Cp′ = − u′ ρ ′   − v′ ρ ′   .
ρ0
∂x ∂z
ρ0
∂y ∂z

(5)
Here, u and v denote zonal and meridional velocities(24-h-running-mean filtered), respectively, and overbars
and primes indicate the temporal mean and anomalies
from the temporal mean, respectively. MKE, EKE, MPE,
and EPE denote the mean kinetic energy, eddy kinetic
energy, mean potential energy, and eddy potential
energy, respectively. Positive values denote energy transfer from the mean field to the eddy field in Eqs. 4 and5. Each component of Eq. 4 is interpolated to the longitude/latitude of the temperature and salinity grid for the
JCOPE-T DA.
Next, we estimated the theoretical propagation speedof the baroclinic instability for comparison with that of
the meanders detected by the HFR observation assuming
a flat bottom. Following K21, we calculated vertical normal modes (e.g., Gill 1982; Emery and Thomson 2001)
and defined the upper layer depth H1 as the node depthof the first vertical mode. Then, following the derivationof Pedlosky (1987; his Eq. 7.11.9), the phase speed of thebaroclinic instability in the case of zero planetary beta(β = 0) in the two-layer stratified model may be written
as follows:
U1 K 2 + 2/R22 + U2 K 2 + 2/R12c=
2 K 2 + 1/R12 + 1/R22
(6)
1/2

(U1 − U2 ) 4/R12 R22 − K 4i,±
2 K 2 + 1/R12 + 1/R22

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 6 of 22

where K, U1, U2, and i are the total wavenumber, themean velocity of the upper and lower layers, and theimaginary unit, respectively. Here,
2
f41.5
1
◦N
=
,
Rn2
g ′ Hn(7)where Hn is the thickness of the nth layer (we assumed amean water depth of 250 m, and H2 was estimated as 250
minus H1) and g’ is the reduced gravity calculated fromthe eigenvalue of the first vertical normal mode c1st andH1 as c1st2/H1 (K21). Instability occurs when K2 < 2/R1R2(that is, 4/R12R22 > K4). Assuming that the wavenumberof the perturbation observed in the strait is sufficiently
small for such instability, we employed the propagation
speed of the instability (real part of Eq. 6), as mentioned
in Itoh and Sugimoto (2008), as follows:
U1 K 2 + 2/R22 + U2 K 2 + 2/R12


c=
.
(8)
2 K 2 + 1/R12 + 1/R22

This equation indicates that the propagation speed,c, is a value between U1 and U2. If we assume that thehorizontal wavenumber K is far smaller than 1/Rn2,
1/Rn2 would be regarded mathematically as the weighting function. Notably, however, the wavelength at which
it grows the most is several times as long as the internal
deformation radius, as described below. In the present
study, U1 and U2 were estimated in two ways: from the
shipboard observations and from the JCOPE-T DA output. From the shipboard observations, the spatial meanof the geostrophic velocity in the upper and lower layers along the SE line was employed. It should be notedthat we changed the zonal range of the mean for U1 andU2 for each season, considering the seasonal structure of
the TgWC. That is, we extracted the strong eastward current part of the TgWC. For the geostrophic velocity case,
we used the range SE4–SE8 in summer and SE3–SE6 inautumn. From the model output, the meridional average from 41.575°N (41.55°N) to 41.75°N (41.7°N) in eachlayer at 141.3°E was used in summer (autumn).
For wavenumber K, we first assumed that the perturbation has a length scale similar to that of the fastest
growing baroclinic instability in the two-layer model:
λ = 2πLD/1.79 (e.g., Vallis 2006). Here, LD is the internal
deformation radius calculated from the eigenvalue of thefirst mode of the vertical normal mode, which is equivalent to the phase speed of the internal gravity wave (firstbaroclinic mode) and the Coriolis parameter at 41.5°N(LD = c1st/f41.5°N; K21). Then, we defined K = 2π/λ. We also
considered the wavelength of Eady’s case, λ’ = 2πLD/1.61(Eady 1949; Gill 1982), for comparison with the zonal
scale of meanders of the TgWC axis estimated from the
HFR and JCOPE-T DA data. The zonal scale of meandersof the TgWC axis Lp was defined as the adjacent peak distances (i.e., “crests”) of the axis latitude. Comparing thedifference between the first peaks at the surface from
141.0°E and the lower depths, such as 50 m and 150 m(Dp) to Lp, we estimated a vertical shift of the wave crest
using the JCOPE-T DA data.

3 Results
3.1 Seasonal change in the internal structurein the eastern part of the strait

The seasonal mean distributions of the temperature,salinity, and σθ obtained from shipboard observations
show characteristic seasonal changes, as reported bya previous study (e.g., Nishida et al. 2003; K21; Yasui
et al. 2022; Fig. 2a–d). That is, (1) higher (lower) temperature and salinity water is generally observed on
the southern (northern) side, which corresponds to thewater transported by the TgWC (the water modified
by the Oyashio Water and/or Coastal Oyashio Water)[according to Hanawa and Mitsudera 1987, the TgWC
Water, Oyashio Water, and the Coastal Oyashio Water
are defined as T (temperature) > 5 °C and 33.7 < S (salinity) < 34.2, T < 7 °C and 33.0 < S < 33.7, and T < 2 °C andS < 33.0, respectively]; (2) the vertical gradient of thetemperature is larger in summer and smaller in winter (when the stratification is weak in winter, H1 generally becomes larger beneath all stations); and (3) theisotherms are generally parallel to those of σθ and crosswith isodepths of approximately 41.5–41.7° N, especially in summer and autumn. The characteristics of thenorth–south water mass distribution and the seasonalchanges in the stratification are well represented by the
JCOPE-T DA section along 141.3°E (Fig. 2e–h).
As reported in K21, the seasonal change in the zonal
velocity structure, based on a SADCP (not shown here),is also represented well by geostrophic velocity along
the SE line (Fig. 3a–d) except for winter: eastward flow
occurs near the southern boundary during spring anda northward shift of the TgWC axis occurs in summer
and autumn. These features are also reproduced by the
JCOPE-T DA along the 141.3°E section (Fig. 3e–h).
Furthermore, during the summer and autumn seasons,in addition to marked eastward flow (> 1.0 m ­s−1) near
the center of the strait, westward flow (< − 0.2 m ­s−1)
between the axis and the Shimokita Peninsula is also
represented (Fig. 3c d, and g). Eddy kinetic energy(EKE), defined as the squared sum of anomaly velocities
from the seasonal temporal mean, EKE = 1/2 (u’ 2 + v’2),
shows greater values during summer and autumn thanduring winter and spring, especially near the surface(Fig. 3e–h). The vertical difference in the seasonal meanof the zonal velocity between the upper and lower
layers (surface to H1 and H1 to bottom, respectively;

2

41.6

200

Pressure [dbar]

41.4

3.9 .834 3 33

41.5

0 (d)

338.7
24.

33

100

41.4

34

200
41.5

.9

33

.8

33

33.7

32.4
32.5
32.6
32.7
23 33
32.8
32.9
33
33.1
.2 24
.3
.4
.5
3.6
25 333
26

0 24

41.6

.6
33.7

33.6

41.8

33.
3325.4
133
.2
25.8
26
33.4
33.5

26.2

.6

26

41.5

41.6

41.7

33.8
33.9
34
25

41.8

33.7 33.624
33.5
25 33.8
33.9

-100

26

34

-200 (g)0-200 (h)

41.8

41.5

41.6

41.7

41.4

41.8
33.9

33.9 25

-100

26.4

41.7

41.4

41.8

33.8
25.4
25.6
25.8
26
26.2

33.7

Latitude [ oN]

41.7

4

41.4

25.2

.9

34

26.

41.8

41.7

25

25.6
33.8

33.9

-100

33.6

41.6

26

41.6

-200 (f)

100
.7
33

41.5

0 25.841.7

33.933.8

34

33.6

34

33.6

24

Depth [m]

7

33.9
33.8
33.

33
.9

41.5

Depth [m]Pressure [dbar]

25.4
32.6
25.6
32.7
25.8
32.8
32.9
33
26.23333.1
33..32
3
26.4 3.4.833 33.7
6
33..6
26

2

41.4

Depth [m]

4

0 (c)

41.8

Depth [m]6

Pressure [dbar]oT [ C]

200
41.4

41.7

.5

8

26

100

12
10

0 (b)

41.6

4
6.

-200 (e)

33

14

41.5

34

16

41.4

33.5

.9
33

18

26.4
26.6

33.9

-100

.7
33

200

0

33.2
33.3
33.4

33.8

H1

Page 7 of 22

26

0 (a)

100

20

(2022) 9:53

.6
33

Pressure [dbar]

Kaneko et al. Progress in Earth and Planetary Science25.2
34 25.4
25.6
25.8
26
2
26. 6.4
2

41.5

41.6

34

34

Latitude [ oN]

26.6

41.7

41.8

Fig. 2 Vertical transect of seasonal means of temperature (color), salinity (gray contours), and potential density anomaly, σθ (black contours),
obtained from the shipboard observations along the Shiriya–Esan line (estimated from the JCOPE-T DA data) in a (e) winter, b (f) spring, c (g)summer, and d (h) autumn, shown in the left (right) column. Triangles shown in the left column are the latitude of each station. The dashedmagenta line is the depth of the upper layer, H1

meridional range of mean: 41.5–41.7°N) becomes largest in summer and autumn (~ 0.3 m ­s−1) and smallest
in winter (< 0.1 m ­s−1) according to the JCOPE-T DA
output (Additional file 1: Fig. S1).
3.2 Seasonal and shorter timescale variationin the Tsugaru Warm Current axis

The HFR data indicate seasonal shifts of the axis of the
TgWC as reported by previous studies (e.g., Rosa et al.
2007; Abe et al. 2020; K21; Yasui et al. 2022): for 141.1°
E–141.5° E, the shift occurs south of 41.6° N in winterand spring (Fig. 4a and b) and north of 41.6° N in summer and autumn (Fig. 4c and d). Then, the contrast in
the relative vorticity across the axis becomes remarkable in summer at 141.2–141.4° E (Fig. 4c). The seasonalchange in the axis location and increase in the contrastof the relative vorticity are also represented by the

JCOPE-T DA outputs (Fig. 5). The longitude–time distributions estimated from both HFR and the JCOPE-T
DA along the nearest transection of 141.3° E also show
very similar seasonal changes in the axis latitude, as
mentioned above (Fig. 6). Thus, the temporal variationin the axis latitude estimated from the JCOPE-T DA
data seems to properly represent its seasonal variation.
Apart from the seasonal movement of the axis mentioned above, shorter-term oscillation within several
dozen days is also observed (Fig. 6). We applied a wavelet transform to the latitude of the TgWC axis at 141.3°
E longitude (Fig. 7). The wavelet transforms estimatedfrom both the HFR data and the JCOPE-T DA data indicate maxima around a frequency of 0.07 cpd (a periodof 14 days) and at 1 cpd (period of 1 day). In addition
to this 0.07 cpd variation for the whole season, seasonalenhancement of the amplitude is also evident in theKaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 8 of 22

Fig. 3 Vertical transect of seasonal mean geostrophic velocity (zonal velocity) along the Shiriya–Esan line calculated from shipboard observations(141.3°E obtained from JCOPE-T DA data) in a (e) winter, b (f) spring, c (g) summer, and d (h) autumn. Black contours denote the potential density
anomaly, σθ. Eastward is positive. The dashed magenta line denotes the depth of the upper layer, H1. Black bars in c, d, g, and h indicate the mean
range of latitude for the upper- and lower-layer velocities, U1 and U2, respectively. The bathymetry is along 141.3°E. Gray contours in e–h denoteeddy kinetic energy ­[m2 ­s−2]

wavelet transforms between frequencies of 0.07 cpd and1 cpd (period between 14 days and 1 day) (Fig. 7). The
seasonal enhancement from summer to autumn is clearly
represented in the wavelet transform of the JCOPE-T DA(Fig. 7b). Although the wavelet transform obtained fromthe HFR suggests some maxima for 0.2–1 cpd (1 day to
5 days) during winter to early spring (from January to
April), it is not clearly evident in the wavelet transform
obtained from the JCOPE-T DA.
The variation in the TgWC axis with a 14-day timescale
is consistent with that of the current near Cape Esan
(Tanno et al. 2005). Thus, we also examined the coherence of the axis variation obtained from the HFR in each
subregion (Fig. 1c) for 2017–2019 in relation to that at
the reference subgrid, R1 (Fig. 8a). Remarkable coherence (> 0.4) is shown at 14 days from 141.0 to 141.6° E,

although the phase difference |φ/π| increased from
141.0° E (|φ/π|~ 0) to 141.6° E (|φ/π|~ 1). For comparison, we also calculated the coherence of the axis variation
at each subgrid to that at R8 (nearest 141.3° E) (Fig. 8b).
Then, in addition to 14 days, marked coherence is shownat 8 days and approximately 5 days, suggesting subinertial
frequency variation generated at approximately 141.3° E.
It is expected that tides affect the axis latitude variation
by 14 days (Tanno et al. 2005; Matsuura and Isoda 2020).
Thus, we compared the time series of the axis variation at
141.3° E (12- and 15-day bands passed one) to the timingof spring and neap tides, as well as the time series of the
Mf tide component estimated from the harmonic analysisof sea level data at MIO (Additional file 1: Fig. S2; anothercase of the ­K1 and O­ 1 tide components is also shown in
Additional file 1: Fig. S3). The results show that the phaseKaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 9 of 22

/f

(a)

0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

(b)

42°N

42°N

41.80

41.80

41.60

41.60

41.40

1m s

141°E

41.40

-1

141.20141.40141.60141.80

141°E

(c)

-1

141.20141.40141.60141.80141.40141.60141.80

(d)

42°N

42°N

41.80

41.80

41.60

41.60

41.40

1m s

1m s

141°E

41.40

-1

141.20141.40141.60141.80

1m s

141°E

-1

141.20Fig. 4 Seasonal mean of the surface velocity obtained from the high-frequency radar data in a winter, b spring, c summer, and d autumn. The color
denotes the relative vorticity estimated from the radar data as ∂v/∂x − ∂u/∂y, where u and v are the zonal and meridional velocities, respectively. The
yellow dashed (solid) line shows the temporal mean (standard deviation) of the Tsugaru Warm Current axis. The bathymetry is along 141.3°Eof the axis variation is inversely synchronized with thephase with Mf variation (with variation in the envelopeof the K­ 1 and O­ 1 variation). Wavelet analysis of the variation in the TgWC axis at each subgrid in relation to theMf variation shows robust coherence for 141.0–141.6° Efrom April to September of each year (Additional file 1:
Fig. S4a). This seasonal variation in coherence is consistent with the result of Tanno et al. (2005) [based on thisseasonality, the amplitude difference of the axis amplitude in January among 2017, 2018, and 2019 (Additional
file 1: Figs. S2 and S3) may also be explained by the winter density distribution because a weakly stratified condition in relation to the general winter was observed in2018 (not shown)]. The phase difference of the wavelet cross spectrum shows that the phase difference issmaller at 141.4–141.6° E than at 141.0–141.2° E (Additional file 1: Fig. S4a; note that the longitude of MIO is
141.24°E). RP(f1, f2) for 12–15 days tends to decrease withincreasing longitude, especially in summer and autumn

at 141.8° E (Additional file 1: Fig. S4b–e; 10–25% at 141.2°
E to < 10% at 141.8° E). In contrast, the longitudinal trendof RP(f1, f2) for 5–10 days is more ambiguous than thatfor 12–15 days (Additional file 1: Fig. S4b). RP(f1, f2) for
1–5 days is also similar to that for 12–15 days at approximately 141.3° E in summer and autumn (10–20%), suggesting the importance of the subinertial frequency with
1–10-day variation in the axis fluctuation in the region
distanced from the topography (i.e., the outlet of thechannel at 141.1° E, Fig. 1c).
3.3 Features of axis meandering in the eastern partof the strait

Since the subinertial frequency variation in the TgWC
axis and phase change along the downstream direction
have been shown in the eastern part of the Tsugaru Strait(Fig. 8), we focused on the zonal scale of such variations
considering propagation disturbances. By extracting thefirst and second peaks of the meanders from 141.0° E to

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 10 of 22

/f

(a)

1.6
1.2
0.8
0.4
0
-0.4
-0.8
-1.2
-1.6
-2

(b)

42°N

42°N

41.80

41.80

41.60

41.60

41.40

1m s

41.40

-1

141°E

141.20141.40141.60141.80141.20141.40141.60141.80141.20141.40141.60141.80

(d)

42°N

42°N

41.80

41.80

41.60

41.60

1m s

-1

141°E

(c)

41.40

1m s

41.40

-1

141°E

141.20141.40141.60141.80

1m s

-1

141°E

Fig. 5 Seasonal mean of the surface velocity obtained from the JCOPE-T DA data in a winter, b spring, c summer, and d autumn. The color andyellow lines are the same as those in Fig. 4

downstream, we examined the frequency distribution of
the ratio of the zonal scale of adjacent peaks (Lp) to theinternal deformation radius (LD) in each season (Fig. 9).
In the frequency distribution of Lp/LD (subpanels in
Fig. 9), the peak of Lp/LD seems to be larger than 2π/1.79(two-layer case) in winter (Fig. 9a) and spring (Fig. 9b).
However, the peak of Lp/LD is located at approximately
2π /1.79 in summer and autumn (Fig. 9c and d, respectively). This result suggests that the zonal scale of themeanders of the TgWC axis is consistent with the scale ofthe maximum growth wavelength of the baroclinic instability, especially in summer and autumn.
Furthermore, using JCOPE-T DA outputs, we estimated the zonal length scale of meanders in the deeper
layer (50 m and 150 m) and compared the zonal difference of the peak in the deeper layer to that at the surface,
DP (Fig. 10). Here, from a statistical point of view, weused the average of Lp as the wavelength of meanders; Lp(1,1) is the difference in zonal distance around peaks of
the axis between the first and second peaks at the surface,

Lp (1,2) is that between the second and third peaks at thesurface, Lp (2,1) is the difference in zonal distance aroundpeaks of the axis between the first and second peaks atdeeper depths, and Lp (2,2) is that between the second
and third peaks at deeper depths (Fig. 10a). The result
indicates that, at both 50 m and 100 m, many meanders
have zonal scales several times longer than the deformation radius (Fig. 10b and c, respectively). Furthermore, DP
is larger at 150 m than at 50 m, suggesting that the peakof the meander tends to precede with increasing depth(Fig. 10d and e). It is also indicated that the phase of thepeak at 150 m is 1/4 wavelength ahead of that at the surface (Fig. 10e).
3.4 Instabilities suggested from the JCOPE‑T DA outputs

The results mentioned above (Figs. 9 and 10) suggest
the possibility of baroclinic instability in the easternpart of the Tsugaru Strait. Thus, to test whether necessary conditions of the instabilities, including baroclinic
instability, can actually be satisfied there, we focusedKaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 11 of 22(b)

01 Oct. 2019

01 Oct. 2019

01 Jul. 2019

01 Jul. 2019

01 Apr. 2019

01 Apr. 2019

01 Jan. 2019

01 Jan. 2019

01 Oct. 2018

01 Oct. 2018

01 Jul. 2018

01 Jul. 2018

01 Apr. 2018

01 Apr. 2018

01 Jan. 2018

01 Jan. 2018

41.66

01 Oct. 2017

01 Oct. 201741.62

01 Jul. 2017

01 Jul. 201701 Apr. 201701 Apr. 2017

41.7

41.58

Latitude [o N]

(a)

41.54
41.5

01 Jan. 2017
141

141.1

141.2

141.3

141.4

141.5

141.6

Longitude [ oE]

01 Jan. 2017
141

141.1

141.2

141.3

141.4

141.5

141.6

Longitude [ oE]

Fig. 6 Longitude–time plot of the axis latitude of the Tsugaru Warm Current estimated from a the high-frequency radar data and b the JCOPE-T DA
data at 141.3°E

on a case during July 26–27, 2019, using JCOPE-T DA
output (including the period shown in Fig. 10a) as an
example. In this duration, the TgWC at the surface
flows at ~ 41.6° N (Fig. 11a). In contrast, the velocity
maximum at 150 m shows meandering, that is, a convex
structure is observed to the south at 141.20–141.4°E(Fig. 11a). Thus, the positive field of the relative vorticity (− Uy; the first term on the right-hand side of Eq. 3)
at 150 m is located beneath the eastward jet at thesurface. Relative vorticity along the axis of the TgWC
shows a slanted core of a positive (negative) region
from ~ 141.15°E (~ 141.45° E) to ~ 141.4° E (~ 141.5° E)
from the surface to the bottom, suggesting a slanted
trough (crest) of the meander (Fig. 11b). In the regionof 141.35–141.45° E, divergence of the horizontal velocity, defined by the temporal mean of ∂u/∂x + ∂v/∂y,indicates a negative value (i.e., convergence) near thebottom and a positive value (i.e., divergence) near thesurface, suggesting upward velocity at this longitude(Fig. 11b). These results are consistent with the structure of the baroclinic instability.
The north–south derivation of the potential vorticity, Qy (zonal mean between 141.3–141.4° E), changes
its sign in the north–south direction at 41.55–41.6°
N above 100 m and at 41.65–41.7° N from the bottom to the surface, where vertical shear, Uz, is small(< 0.005 ­s−1) (Fig. 11c). This situation can satisfy thenecessary condition of instability [e.g., condition(a) in Sect. 8.4.2 of Holton (2004); condition (i) in
Sect. 6.4.3 of Vallis (2006)]. Moreover, in the regionof 41.6–41.65°N, the sign of Qy is positive under positive vertical shear (Fig. 11c). Due to the variation in thebathymetry in the zonal direction, although it is difficult to determine the lower boundary (e.g., Fig. 11b),

Kaneko et al. Progress in Earth and Planetary Science

Frequency [cycle per day]

0

0.006

10-1

0.004

0.002

10-2
17

17

n

01

0
r. 2

Ap

01

17

17

0
l. 2

Ju

01

0
t. 2

Oc

01

n

Ja

18

18

0
.2

01

0
r. 2

Ap

01

18

18

0
l. 2

Ju

01

0
t. 2

Oc

01

n

Ja

19

19

0
.2

01

0
r. 2

Ap

01

19

19

0
l. 2

Ju

01

Oc

0.01

0.008

10

0

0.006

0.004

10-1

0.002

10-2

01

n.

Ja

0

0
t. 2

(b)

101

Frequency [cycle per day]

0.01

0.008

10

0
.2

Ja

Page 12 of 22

(a)

101

01

(2022) 9:53

7

1
20

01

r.

Ap

7

1
20

01

l.

Ju

7

1
20

01

t.

Oc

7

1
20

01

n.

Ja

8

1
20

01

r.

Ap

8

1
20

01

l.

Ju

8

1
20

01

t.

Oc

8

1
20

01

n.

Ja

1
20

9

01

r.

Ap

9

1
20

01

l.

Ju

9

1
20

01

t.

Oc

9

0

1
20

Fig. 7 Wavelet transform of the axis of the Tsugaru Warm Current at 141.3°E calculated from a the high-frequency radar data and b the JCOPE-T DA
data. The yellow line indicates the inertial frequency at 41.5°N, 1.26 cycles per day (periods of 0.75 days). The blue and black lines denote 1 and 0.07
cycles per day (periods of 1 and 14 days), respectively

the necessary condition of the baroclinic instability[e.g., condition (b) in Sect. 8.4.2 of Holton (2004); condition (iii) in Sect. 6.4.3 of Vallis (2006)] could be satisfied in the eastern part of the Tsugaru Strait.
As it is shown that the necessary conditions of theinstabilities can be satisfied in the example case, we also
computed energy conversion rates for both potential
and kinetic energy for each season (3 months) from the
JCOPE-T DA data for 2019 (Figs. 12 and Additional file 1:
Fig. S5). These results suggest that substantial mean field
to eddy energy conversion of potential energy (i.e., baroclinic instability) occurs near the front in the strait (41.6°
N, 141.0–141.3° E) at depths shallower than 100 m and in
the region shallower than 150 m east of Cape Shiriya during summer and autumn (Fig. 12). Marked energy conversion of kinetic energy from the mean field to the eddy
is also suggested at approximately 141.0° E and 141.5° E(above the spur of Shiriya) for all seasons (Fig. 12) andsouth of the front near the surface (41.5–41.6° N, < 100 m;
Additional file 1: Fig. S5). It should be noted, however,that the c’p term is superior to the c’k term near the surface (< 100 m) at approximately 141.3°E in summer(Fig. 12) and autumn at 41.6° N (Additional file 1: Fig. S5).
Furthermore, although the density field over the topography of Shiriya (~ 141.5° E) in these seasons also indicatesthe possibility of a hydraulic jump, it is worth noting thatc’p is also large in areas more distant from the topography(~ 141.3° E, and ~ 142° E; Fig. 12). It is also worth notingthat eddy to mean energy conversion of kinetic energy issuggested north of 41.6° N during summer and autumn(Additional file 1: Fig. S5). Thus, these energy conversionsof kinetic energy (such as interactions between eddies
frequently excited by the intense tide and mean flow;e.g., Wada et al. 2012, see also Sect. 4.3) would also affectthe variation in the TgWC axis in addition to baroclinic
instability.

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 13 of 22

(a)

(b)
0.6

0.8

0.6

1

0.4

0.4

0.8

20

1

20

0.

4

0.6

0.8

1

0.6

0.8

0.4

0.4

0.4

1

0.5

10

0.6

10

0.4

0.6

0.4

0.4

1
0.6

0.4

0.4

0.4

0.4

1

0.6
0.8

0.4

-0.5

1

0.4
0.4

0.4

-1
0.4

8

0.4

0.

5

0

0.6

Phase difference ( / )

14

0.4

1

Period [day]

0.4

0.6

14

0.

4

1

0.4

0.4

5

0.6

0.6

0.6
0.4

0.4
0.4

0.60.40.4
0.4

0.6 0.4

0.8

0.

0.8

141

0.4

0.4

0.6

3

0.6

0.4

4

0.4

0.4

141.2

141.4

0.6

141.6

141.8

o

Longitude [ E]

3

0.4
0.4

141.3 141.4 141.5 141.6 141.7 141.8

Longitude [ oE]

Fig. 8 Phase difference (color) and coherence (contours) of variation for the axis latitude estimated from the high-frequency radar data at eachsubgrid in relation to that at a 141°E and b 141.3°E for 2017–2019

4 Discussion
4.1 Propagation speed estimation of the meanders
observed from the HFRBased on the JCOPE-T DA outputs, the possibility ofbaroclinic instability is suggested in the region distanced
from the characteristic topography, as mentioned above(Figs. 10, 11, 12). Thus, we examined the propagation
speed of the meanders observed by the HFR following
baroclinic instability theory. As the dominant scale of themeanders in the zonal direction is ~ 35 km in summer(Fig. 9), if we consider the 14-day period variation to havethis zonal scale, the propagation speed is estimated tobe ~ 0.03 m ­s−1. This value is much smaller than the mean
velocity, even at lower depths (U2 ~ 0.11 m ­s−1 m for geostrophic velocity and U2 ~ 0.15 m ­s−1 for the JCOPE-T DA
output, Additional file 1: Fig. S1). Therefore, we focused

the timescale from 1.3 to 3 days, assuming that the timescale of dominant meanders (Fig. 9) would be distinct
from diurnal tides. We also focused on two seasons, summer and autumn, since the zonal scale of the meanders
detected by the HFR agreed well with the wavelength ofthe maximum growth rate for these seasons (Fig. 9).
To examine the relationship between the variations
in each subregion, we calculated the lagged correlationof the time series of the axis latitude obtained from the
HFR between the reference subregion and the other subregions, as mentioned in Sect. 2.4. Here, we employedsubregion R3 as the reference region where the perturbation was expected to be generated after testing othercases from R1 to R3. Examples of bandpassed time series
and lagged correlation are shown in Additional file 1: Fig.
S6a and S6b, respectively. We plotted the lag time of thecorrelation peaks (shown by triangles in Additional file 1:

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 14 of 22

(a)

(b)

41.80

41.80

20 Jan 2018

41.60

Frequency [%]15 Jan 2018

41.40

41.20

141°E

40

2 /1.61
2 /1.79

20
0
0

5

10

Lp/LD

141.5025 May 201820 May 201815 May 2018

41.60

Frequency [%]L D =3km

10 May 2018

L D =4km

30 Jan 201825 Jan 2018

41.40

15

41.20

142°E

141°E

(c)

40
20
0
0

5

10

Lp/LD

141.50

15

142°E

(d)
15 Jul 201825 Jul 201820 Jul 2018
30 Jul 2018

L D =10km

41.80

D

20 Oct 201815 Oct 2018

41.20

41.60

Frequency [%]

41.60

41.40

25 Oct 2018
10 Oct 2018

L =7km

40
41.40

20
0
0

5

10

Lp/LD

15

41.20

Frequency [%]

41.80

40
20
0
0

5

10

Lp/LD

15

141.50141.50
141°E
142°E
141°E
142°E
Fig. 9 Examples of shorter-term variation in the axis of the Tsugaru Warm Current estimated from the high-frequency radar during a winter, b
spring, c summer, and d autumn. The thick–light (thin–dark) lines denote earlier (later) dates. The frequency distribution of the ratio of the zonal
scale of adjacent meandering peaks (Lp) to the internal deformation radius (LD) for each season is shown in the subpanels

Fig. S6b) for the positive range (i.e., lag > 0 in Additional
file 1: Fig. S6b) against the distance from the reference
subregion for each season and each year (Fig. 13). We
regarded the slope of the symbol plots in Fig. 13 as the
propagation speed of the axis meander observed by the
HFR.
To calculate the theoretical propagation speed as mentioned in Sect. 2.4, we also estimated the timescale ofadvection owing to the upper- and lower-layer velocities (U1 and U2, respectively) in two ways: the mean
geostrophic velocity (gray broken lines in Fig. 13) andthe JCOPE-T DA data (Additional file 1: Fig. S1) (bluebroken lines in Fig. 13). It should be noted that because
the westward velocity south of the axis, especially in theupper layer (Figs. 3, 4, and 5), is excluded, U1 is greaterthan another mean velocity for 41.5–41.7°N in Additional
file 1: Fig. S1. We used the following baroclinic instability wavelengths for each season: 34 km (summer) and
26 km (autumn). These wavelengths satisfy the instability

condition of the two-layer model (e.g., Eq. 7.11.10 of Pedlosky 1987).
Then, the propagation speed of the baroclinic instability ~ 0.33 to ~ 0.35 m ­s−1 is consistent with that of
the slope of the plots estimated from observations insummer (Fig. 13a). In autumn, the propagation speed
appears to be similar to that of the two-layer model,
especially for 2018 and 2019 in the region west of Cape
Shiriya (Fig. 13b). Therefore, the propagation speed of theobserved perturbation appears to agree with that of thebaroclinic instability in the case of the two-layer model insummer and autumn. It should be noted that during thesummer of 2017, there are no observations (Table 2) or
outputs of JCOPE-T DA; thus, the difference in the propagation speed may be caused by the lack of velocity data.
Because a larger internal deformation radius than thatin the present study has been reported for the area eastof Cape Shiriya (i.e., the Pacific Ocean that is out of the
HFR range) (Conlon 1982), the dominant zonal scale of(2022) 9:53

Page 15 of 22

20
Dp

2 /1.79L D =34km

41.40
141.20

20

40

0
0.

150m

141°E

5

5

L p (2,2)0m

141.40141.60141.80Frequency [%]

41.60

10

10

0
0

L p (1,1)

s

(c)

150m

15

15

(e)

1
25
1.
5

L D =10km

'

s

50m

150m

10

10
5

5
0
0

20

40

Wave length ( Lp ) [km]

0
0
25
0.
5
0.
75

41.80

w

(d)

1.

p

'

15

1
25
1.
5

L (1,2)w

50m

D p/ Lp

1.

26 Jul. 2019 03:00

15

(b)

0.

42°N

(a)

Frequency [%]

20

0
25
0.
5
0.
75

Kaneko et al. Progress in Earth and Planetary ScienceFig. 10 a An example of the axis latitude distribution obtained from the JCOPE-T DA data. The black (gray) color is that at the surface (150 m). b
and c: Frequency distribution of the representative zonal scale of adjacent peaks of the axis latitude obtained from the JCOPE-T DA (Lp) at 50 m and
150 m, respectively. d and e: Frequency distribution of the ratio of the difference in the first axis latitude peaks (from west) between the surface andlower depths (Dp, 50 m and 150 m, respectively) to Lp. The black (gray) vertical lines in b and c denote wavelengths with maximum growth rates inthe two-layer model (Eady’s model). Subscripts w and s indicate winter and summer, respectively

the meander may also become larger in this region. Conlon (1982) showed the internal deformation radius to be
18.4–23.2 km from July to September and 14.2–22.7 km
from October to December based on the observational
data obtained at 40.54° N, from ~ 142° E to ~ 144° E.
Therefore, estimation of the length scale of the instability
should still be addressed, especially east of Cape Shiriya.
Outside of the strait, other subinertial frequency variations in the TgWC (from 10 days to one month) were also
reported by Yasuda et al. (1988). The relationship of fluctuations with periods longer than 10 days was captured
in this study (Fig. 7), and the previously reported variations will also be the subject of future work.
4.2 Seasonal variation in the wind effects
on the several‑day variation in the axis

In the present study, we found perturbations of the axis
with timescales between 1 and 14 days, especially from
July to September (Fig. 7). In these months, the local
wind in the eastern part of the strait switches from easterly to westerly (K21). K21 also referred to the possibility
that strengthening of the downfront (i.e., westerly) windfrom the end of summer to early autumn could generate
frontal variations and subsequent instabilities, including

baroclinic instability, as suggested by previous studies(e.g., Boccaletti et al. 2007; Yoshikawa et al. 2012; Thomas
et al. 2013). Thus, we examined the seasonal wind influence on the variation in the TgWC axis using wind dataat three capes, Shiriya, Esan, and Ōma (Fig. 14a).
First, we compared the variation in the latitude of the
TgWC axis at each subgrid with the hourly averaged
zonal wind (eastward positive) at each point for 2017–2019. Marked coherence is shown from 1.3 to 3 days (1.5,
2.0, 2.5, and 3.0 days, for example) in the region of 141.0–
141.6° E for each case (Fig. 14b–d). Then, to examine thetemporal variation, we also calculated wavelet coherence
between the variation in the axis at each subgrid (Fig. 1c)and the mean wind for each point (i.e., Shiriya, Esan, andŌma). Here, the longitudinal (statistical) average of the
wavelet coherence (141.3–141.6° E) calculated from theaxis variation at each subgrid is shown in Fig. 15a. Subsequently, we statistically averaged the coherence from 1.3
to 3 days to estimate the seasonal variation in the coherence (Fig. 15b). Relatively high coherence (> 0.3, 30-day
running mean) is shown from September to October,especially for 2018 (Fig. 15b). Then, each year average ­(〈CW〉yr) was estimated using the 30-day running mean
coherence from 2017 and 2019 (Fig. 15c).

-2e

-150

1.

0.6

75

1
11..525

41.50

0
.1
.2
0. 000
.3
0.45

1.5
1.251

0m -250

141

0.4
0.2
U150m

0

141.1

-50

141.400

0.0 0.01
0 05-0.0050-U y /f

1

0

0.2

-1

0.4

-100
-150
-200
-250
41.4

41.45

141.3

41.5

0.4
05
0.0 .2041.55 41.6

-1

141.4

1.4
1.2 18.
10 0.6
0.0

141.5

-1.5

2

41.65

41.7

Latitude [ oN]

-0.5

-05

-2e

0

Longitude [ oE]-0.005
-0.
2

0

0
0

141.2

(c)
0

141.20

141°E

-200
U

0.
3

0.4 0.5-05

Depth [m]

41.70

0.5

4e-05

-U y/ f

05

1

0

0.

5

0

0

0
41.75

0
41.8

Qy

0 -6e-

-100

8e-05

4e-05

0

-2e-05-4e-050.
4

05 -8e-05-6e-Depth [m]

41.80

-50

(b)

0

0

Page 16 of 22

05

0

(a)

41.60

(2022) 9:53

0.0

Kaneko et al. Progress in Earth and Planetary Science

-5
-10
10 -8

Fig. 11 a An example of the velocity at the upper layer (0 m: black contours, m s­ ) and lower layer (150 m: gray contours, m ­s−1) estimated fromthe JCOPE-T DA data for July 26–27, 2019. The standardized relative vorticity term in Eq. 3 at 150 m is shown by color. The yellow line shows theaxis of the Tsugaru Warm Current. b Vertical section of standardized relative vorticity along the axis (color) and divergence of the horizontal velocity(contour: ­s−1). c Qy (differential of Q in the north–south direction) distribution in the cross front direction (141.3–141.4°E average) (color) withvertical shear (black contours: ­s−1). Gray contours in c denote zonal velocity. Dashed contours in b and c denote negative values. Topography in c isthe zonal mean for 141.3–141.4°E−1A relatively large value of 〈CW〉yr > 0.3 is shown from
September to October, when the zonal wind changes its
sign from negative (i.e., easterly) to positive (westerly)(Fig. 15c). Thus, around September, the variation in zonal
wind over the strait with a timescale of several days along
the TgWC current is expected to be closely related to thatof the TgWC axis. The coherence from December to thefollowing February tends to be smaller than that in September despite the marked westerly wind (Fig. 15c) andits variance (Fig. 15d). Thus, the remarkable coherence in
September is characteristic. This characteristic is consistent with the theory of the downfront wind. The processes
due to the downfront wind can proceed with stratification in the eastern part of the Tsugaru Strait, as mentioned by previous studies (e.g., Boccaletti et al. 2007;
Yoshikawa et al. 2012; Thomas et al. 2013), which may
result in a situation similar to the two-layer model in thestrait. More precise quantitative evaluation of both horizontal and vertical transport (such as Tanaka et al. 2021)
of heat and materials should be addressed in the future in
addition to evaluation of the wind effects. The elucidationof the material circulation process in the strait is important for commercial activities, such as fisheries, including the nearby aquaculture industry, as well as scientificunderstanding, such as rapid acidification in the strait(Wakita et al. 2021).
4.3 Other issues to address

The impact of the characteristic topography in the straiton the instability is another issue to be considered.
Although the topography in the Tsugaru Strait is complex, the northern part of the strait is open east to 141.2°
E and the topography generally deepens toward the northat 141.2–141.5° E (Fig. 1c), which does not seem to matchthe stable configuration as it relates to the slope condition of the baroclinic instability (Fig. 1d of Blumsack &Gierasch 1972). However, the TgWC sometimes rises
across the ridge in summer and autumn (Fig. 9c and d).
Baroclinic flow that overrides topography can cause horizontal eddies downstream of the topography throughstretching of the water column, subsequently affecting
the pathway of the coastal current (e.g., Nakada et al.
2003; Igeta et al. 2017, 2021). Thus, this effect should
also be re-examined from the perspective of the seasonal
path change in the TgWC during the stratified season(e.g., gyre mode) in addition to the effect examined inK21. The path change may also be important from theperspective of balance of the frictional torque due to theKaneko et al. Progress in Earth and Planetary Science(2022) 9:53

Page 17 of 22

C' /C' component at 41.6 o N (positive: energy transfer from the mean to the eddy )

-200

141.5

142

6

.5

-100 26

141.5

142

-300
141

0

0

-100

-100

141.5

142

-200

-300
141

141.5

142

0
.5

-100 26

141.5

142

0

-100

-100

6

141.5

142

-200

-300
141

141.5

142
o

141.5

142

-300
141

141.5

142

6

-300
141

141.5

142

-300
141

o

Longitude [ E]

141.5

10 -6

2.4
1.8
1.2
0.6
0
-0.6
-1.2
-1.8
-2.4
-3

26

-200

o

Longitude [ E]26-100 2

-200

-300
141

4
3
2
1
0
-1
-2
-3
-4
-5

0

26

-200

142

-200

-300
141

0

141.5

-100 2

-200

-300
141

10 -6

-300
141
0

26

-200

26

-200

p

-100 2

-200

-300
141

4
3
2
1
0
-1
-2
-3
-4
-5

C'

-100
26

-200

Autumn0[m2 s -3 ]

-100

0

Depth [m]Summer0k

Depth [m].5-100 26-300
141

Depth [m]Spring0C'

Winter0[m2 s -3 ]klog 10 ( C ' p / C ' k )

p

142
o

Longitude [ E]Longitude [ E]Fig. 12 Vertical distribution of the energy conversion rate calculated from the JCOPE-T DA data during 2019 (upper row: potential energy; middle
row: kinetic energy) and their ratio (that of potential energy to that of kinetic energy, lower row) in each season at 41.6°N. Black contours denote thepotential density anomaly, σθ. The green line denotes 141.3°E (see Additional file 1: Fig. S5)

5

(a)
2017
2018
2019

4

Lag [Days]

CTD estimation

0.11 m s -1

5

JCOPE-T DA

4
0.33 m s -1

3

(b)

3

U 2 : 0.31 m s -1

0.35 m s -1

2

0.4 m s -1

2

141.3°E
0.62 m s -1100Cape Shiriya
20

40

60

Distance from the reference sub-grid [km]0.72 m s -1

1
U1
80

0
0

20

40

60

Distance from the reference sub-grid [km]Fig. 13 Distance–lag plot calculated from the high-frequency radar data in a summer and b autumn

80

1.11 m s -1

Kaneko et al. Progress in Earth and Planetary Science

Page 18 of 22

(a)

500
Esan

41.80

0

Oma

41.60

Shiriya

Altitude [m]42°N(2022) 9:53

41.40

Period [day]

5
4.5

(b)

5
4.5

-500

(c)

5
4.5

(d)

4

4

4

3.5

3.5

3.5

3

3

3

0.6

2.5

2.5

2.5

0.5

2

2

2

0.4
0.3

1.5

1.5

0.2

1.5

Coherence

140.60 140.80 141°E 141.20 141.40 141.60

0.1
0

1
141

141.2

141.4

Longitude [ oE]

141.6

1
141

141.2

141.4

Longitude [ oE]

141.6

1
141

141.2

141.4

Longitude [ oE]

141.6

Fig. 14 a Location of wind observation points. b, c, and d: Coherence of the axis latitude variation in each subregion with zonal wind at Shiriya,
Esan, and Ōma, respectively, for 2017–2019

coastal boundary current system around Japan, such as
the Kuroshio, TsWCs, and TgWC (Sasaki et al. 2014; Kida
et al. 2016, 2020).
Moreover, Yasui et al. (2022) recently suggested that
the TgWC tends to flow with an increase in inertia over
the topography at Cape Shiriya, even in winter. Althoughwintertime stratification is weak in the strait and barotropic disturbance dominates (e.g., Figs. 2a e, 3a, e, and12), confluence of the TgWC Water and Coastal Oyashio
Water may form a baroclinic structure and disturbances.
Thus, the relationship between the topography, baroclinicity, and path of the TgWC is also an issue to addressin winter and early spring, together with the effect ofbarotropic shelf-trapped waves (e.g., Ohshima 1994).
Furthermore, as shown in Fig. 12, the kinetic energy conversion from eddy to mean in the eastern part of the strait(141.2–141.4° E) could also be important for the variation in the TgWC axis in addition to that from the mean
to eddy at ~ 141.2° E. Because remarkable eddies are

generated at approximately 141.0°E due to intense tides(e.g., Asano et al. 2020; Ishizaki et al. 2022), the effectsof the advection of such eddies downstream (Wada et al.
2012) on the meandering of the TgWC should also be
investigated.

5 Conclusions
In the present study, using data obtained from the HFR
system and that from the JCOPE-T DA data assimilated
model (Miyazawa et al. 2021) with high resolution (1/36°,
hourly), we focused on the frontal variation along theaxis of the TgWC that varies on a shorter-than-seasonal
timescale in the eastern part of the Tsugaru Strait. Variations between 1 and 14 days, especially during summer
and autumn, are seen in the HFR data and are also represented by the JCOPE-T DA.
The seasonal variation in the ~ 14-day coherence isconsistent with a previous study focusing on tides atapproximately 141.0°E (Tanno et al. 2005), and thePage 19 of 22

18

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

100
17
n.
Ja

17

ul.

J
01

17

ct.

O
01

17

8

.1

an

J
01

pr.

A
01

ul.

J
01

18

18

9

.1

an

J
01

pr.

A
01

19

ul.

J
01

19

ct.

O
01

19

0

.2

an

J
01

o

(b)

0.4
0.2

01

7

l. 1

Ju

ct.

O
01

17

.1

an

J
01

8

pr.

A
01

18

(c)

01

8

l. 1

Ju

0.4

6

5

0.3

0
-5

0.2

9

.1

an

J
01

pr.

A
01

19

ul.

J
01

19

ct.

O
01

19

(d)

0

.2

an

J
01

0.4

4

0.3

2

0.2
Moving standard deviation (2-day)

0.1

01

Ja
01

18

Mean zonal windn.
F
01 eb.
M
a
01 r.
Ap
01 r.
M
a
01 y.
Ju
01 n.
J
01 ul.
Au
01 g.
Se
01 p.
O
01 ct.
N
01 ov.
D
e
01 c.
Ja
n.

-15

C w yr

10

-10

ct.

O
01

C w yr

15

17

0

0.1

n.
F
01 eb.
M
a
01 r.
Ap
01 r.
M
a
01 y.
Ju
01 n.
J
01 ul.
Au
01 g.
Se
01 p.
O
01 ct.
N
01 ov.
D
e
01 c.
Ja
n.

pr.

A
01

01

J
01

[m s -1 ]

0
17

.
an

u yr [m s -1 ]

ct.

O
01

u yr

C w 1.3-3day

0.6

pr.

A
01

Ja

01

101

01

Period [day](a)w 141.3-141.6 E(2022) 9:53

C

Kaneko et al. Progress in Earth and Planetary ScienceFig. 15 a Wavelet coherence in the axis variation with the spatial mean of zonal wind for each point (141.3–141.6°E mean). b Seasonal variation
in a statistical average (from 1.3 to 3.0 days) of the coherence shown in (a). c and d: Seasonal variation in the coherence shown in b compared toseasonal variation in the spatial mean of zonal wind and 3-yr mean of moving standard deviation of the spatial mean zonal wind for each year,
respectively

phase change downstream (to the east) is shown basedon the HFR data. The zonal scale of the TgWC axis
meanders estimated from the HFR and the verticalstructure of the meanders estimated from the JCOPET DA are consistent with the baroclinic instability.
The propagation speed of the 1.3–3-day variation in
the axis estimated from the HFR agrees well with that
calculated from the two-layer baroclinic instability
theory from summer to autumn. Moreover, based on
the JCOPE-T DA outputs, it is indicated that potential
energy conversion from the mean to the eddy occurs at
approximately 141.3° E and east of Cape Shiriya in summer and autumn, in addition to kinetic energy conversion near the outlet of the channel (~ 141.0° E). These
results suggest baroclinic instability in the eastern partof the Tsugaru Strait that is distanced from some of thecharacteristic topographies, especially from summer toautumn, as well as other instabilities near these topographies. This baroclinic instability with a several-day
timescale during summer and autumn may be causedby the seasonal downfront (westerly) wind in the strait
and subsequent instabilities near the surface (Boccaletti
et al. 2007; Yoshikawa et al. 2012; Thomas et al. 2013).
In conclusion, this study reveals part of the subinertial frequency variation process in the eastern Tsugaru
Strait related to meanders by combining shipboard
observations and high-resolution HFR remote sensing with high-resolution model output. The variations
can affect the north–south water mass mixing andthe stratification in the eastern part of the strait. The

Kaneko et al. Progress in Earth and Planetary Science(2022) 9:53

findings of this study and the extension of the methodology can also be applied to the improvement in K21
using information about internal structures within andoutside the strait provided by the JCOPE-T DA.
Abbreviations
CTD: Conductivity–temperature–depth (observation); cpd: Cycles per day;
HFR: High-frequency radar; JAMSTEC: Japan Agency for Marine-Earth Scienceand Technology; JCOPE-T DA: Japan Coastal Ocean Predictability Experiment,tide enabled, data assimilated version; K21: Kaneko et al. (2021); MIO: Mutsu
Institute for Oceanography; MORSETS: MIO Ocean Radar data Site for the
Eastern Tsugaru Strait; R/V: Research vessel; SADCP: Acoustic Doppler current
profiler mounted on some ships; SE: Shiriya–Esan (line); T/S: Training ship;
TgWC: Tsugaru Warm Current; TsWC: Tsushima Warm Current.

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​022-​00509-z.
Additional file 1. Fig. S1: Time series of zonal velocity estimated by
JCOPE-T DA. a Upper layer (vertical mean) velocity U1, b lower-layer (vertical mean) velocity U2, and c meridional mean of U1 and U2. The solid line
in c denotes the meridional mean for 41.5–41.7°N. The dashed lines in cfor summer and autumn correspond to the meridional mean for the range
represented by the dashed lines in a and b. Fig. S2: Time series of variationin the bandpass-filtered axis latitude at 141.08°E (between 12 and 15 days)
from 2017 to 2019 (black line). The gray line denotes the tidal variation in
the Mf component estimated from sea level data at the Mutsu Institutefor Oceanography through harmonic analysis. Solid (open) circles show
the timing of a new (full) moon. Fig. S3: Same as Fig. S2, but the grayline denotes the tidal variation in the ­K1 and O­ 1 components estimatedfrom sea level data at the Mutsu Institute for Oceanography throughharmonic analysis. Fig. S4: a Phase difference of wavelet cross spectrum oflatitude variation around the axis at each subgrid in relation to the Mf tidecomponent (color). The contours denote their wavelet coherence. b–e:Longitudinal distribution of spectrum ratio RFP(f1,f2) defined by Eq. 2 foreach season. Fig. S5: Same as Fig. 12 but along 141.3°E. Fig. S6 a Exampleof the time series of bandpass-filtered latitude variation in the axis of the
Tsugaru Warm Current calculated from the high-frequency radar data
in 2017. The cutoff timescales are 1.3 and 3.0 days. b Examples of thelagged correlation (r) of various subregions with respect to the reference
subregion (R1). Triangles show peaks in the lagged correlation. Thin lines
denote the 95% confidence interval.
Acknowledgements
The authors acknowledge the assistance of the staff at the Mutsu Institute for
Oceanography and the Research Institute for Global Change of JAMSTEC. We
also acknowledge the assistance of the captains and crews of T/S Ushio-Maru,
Oshoro-Maru, and R/V Wakataka-Maru for their cooperation during sample
collection and hydrographic measurement for cruises during 2009–2019. We
appreciate the work of the technical support staff from Marine Work Japan.
We also thank T. Yasui, T. Hashimukai, T. Nakayama, and S. In for their helpfulcomments.
Author contributions
HK conceptualized the present study, performed analysis of the data obtained
from the HFR and shipboard observations, created the figures, and wrote themanuscript based on comments from all authors. HK, TT, HA, MW, KS, and TO
devised the observation plan and engaged in the collection of in situ data
together with ST. SW and KS were involved in the planning and installationof the HFR, and they facilitated and supervised the continuous observationof the HFR. YM is a developer and established the JCOPE-T DA system. YS was
responsible for the management and retention of the HFR data. All authors
contributed to discussions of the results and commented on the manuscript.
All authors read and approved the final manuscript.

Page 20 of 22

Funding
This study was supported by the research and assessment program for fisheries resources of the Fisheries Agency of Japan.
Availability of data and materials
The datasets of surface velocity obtained from the HFR analyzed for this study
are distributed through the Mutsu Institute for Oceanography, JAMSTEC(https://​www.​godac.​jamst​ec.​go.​jp/​morse​ts/e/​top/). The JCOPE-T DA data are
distributed by JAMSTEC from http://​www.​jamst​ec.​go.​jp/​apl/j/​datab​ase/. The
wind speed data are available from the Japan Oceanographic Data Center(https://​jdoss1.​jodc.​go.​jp/​vpage/​wave.​html). Topographic data were provided
by the NOAA National Geophysical Data Center (https://​www.​ngdc.​noaa.​gov/​
mgg/​global/​relief/​ETOPO1/). The other data analyzed in this study are available from the corresponding author upon reasonable request.

Declarations
Competing interests
The authors declare that they have no known competing interests.
Author details
1
Mutsu Institute for Oceanography, Research Institute for Global Change,
Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 690
Kitasekine, Sekine, Mutsu, Aomori 035‑0022, Japan. 2 Fisheries Resources Institute, Japan Fisheries Research and Education Agency, 3‑27‑5 Shinhama‑cho,
Shiogama, Miyagi 985‑0001, Japan. 3 Faculty of Fisheries Sciences, Hokkaido
University, 3‑1‑1 Minato‑cho, Hakodate, Hokkaido 041‑8611, Japan. 4 Application Laboratory, Research Institute for Value‑Added‑Information Generation,
Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173‑25,
Showa‑machi, Kanazawa‑ku, Yokohama, Kanagawa 236‑0001, Japan.
Received: 24 June 2021 Accepted: 21 September 2022

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