Nagano et al.
Progress in Earth and Planetary Science(2024) 11:48
https://doi.org/10.1186/s40645-024-00649-4

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

Kuroshio Extension cold‑core ring and winddrop‑off observed in 2021–2022 winter
Akira Nagano1* , Minoru Kitamura2 , Kensuke Watari3 and Iwao Ueki1   

Abstract
Energetic cyclonic mesoscale eddies, which are called cold-core rings and are shed southward from the Kuroshio
Extension jet and form closed streamlines, affect the atmosphere through the heat exchange across the sea
surface. To investigate the effect of rings on the atmosphere, we performed atmosphere and ocean observations
across a cold-core ring centered around 34.5° N, 150.0° E using a research vessel from November 2021 to January2022 and a shallow-water profiling float from November 23 to 28, 2021. As heat is released from the sea surface,no significant spatial contrast in the sea surface and mixed layer temperatures was detected across the ring.
Meanwhile, the sea surface wind was occasionally observed to be weak around the ring, possibly through the air–sea
interactions. The wind drop-off maintained a turbulent heat flux small around the ring. The wind field associatedwith the wind drop-off was examined by the rotary empirical orthogonal function analysis of the satellite sea surface
wind data. The minimum of the sea surface wind is found to shift northward relative to the ring center and to be
more than approximately 5 m s−1 lower than the surrounding region. The shallow-water profiling float deployedaround the ring center observed a rapid freshening event in the mixed layer, which can be attributed to the water
intrusion from the north of the Kuroshio Extension jet through the interaction with the jet. This suggests that the cold
water from the north continually affects the atmosphere without leaving traces in the shipboard sea surface
temperature observations.
Keywords Kuroshio Extension, Cold-core ring, Mixed layer, Turbulent heat flux, Air–sea interaction*Correspondence:
Akira Nagano
nagano@jamstec.go.jp
1Center for Coupled Ocean–Atmosphere Research, Japan Agency
for Marine-Earth Science and Technology (JAMSTEC), 2‑15
Natsushima‑cho, Yokosuka, Kanagawa 237‑0061, Japan
2
Earth Surface System Research Center, Japan Agency for Marine-Earth
Science and Technology (JAMSTEC), 2‑15 Natsushima‑cho, Yokosuka,
Kanagawa 237‑0061, Japan
3
Engineering Department, Japan Agency for Marine-Earth Scienceand Technology (JAMSTEC), 2‑15 Natsushima‑cho, Yokosuka, Kanagawa
237‑0061, Japan© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

1 Introduction
The Kuroshio and the Kuroshio Extension (KE),the western boundary current of the North Pacificsubtropical gyre, transport a significant amount of heatfrom the tropics to subtropics (e.g., Bryden and Imawaki
2001; Nagano et al. 2009, 2010) and redistribute heat in
the western subtropical North Pacific (e.g., Ando et al.
2021). Heat is released from the sea surface as turbulent(sensible and latent) heat fluxes in the KE region
because of cold dry wind from the Eurasian Continent(e.g., Konda et al. 2010). Through the heat fluxes,
the atmosphere is affected by the Kuroshio and KE.
Furthermore, many energetic mesoscale eddies are shedfrom the KE jet through the development of the current
meander and exist in the KE region. Such cyclonic andanticyclonic eddies are called cold-core rings (CCRs) andwarm-core rings, respectively. Eddies in the KE region
have kinetic energy equivalent to or larger than that of
the climatological mean current of the Kuroshio and theKE (e.g., Wunsch 1981) and affect on the atmosphere(Yang et al. 2019). Therefore, cold- and warm-core rings
are considered to play an important role in the climate.
The upward (downward) displacement of the main
thermocline due to the baroclinic structure of rings
occasionally exhibits low (high) temperatures near thesea surface. Such strong eddies, which swirl speed ishigher than the propagation speed of the Rossby wave,
can transport water holding it in the eddy interior. The
strength of the capability of eddies to keep waters insideis measured by the local Rossby number, which is definedas U /(βR2 ), where U represents the eddy current speed,
β represents the latitudinal variation of the Coriolis
parameter, and R is the radius of the eddy (e.g., Chelton
et al. 2011; Nagano et al. 2016). For example, Nagano
et al. (2016) observed a CCR with a swirl speed exceeding
50 cm s−1. The local Rossby number of the ring was
significantly greater than 10; thus, it is in the strongly
nonlinear regime. Cold, fresh waters from the north of
the KE have been frequently observed within CCRs in
the southern KE region.
The low (high) sea surface temperature (SST) aroundthe center of cyclonic (anticyclonic) mesoscale eddies
makes the temperature difference across air–sea interface
low (high); thus, the turbulent heat flux is reduced(enhanced) in the central part (e.g., Kouketsu et al.
2012; Ma et al. 2015; Tomita et al. 2019). The SST andtemperature in the mixed layer in rings vary through theair–sea heat exchange, which affects on the atmosphericboundary layer. In addition to the sea surface cooling,horizontal and vertical currents caused by various
processes can change the temperature in the mixed
layer. During the attenuation of a CCR after detachmentfrom the KE, convergent flows toward the center ofPage 2 of 28

the ring occur around the edge of the ring throughthe downward displacement of the main thermocline(Nakajima et al. 2024). Different wind speeds relative toalternating currents due to a CCR can cause convergenceof the Ekman current toward the eddy center regardlessof the wind direction (McGillicuddy Jr 2016). Spatial
variations in the heat release from the ocean into theatmosphere may induce downwelling around the rimof a CCR and then be associated with the convergenceof surface currents toward the center, as Worthington(1972) hypothesized about active heat releases over the
Kuroshio and other western boundary currents.
The atmosphere is affected by mesoscale eddies in
the KE and other western boundary current regions.
Sea surface wind speeds were found to be positively
correlated to mesoscale SST structures by highresolution satellite observations (e.g., Nonaka and Xie
2003; Chelton and Wentz 2005; Small et al. 2008; Chelton
and Xie 2010; Ma et al. 2015). In other words, sea surface
wind is weakened (strengthened) over the cold (warm)
sea surface water within a cyclonic (anticyclonic) eddy.
The wind weakening (strengthening) is attributable tothe attenuated (enhanced) vertical mixing in the stable(unstable) atmospheric boundary layer (Wallace et al.
1989; Hayes et al. 1989) or the adjustment to a negative(positive) pressure anomaly (Lindzen and Nigam 1987)
over a cyclonic (anticyclonic) eddy. Ma et al. (2015)
suggested that the vertical mixing mechanism changes
winds over mesoscale eddies in the KE region from thesea surface to a height of approximately 850 hPa.
From November 2021 to January 2022, we performed
atmosphere and ocean observations using the research
vessel (R/V) Mirai of JAMSTEC in the southern KE
region, focusing on individual CCRs, to investigate theeffects of rings on the atmosphere in winter. During theseresearch cruises, we obtained atmosphere and ocean
variables through the cruises and three whole sections
and one half section of a CCR centered around 34.5° N,
150.0° E. In addition, a shallow-water profiling float was
deployed around the center of the ring. We calculated
the turbulent heat flux using a bulk flux algorithm (Fairall
et al. 2003) and found that it was reduced around the ring
due to the weakening of the overlying wind, the so-calledwind drop-off, around the ring.
In this study, we describe the upper-ocean(< 1000 dbar or m) hydrographic structure of the ringand its relationship with the variation in the turbulent
heat flux along the sections observed during the cruises
and discuss the impact on the atmosphere by using a
multi-satellite wind vector product. Furthermore, we
examined the mixed layer temperature and salinity
variations obtained near the ring center using a shallowwater profiling float. The R/V Mirai observations andNagano et al. Progress in Earth and Planetary Science(2024) 11:48

data are described in Sect. 2. In Sect. 3, we describe
the hydrographic structure of the CCR, examine theturbulent heat flux, and reveal the impact of the ringon the wind by the shipboard data, and examined thecharacteristics of the wind variation by the rotary
empirical orthogonal function (EOF) analysis of thesatellite vector wind data, and discuss a possible oceanic
process in the mixed layer affecting the atmosphere.
Finally, we summarize the results in Sect. 4.

2 Observations and data
2.1 R/V Mirai observations

We performed the observations during the R/V Mirai
cruise (MR21-06), which consists of two parts: Leg 1
from November 3 to November 27, 2021, and Leg 2
from December 18, 2021, to January 13, 2022. Detailed
information about these cruises can be obtained fromthe report of the research cruises (Kitamura 2022).
Referring to near-real-time altimetric sea surface
height (SSH) distributions in late November 2021, we
intensively observed a CCR centered around 34.5° N,
150.0° E (Fig. 1). We performed the observations using
conductivity–temperature–depth (CTD) and expendable CTD (XCTD) sensors down to depths exceeding 1000 dbar or approximately 1000 m, respectively.
Three whole sections and one half section of the CCR
were obtained (Fig. 3): an XCTD section on November 23–24, 2021; an XCTD section on December 30,
2021; a CTD section on January 6–7, 2022; and a CTD
section on January 8–9, 2022. In addition, we obtained
atmosphere and ocean data near the sea surface acrossthe ring centered around 34.5° N, 156.5° E.
We used an SBE911plus CTD system (Sea-Bird
Electronics, Bellevue, WA) for the CTD observations
and XCTD-1 and XCTD-1N probes with the MK-150N
data logging system (Tsurumi-Seiki, Yokohama) for the
XCTD observations. The nominal accuracies for the
CTD temperature, electrical conductivity, and pressure
were 0.001 °C, 0.0003 S m−1, and 0.015% of the fullscale range (10,500 dbar), i.e., 0.16 dbar, respectively.
Using 12-l Niskin-X bottles (Sea-Bird Electronics)
installed in the CTD frame, we collected water samples
and measured salinity. Based on the root-meansquare (RMS) difference between the CTD sensor
and sampling salinity values above 1000-dbar depths,
the accuracy for the CTD salinity sensor is higher
than 0.003 on the practical salinity scale. According
to the RMS differences between the XCTD and CTD
values calculated by Mizuno and Watanabe (1998),
the accuracies for the XCTD temperature and salinity
are 0.05 °C and 0.05, respectively. Note that the XCTD
probe depth was estimated from the fall rate because
no pressure sensor was installed; the depth error isPage 3 of 28

approximately 5 m or 2%, whichever is larger; thus,
the error can be ∼ 20 m. Vertical hydrographic profiles
collected by CTD and XCTD probes are presented
with pressure (dbar) and depth (m), respectively. A
1 dbar pressure increase is almost equivalent to a 1-m
depth increase (e.g., Talley et al. 2011).
The temperature, electrical conductivity, and otheroceanographic parameters of water taken in the
R/V Mirai at a depth of approximately 4.5 m were
measured at intervals of 1 min using an SBE45 (SeaBird Electronics) and other sensors. The nominal
accuracies of temperature and salinity are 0.002 °C and0.003, respectively. Meteorological sensors of R.M.
Young (Traverse City, MI), Vaisala (Vantaa, Finland),
Setra Systems (Boxborough, MA), R.M. Young, andEppley Laboratory (Newport, RI) installed at heightsof 25, 21, 13, 24, and 25 m on the mast of the vessel,
respectively, observed the wind speed/direction, airtemperature/relative humidity, barometric pressure,rainfall amount, and longwave/shortwave radiation
at intervals of 6 s. Using the COARE3.0b bulk flux
algorithm (Fairall et al. 2003), we calculated the sea
surface latent and sensible heat fluxes from the 10-min
averaged values of SST, air temperature, relative
humidity, wind speed, air pressure, and longwave/
shortwave radiation data.
2.2 Shallow‑water profiling float observations

To observe temperature and salinity variations within
the CCR on timescales of days and shorter timescales,a shallow-water profiling float, a multipurpose
observation float (MOF) (Offshore Technologies,

Fig. 1 Map of SSH averaged from November 2021 to January 2022
and locations of hydrographic profiles collected by the R/V Mirai(open circles) and Argo floats (dots) from November 2021 to January
2022. The blue and red dots represent locations of typical spicinessprofiles to the south (cluster 1) and north (cluster 2) of the KE,
respectively. Green dots denote locations of profiles not classified
into either cluster. Contour intervals of SSH are 10 cm. Regionsof lower SSH than the current axis of the KE indicated by the 100 cm
contour, following Nagano et al. (2016), are indicated by gray shades

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Yokohama), was deployed near the center of the CCR(34.75° N, 149.75° E) at 13:03 (UTC) on November
23, 2021. A CTD probe, JES10mini (Offshore
Technologies), was installed on the float. The accuraciesof the temperature and electrical conductivity
sensors are 0.005 °C and 0.005 S m−1, respectively.
The accuracy of salinity is higher than 0.04. The float
was set to drift at a parking depth of 130 dbar and tocollect data every 12 h ascending from 100 dbar tothe sea surface at intervals of 10 s. Data observed by
the float were transmitted to land through the Iridium
communication system. We obtained 10 profiles ofwater temperature and salinity from the deployment to
the end of the observation (00:40 November 28). Data
were processed with a 5-point (50 s) median filter toreduce noisy features and interpolated onto the verticalgrids at intervals of 1 m down to a depth of 80 m using
the Akima (1970) method.
2.3 Argo float data

We used water temperature and salinity profile datacollected by Argo floats in the region of 27–42° N, 142–
165° E from November 2021 to January 2022. According
to the Argo Science Team, the accuracies of the Argo
temperature, salinity, and pressure data were reported tobe 0.005 °C, 0.01 (psu), and 5 dbar, respectively (Hosoda
et al. 2008). The profile data were interpolated onto thevertical grids at intervals of 10 dbar from 10 to 1000 dbar.
To classify hydrographic profiles based on the
isopycnal water mass distribution, we adopt a parameter
whose isopleths are orthogonal to those of the potential
density in the potential temperature–salinity plane,
called the spiciness parameter (Veronis 1972; Jackett
and McDougall 1985), as a state variable of seawater.
Using the polynomial prepared by Flament (2002), we
calculated the spiciness parameter π in kg m−3 from theArgo float data and the data collected during the R/V
Mirai cruises. As performed by Nagano et al. (2022a,
2022b, 2022c), we performed cluster analysis by applying
Ward’s criteria (e.g., Ward 1963; Anderberg 1973) tospiciness parameter distributions in the isopycnal layer
between 24 and 27 σθ with intervals of 0.01 kg m−3 andclassified all the hydrographic profiles into three clusters.
As described in Sect. 3, typical spiciness profiles to thesouth and north of the KE were classified into clusters 1
and 2, respectively. Profiles that cannot be classified into
these clusters were assigned to cluster 3.
2.4 Satellite SSH and SST data

As mentioned above, we used near-real-time daily
altimetric absolute SSH maps to determine the locationsof the observation lines across the CCR and the MOF
deployment position. For the following analysis, we used

Page 4 of 28

Fig. 2 Potential temperature versus salinity diagram basedon the data collected by the R/V Mirai and Argo floats
from November 2021 to January 2022. The blue and red
dots represent spiciness profiles classified into clusters 1
and 2, respectively. Green dots denote profiles not classified
into either cluster. Potential density is indicated by solid contours
at intervals of 0.5 kg m−3

daily delayed-time altimetric absolute SSH mapped onto
1/4◦ × 1/4◦ grids in the region of 24–42° N, 135–176° E
from November 2021 to January 2022. The data are thegridded delayed-time updated SSH (Level 4) anomaly
data (Pujol and Mertz 2020) added to the mean SSH data
provided by Rio et al. (2011). In addition, we used daily
gridded satellite-observed SST data (NOAA OI SST V2
High-Resolution Data Set) from January 6 to January 10,2022, in the region of 32–40° N, 143–157° E provided by
Reynolds et al. (2007). The resolution of the SST dataset
is 1/4◦ × 1/4◦.
2.5 Satellite vector wind data

Furthermore, to examine the spatiotemporal variationin sea surface wind vector, we used 6-hourly 1/4◦ × 1/4◦
gridded vector wind data from November 1, 2021, toJanuary 31, 2022, in the region of 30–40° N, 140–160°
E of the cross-calibrated multi-platform (CCMP) ocean
vector wind analysis Version 3.1 (Mears et al. 2022a;
Mears et al. 2022b). The CCMP V3.1 vector wind data
are merged vector wind data at a height of 10 m above
the sea surface based on measurements by multiple typesof satellite microwave sensors and have the equivalentspatial resolution to the SSH and SST data describedabove.

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 3 Locations of CTD (dots) and XCTD (crosses) profiles collected by the R/V Mirai on a November 23, 2021, b December 29–30, 2021, c January
6–7, 2022, and d January 8–9, 2022. Dots and crosses with profiles classified into clusters 1 and 2 are colored blue and red, respectively. Maps of SSH
around the CCR observed in the R/V Mirai cruise on a November 23, 2021, b December 29, 2021, c January 6, 2022, and d January 8, 2022, areshown by color shades with contour intervals of 10 cm

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

3 Results and discussion
3.1 Characteristics of CCRs

Figure 1 shows the distribution of SSH averaged during
the R/V Mirai observations. The KE jet is illustrated asa meandering path characterized by a sharp southward
SSH elevation. CCRs, delineated by significantly low SSH
compared with the surrounding values, were observed
around 34.5° N, 150.0° E and 34.5° N, 156.5° E south tosoutheast of the KE jet meander troughs.
The locations of spiciness profiles classified into thethree clusters by the cluster analysis based on the spiciness parameter π are plotted in Fig. 1. Spiciness profiles
classified into cluster 1 (blue dots) are mostly distributed in the subtropical region south of the KE. Althoughmost of the profiles classified into cluster 2 (red dots) aremainly present to the north of the KE (i.e., the perturbedarea), there are those trapped in the interior region of
the CCRs centered around 34.5° N, 150.0° E and 34.5° N,
156.5° E, as described below. The salinity of cluster 1 profiles is higher than that of cluster 2 profiles in layers ofdensity lighter than 26.0 σθ (Fig. 2). Thus, clusters 1 and 2
represent typical hydrographic profiles to the south andnorth of the KE, respectively. Other spiciness profiles(green dots) observed near the current axis are classified
into cluster 3. They represent mixtures of water masses tothe north and south of the KE in layers of density lighter
than 26.0 σθ and intrusions of very fresh water into
denser layers, as reported by Nagano et al. (2016).
Notably, all the spiciness profiles near the center of thewestern CCR around 34.5° N, 150.0° E are classified into
cluster 2. The water masses, which were derived fromthe north of the KE and are represented by cluster 2, arebelieved to be kept inside of the strong ring with a highlocal Rossby number, as described below and observed ata moored buoy station by Nagano et al. (2016). The SSH
at the western CCR center is approximately 50 cm lower
than the surrounding values (Fig. 3), and the swirl speed
is estimated to be ∼ 50 cm s−1 on average. The local
Rossby number is greater than 10; thus, the CCR is sufficiently strong to hold water in the interior. Because of
the substantial wind and intensive turbulent heat releaseduring winter, there may be convergent flows (Worthington 1972), the wind-driven Ekman current (McGillicuddy
Jr 2016), etc. Cluster 1 profiles, along with cluster 2 profiles, were observed near the ring center around 34.5° N,

Page 6 of 28

156.5° E; therefore, the subtropical gyre water had beenbrought into the eastern ring. Because the western ring ismore capable of holding water masses in the interior thanthe eastern ring, we examined the sections of the westernring in the following subsection.
3.2 Hydrographic sections of western CCR​

Sections of potential density σθ across the western CCR
are shown in Fig. 4. Because of the baroclinicity, themain pycnocline between approximately 25.4 and 27.0 σθshoals toward the center of the ring. The mixed layer is
identified as a layer of vertically uniform potential density. In this study, following the procedure described by
Suga et al. (2004), we determined the mixed layer base as
the pressure or depth at which the potential density difference from the sea surface value was 0.125 kg m−3. The
depth of the mixed layer base is indicated by thick blacklines in Fig. 4. The depth increased from approximately
100 m in late November 2021 (Fig. 4a) to 200 dbar or
more in early January 2022 (Fig. 4d). In particular, in early
January (Fig. 4c and d), the thickness of the mixed layer
was greater toward the rim of the ring with the depth ofthe main pycnocline, probably because the strong verticalgradient of potential density in the pycnocline prevents
vertical mixing at the bottom of the mixed layer. The
potential density in the mixed layer decreases toward thering center in association with the low-salinity water in
the interior, as described below.
The fresh cold water derived from the north of the
KE is represented by the negative spiciness anomaly πaat the stations within the CCR indicated by red inverted
triangles in Fig. 5 and the saline warm subtropical water
the positive spiciness anomaly (at the stations of blue
inverted triangles). They are clearly separated from thelightest layer (or the mixed layer) to a layer of approximately 26.0 σθ . Note that the water from the north of theKE exists only above a depth of approximately 200 m (ordbar) around the ring center (the depth of the 26.0 σθ
isopycnal layer is denoted by white contours in Fig. 4)
and mostly within the mixed layer (above the thick blackline). Therefore, the mixed layer water derived from thenorth of the KE and trapped by the CCR is modified by
the atmospheric thermal forcing, i.e., cooling. In layers
deeper than an isopycnal layer of approximately 26.0 σθ ,the spatial variation in spiciness is small across the ring;(See figure on next page.)
Fig. 4 Sections of potential density, σθ , (kg m−3) across the CCR. These sections were plotted using the data obtained on a November 23, 2021, b
December 29–30, 2021, c January 6–7, 2022, and d January 8–9, 2022, in the Mirai cruise. The intervals of thin contours for σθ are 0.2 kg m−3. Verticalcoordinates for the southwestern half section in c and the northeastern half section in d by CTD casts are pressure, and those for other sections
by XCTD casts are depth. The 26.0 σθ contours are colored white. The thick black lines represent the mixed layer base. The inverted blue and red
triangles at the top of the panels represent locations of hydrographic profiles classified into clusters 1 and 2, respectively

Nagano et al. Progress in Earth and Planetary ScienceFig. 4 (See legend on previous page.)(2024) 11:48

Page 7 of 28

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Fig. 5 Sections of spiciness anomaly, πa, (kg m−3) with respect to potential density σθ from the mean distributions. These sections were plottedusing the data obtained on a November 23, 2021, b December 29–30, 2021, c January 6–7, 2022, and d January 8–9, 2022, in the Mirai cruise.
Contour intervals of πa are 0.1 kg m−3. No data are denoted by meshes. The blue and red inverted triangles represent hydrographic points classified
into clusters 1 and 2, respectively

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Fig. 6 Same as Fig. 4, but for potential temperature (°C). Contour intervals are 1 °C

Page 9 of 28

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Fig. 7 Same as Fig. 4, but for salinity. Contour intervals are 0.1

Page 10 of 28

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Page 11 of 28

the ring decreased by approximately 3 °C from November
23, 2021 (Fig. 6a), to December 29, 2021 (Fig. 6b), with anestimated cooling rate of ∼ 0.1 °C day−1. The evaporationof freshwater from the sea surface and the entrainment of
the deep saline water increased salinity in the mixed layer(Fig. 7). The salinity increase rate of the mixed layer near
the ring center from November 23 (Fig. 7a) to December
29 (Fig. 7b) was ∼ 0.005 day−1. The cooling and salinification rates after December 2021 have the same order ofmagnitude as or are less than the values from November
23 to December 29, 2021. The mixed layer potential temperature similarly changed regardless of whether it was
inside or outside the CCR. The mixed layer water inside
the ring is kept fresh even in winter, while that outside
the ring becomes saline because of the entrainment of
the deep water as in these observations and in the resultsof Nagano et al. (2014).
3.3 Sea surface turbulent heat flux

Fig. 8 Sea surface turbulent (latent plus sensible) heat flux in W m−2
on tracks of the R/V Mirai a from November 3 to 26, 2021, and bfrom December 18, 2021, to January 10, 2022. The positive values
represent fluxes from the ocean to the atmosphere. Maps of SSH
during the periods are shown with contours. Contour intervals of SSH
are 10 cm, and low SSH (< 100 cm) regions are indicated by grayshadestherefore, the water from the north of the KE is indistinguishable from that of the subtropical water in the deep
layer.
Although the salinity within the CCR (defined as thenegative-πa region here) is significantly lower than that in
the surrounding regions (the positive-πa region) (Fig. 7),
there is no significant horizontal difference in the potential temperature of the mixed layer water across the ring,particularly in December 2021 (Fig. 6b) and January 2022
(Fig. 6c and d). The strong sea surface cooling due to thelarge difference between SST and atmospheric temperature outside the CCR (Kouketsu et al. 2012) mainly modified the mixed layer water temperature and substantiallyreduced the temperature contrast immediately after thedetachment from the KE. Subsequently, the spatial temperature contrast disappeared. The uniform SST andmixed layer temperature are thought to be the result of
the air–sea interactions.
The seasonal changes in the potential temperature andsalinity of the mixed layer in the CCR from autumn towinter were observed through the shipboard CTD/XCTD
observations. The mixed layer potential temperature in

We calculated the latent and sensible heat fluxes along
the cruise tracks of Legs 1 and 2. The mean values of thelatent heat flux (172 W m−2 for Leg 1 and 290 W m−2
for Leg 2) were much larger than those of the sensible
heat flux (20 W m−2 for Leg 1 and 82 W m−2 forLeg 2). The standard deviations of the latent heat flux
(104 W m−2 for Leg 1 and 120 W m−2 for Leg 2) werealso much larger than those of the sensible heat flux
(19 W m−2 for Leg 1 and 68 W m−2 for Leg 2). The sea
surface turbulent (sensible plus latent) heat fluxes along
the tracks of the R/V Mirai cruises are shown in Fig. 8.
Following the procedure described by Nagano and Ando(2020) and Nagano et al. (2022a,b), we decomposed thevariation in latent heat flux FL, which is much greaterthan the sensible heat flux variation, into components
based on the variations in SST TS, air temperature TA ,specific humidity q, and wind speed U to investigate thecontributions of the individual variables to the heat flux
variation, as follows:
�FL ≈










∂FL
∂FL
∂FL
∂FL
�TS +
�TA +
�q +
�U ,
∂TS
∂TA
∂q
∂U

(1)
where TS, TA, q , and U denote the variations in
SST, air temperature, specific humidity, and wind speed,
respectively. Because the function of the bulk flux algorithm is very complex, the rate of change of each termon the right-hand side of Eq. (1) was computed by setting
the other three variables to the mean values during eachcruise period. The units of all the terms of Eq. (1) are thesame as that of the turbulent heat flux, i.e., W m−2.
As described above, the sea surface turbulent heat flux
is positive during the observation periods (Fig. 8), principally due to dry cold wind (Figs. 9b–d and 10b–d) fromNagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 9 Components of latent heat flux variation due to the variations in a SST (∂FL /∂TS )�TS in Eq. (1), b air temperature (∂FL /∂TA )�TA, c specifichumidity (∂FL /∂q)�q, and d wind speed (∂FL /∂U)�U on the R/V Mirai track from November 3 to 26, 2021. The positive values represent fluxes
from the ocean to the atmosphere. SSH map during the period is shown on each panel with contour intervals of 10 cm, and low SSH (< 100 cm)
regions are indicated by gray shades

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Fig. 10 Same as Fig. 9, but on the R/V Mirai track from December 18, 2021, to January 10, 2022

Page 13 of 28

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Fig. 11 Time series of a SSH (cm) and b latent heat flux components (W m−2) due to the variations in SST (∂FL /∂TS )�TS in Eq. (1) (magenta lines), airtemperature (∂FL /∂TA )�TA (green lines), specific humidity (∂FL /∂q)�q (cyan lines), and wind speed (∂FL /∂U)�U (orange lines) along the R/V Mirai
track from November 3 to 26, 2021. In panel (a), SSH depressions less than approximately 100 cm indicate KE meander troughs and cold-core rings

the Eurasian Continent, which appears to be enhancedin the KE region and is described in the following rotary
EOF analysis. This enhancement of the wind is primarily responsible for the larger heat flux near the KE thanthose in the surrounding regions. Meanwhile, the contribution of SST to the heat flux has no remarkable peak in
the KE current but increases toward the south because of
the southward increase in SST. This is different from thecase of the Kuroshio south of Japan studied by Nagano andAndo (2020). Because the Kuroshio south of Japan exhibits a warm core near the current axis of the Kuroshio (e.g.,
Taft 1978), the SST is a dominant factor and has a maximal SST contribution to the turbulent heat flux along thecurrent axis of the Kuroshio south of Japan (Nagano andAndo 2020).
The R/V Mirai crossed the western and eastern CCRs
in the weak wind during the first 4 days from November
3 to 6, 2021, of Leg 1 (Fig. 11b). A sharp wind drop-off

was observed near the western ring on November 23,
immediately after the eastward passage of the strong
wind disturbance. The wind drop-off can be attributed
to the wind reduction caused by the KE meander trougharound 35.5°, 147.5° E (not shown). On December 29,
2021 (Fig. 12a), the R/V Mirai crossed the meander
trough (Fig. 8b). The anomalously low SST (the dashedarrow in Fig. 12b) associated with the KE meander negatively contributed to the latent heat flux (Fig. 10a). At thistime, the wind speed was also significantly decreased(Fig. 12b). The weak wind was observed over the meander trough at 06:00 on December 29 in the CCMP satellite data (Fig. 13a). Tomita et al. (2013) reported asimilar response of the atmosphere to a meandering KE
front associated with a cloud hole and sea surface winddivergence over sea surface warm water south of the KE.
Although the R/V Mirai passed by the ring on December 30, we found no ocean imprint because of the passage

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 12 Same as Fig. 11, but for the period from December 18, 2021, to January 10, 2022. The dashed and solid arrows indicate wind drop-offs
over the KE meander trough and the CCR, respectivelyof an atmospheric disturbance accompanied by a strong
wind.
Despite the horizontally uniform SST and mixed layer
temperature observed by the R/V Mirai, the turbulent
heat flux was suppressed near the western CCR centered around 34.5° N, 150.0° E (Fig. 8b) in January 2022.
Kouketsu et al. (2012) and Ma et al. (2015) reported thatmesoscale cyclonic eddies in the KE region affect on thelatent heat flux through the low SST in the interior, possibly because the past studies did not treat KE meanders
and detached eddies differently. In this study, the low
latent heat flux events around the detached ring were
mostly attributed to the wind speed drops on January
6, 9, and 10, 2022 (the solid arrows in Fig. 12b). For thewind drop-offs on January 6 (Fig. 14a), 9 (Fig. 15a), and
10 (Fig. 16a), we identified wind speed minima near the
CCR from the satellite-observed CCMP data. The winds
appear to be convergent over the ring (Figs. 14b, 15b, and16b). However, as examined in the following rotary EOF

analysis, the convergent wind on January 6 is revealed
not to be attributed to the wind drop-off.
Decomposition of the wind vector variation by therotary EOF modes is useful to reveal the characteristicsof the variation (Denbo and Allen 1984; Thomson andEmery 2014). To examine the characteristics of the variation in the sea surface wind vector, we tried to computethe rotary EOF modes which express the wind drops
near the CCR. Because the atmospheric disturbances
have complicated and diverse forms as shown in Figs. 13,
14, 15, and 16, there would be no versatile modes representing all the disturbances. Nevertheless, we obtainedmode patterns with wind depressions around the CCR
by taking the calculation region to 31–39° N, 144–155°
E around the ring center. The rotary EOF modes may
represent common features of the atmospheric disturbances with the wind drops observed in the Mirai cruise.
The first rotary EOF mode, which accounts 68% of thetotal variance, represents the variation with a uniform

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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EOF modes can be convergent and divergent (Figs. 18c–f
and 19c–f ). The leading three rotary EOF modes explain
approximately 87%. The percentages of the higher rotary
EOF modes are smaller than 4%.
The wind speeds and vectors on January 6, 9, and 10,2022, by the second and third rotary EOF modes areshown in Fig. 21. The wind drop-offs around the CCR
observed by the R/V Mirai are presented by the second
and third rotary EOF modes as decreases in wind speedby more than approximately 5 m s−1 near the ring. The
attenuation of the wind is greater than < 3 m s−1 and< 0.3 m s−1 reported by Nonaka and Xie (2003) and Ma
et al. (2015), respectively. The discrepancies would be
mainly attributed to the time filtering (Nonaka and Xie
2003) and time averaging (Ma et al. 2015).
Note that the wind field in association with the winddrop-off is not always convergent; for example, the divergence is positive on January 6 (Fig. 21b) and almost vanishes on January 9 (Fig. 21d). If the pressure adjustment
mechanism was effective on the wind reduction, the windfield would have always been convergent. Thus, the winddrop-off around the CCR is considered to be caused notby the pressure adjustment but the vertical mixing reduction due to the stabilization of the atmosphere aroundFig. 13 Satellite-observed a wind speed (m s−1, color shades
and white contours) and b wind vector (m s−1, arrows)
and divergence (10−5 s−1, color shades) near the sea level at 06:00
on December 29, 2021, on the absolute SSH map (cm, black
contours). Intervals of white contours for wind speed and black
contours for SSH are 1 m s−1 and 10 cm, respectively. A reference
wind vector with a magnitude of 10 m s−1 is shown on the lower
right corner of panel (b)eastward phase increase (Fig. 17b) and a slight amplification over the meandering KE front (Fig. 17a). The divergence of the wind by the first rotary EOF mode variation
is not substantial, despite that the wind direction greatly
varies (Fig. 17c–d) mostly from southward to eatward, as
indicated by the distribution of the time coefficient phaseof ∼ 180°–270° (Fig. 20a).
The wind drop-off around the CCR observed by the
R/V Mirai can be represented by the second and thirdrotary EOF modes, which exhibit the minima in amplitudes immediately to the northwest and northeast of themean center of the ring (Figs. 18a and 19a), accounting
12 and 7% of the total variance, respectively. The phaseof the second (third) rotary EOF mode increases counterclockwisely (clockwisely) around the amplitude minimum (Figs. 18b and 19b). Because the phases of theirtime coefficients mostly distribute between 120° and 360°
(Fig. 20b and c), the wind vector variations of both rotary

Fig. 14 Same as Fig. 13, but at 18:00 on January 6, 2022

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Fig. 15 Same as Fig. 13, but at 00:00 on January 9, 2022

the ring. As the atmospheric boundary layer become
more stable toward the north due to the northward
cooler sea surface water in the KE region (Tokinaga et al.
2006), the northward shifts of the wind drops (i.e., theminima of the amplitudes of the rotary second and third
EOF modes) relative to the ring center may be related
to the more stable background atmospheric condition
toward the north. The vertical mixing reduction near the
CCR would disconnect the atmospheric boundary layerfrom the upper atmosphere. Therefore, the wind near the
ring is considered to be weak in speed but quite variablein direction.
Even if the CCR contained cold water in the interior
immediately after the separation from the KE jet (lateJune 2021), the influence of the low SST is not considered to have remained persistent in the atmosphere forapproximately 6 months. Satellite SST observations may
detect the variation associated with the reduction in the
turbulent heat flux around the CCR. Figure 22 shows
satellite-observed SSTs on the occasions with wind dropoffs observed by the R/V Mirai. Although there is no SST
trace on January 6 and 9, 2022 (Fig. 22a and b), in association with the CCR, a cold tongue was observed to extend

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Fig. 16 Same as Fig. 13, but at 00:00 on January 10, 2022

toward the ring on January 10 (Fig. 22c). Therefore, thewind drop-offs over the ring may have been forced byintermittent cold water intrusions into the ring. However,spatiotemporal scales of such temperature fluctuations
may be too small to be fully resolved by both satellite andshipboard observations.
3.4 Short‑term hydrographic variations within western
CCR​

After deployment on November 23, 2021, the MOF
moved cyclonically along with the eddy current within aradius of approximately 30 km from the center (Fig. 23).
When the float was deployed, the measured potential
temperature and salinity were 22.0–22.1 °C and 34.25–
34.40, respectively, which are consistent with the XCTD
observations on November 23 (Figs. 6a and 7a). We
obtained a reasonable time series of the potential temperature and salinity near the ring center down to a depthof 80 m (Fig. 24a and b), below which the mixed layerbase was present (Fig. 4a).
Diurnal intrusions of warm and saline water, whichwere probably due to the entrainment of water frombelow the mixed layer, were observed around 12:00 on

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 17 a Amplitude and b phase of the first rotary EOF mode of the 10-m height wind vector variation from November 1, 2021, to January 31,
2022. White contour intervals for amplitude and phase are 0.002 and 30°, respectively. Wind vectors (arrows) and their divergences (color shades)
at time coefficient phases 0°, 90°, 180°, and 270° are shown in panels (c–f), respectively; for the calculations, the amplitude of the time coefficient
was set to 300. The SSH map averaged during the observation is shown by black contours at intervals of 10 cm

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 18 Same as Fig. 17, but for the second rotary EOF mode of the 10-m height wind vector variation

November 23, 25, and 26, 2021 (Fig. 24a and b). The
rates of changes in the potential temperature and salinity
due to the entrainment reached maxima of 0.1 °C day−1(Fig. 25a) and 0.4 day−1 (Fig. 25b) around the deepest

layer of the observation (∼ 80-m depth), respectively.
The fluctuations in the potential temperature were vertically attenuated, whereas those in the salinity extended
to near the sea surface. Thus, in addition to the sea

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Fig. 19 Same as Fig. 17, but for the third rotary EOF mode of the 10-m height wind vector variation

surface forcing, the entrainment from the deep layer wasobserved to modify the mixed layer water.
Because of their accumulated effects, the mixed layerwater became cooler and more saline toward winter, as
observed by the shipboard CTD/XCTD observations(Figs. 6 and 7). The potential temperature of the mixed
layer water smoothly decreased at a rate of approximately
0.1 °C day−1 through the MOF observation of 4 days anda half (Fig. 25a), being rapidly adjusted to the sea surface
cooling and equivalent to the seasonal change obtainedNagano et al. Progress in Earth and Planetary Science(2024) 11:48

Page 21 of 28

in potential density (Fig. 25c). The water to the northof the KE is colder and fresher than that to the south(Fig. 2; Kawai 1972; Nagano et al. 2014). Thus, the MOFobserved opposite salinity change, i.e., freshening, of themixed layer water, suggests that cold water intrudes fromthe north of the KE on a time scale no longer than days
and imprints the ring signal on the atmosphere.
Note that, in contrast with the westward propagating
character of the Rossby wave, the ring remained in theregion east or southeast of the trough of the KE meander
for more than 3 months during the observations,
possibly interacting with the eastward flowing KE jet.
The horizontal entrainment of water from the northof the KE can be caused by the interaction with the KE
jet through processes associated with such as filamentlike water intrusions with a smaller spatial scale, i.e.,
submesoscale, which was barely observed by the satellite
SST observation on January 10, 2021 (Fig. 22c). In otherwords, the mixed layer water within the CCR would beconstantly affected by the advection of water from thenorth of the KE.
The unidentified contrast in the SST and mixed layer
potential temperature between inside and outside thering indicates that a rapid convective adjustment had
occurred. Perhaps, there had been more intensive
convective adjustments in the region along the outer
periphery of the CCR, where the KE water warmer thanthat north of the KE was advected, than in the central
part of the ring. The computation of the turbulent heat
flux using the bulk algorithm uses SST, air temperature,humidity, and wind speed. Of these variables, SST is
the only parameter that accounts for changes in theocean state. If the convective adjustment in the mixed
layer is too rapid for the variation to be fully detectedusing sparse shipboard and satellite temperature
measurements, the computation based on the bulk
algorithm can be underestimated. For more exact
measurements of the turbulent heat flux, additional
appropriate methods such as the eddy correlation flux
measurement technique are required in the intensive
heat release regions such as the KE region.
Fig. 20 Histograms of the phase of the time coefficient of the a first,
b second, and c third rotary EOF modes

by the shipboard observation. Remarkably, the salinity decreased at rates up to 0.4 day−1 (Fig. 25b), which is
opposite to and two orders of magnitude larger than theseasonal change (∼ 0.005 day−1). Because the effects ofthe potential temperature and salinity changes on density
almost cancel each other, there is no significant tendency

4 Summary
Strong cyclonic mesoscale eddies, called CCRs witha high local Rossby number greater than unity, arefrequently generated in the southern KE region
through the development of the jet meanders. Suchstrong mesoscale eddies play critical roles in modifying
turbulent heat flux in the KE region. To examine theimpact of CCRs on the atmosphere, we performed
atmosphere and ocean observations using the R/V Mirai(MR21-06) in the southern KE region from November
3 to 27, 2021 (Leg 1), and from December 18, 2021, toNagano et al. Progress in Earth and Planetary Science(2024) 11:48

Page 22 of 28

Fig. 21 Wind speeds (left), and wind vectors and divergences (right) by the second and third rotary EOF modes; a and b at 18:00 on January 6, cand d at 00:00 on January 9, and e and f at 00:00 on January 10, 2022. White contour intervals for wind speeds are 1 m s−1. The SSH map averaged
during the observation is shown with black contours at intervals of 10 cm

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Page 23 of 28

Fig. 23 Map of SSH (cm, top color bar) on November 23, 2021,
and locations of hydrographic profiles (bottom color bar) collectedby a multipurpose observation float (MOF). Contour intervals of SSH
are 10 cm. Measurements were performed at 00:00 and 12:00 (UTC)except for the first measurement (November 23 14:29 UTC). Profiles
were sequentially numbered from the first

Fig. 22 Satellite-observed SST in °C on January a 6, b 9, and b 10,
2022. Contour intervals are 0.5 °C

January 13, 2022 (Leg 2). Referring to satellite SSH data,
we detected sufficiently strong CCRs centered around
34.5° N, 150.0° E and 34.5° N, 156.5° E. During the cruises,
we obtained three and a half hydrographic sectionsof the western ring, concurrent with the collectionof atmosphere and ocean data along the ship track.
Furthermore, we deployed a shallow-water profiling float(MOF) around the center of the ring.
We performed cluster analysis for the spicinessparameter calculated using the temperature and salinity profiles collected by Argo floats and the R/V Mirai
and classified them into three clusters. The classification was consistent with the distributions of hydrographic profiles to the north and south of the KE. Theinterior of the western CCR was occupied with a fresh(negative spiciness anomaly) water mass from the northof the KE down to a depth of approximately 26.0 σθ(above a depth of approximately 200 dbar around thering center). Unexpectedly, the SST and mixed layerwater temperature were found to be uniform across the
CCR. The SST signal within the ring could not be fully
monitored by the satellite observation. Accordingly, we
treated the impact of the detached CCR on the atmosphere differently from that of the KE meander with the
SST signal. The turbulent heat flux estimated using thebulk flux algorithm was suppressed by wind drop-offs
around the ring.

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 24 Time–depth plots of a potential temperature in °C, b salinity, and c potential density σθ in kg m−3 observed by the MOF. Contour intervals
for potential temperature, salinity, and potential density are 0.05 ◦ C, 0.05, and 0.05 kg m−3, respectively

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

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Fig. 25 Time–depth plots of the variation rates in a potential temperature (°C day−1), b salinity (day−1), and c potential density (kg m−3 day−1)
observed by the MOF. Contour intervals for potential temperature, salinity, and potential density variation rates are 0.05 °C day−1, 0.1 day−1,
and 0.1 kg m−3 day−1, respectively

Nagano et al. Progress in Earth and Planetary Science(2024) 11:48

Furthermore, using the CCMP satellite sea surface
vector wind data, we examined the characteristics of
the wind drop-off by the rotary EOF analysis of thewind vector variation. The first rotary EOF mode (68%)
represents the wind variation associated with a slight
amplification over the KE current. The wind dropoff around the CCR was found to be represented by
the second (12%) and third (7%) rotary EOF modes
with the minima in the amplitudes immediately to thenorthwest and northeast of the CCR. The reductionin the wind speed relative to the surrounding region
exceeded approximately 5 m s−1, which is notably larger
than values reported in preceding studies. Systematicconvergent wind field was not associated with the winddrop-off. Thus, the reduction in wind speed is considered
to be caused by the attenuation of the vertical mixing due
to the stabilization of the atmospheric boundary layer.
The northward shift of the minima of the wind dropoff may be attributed to the northward increase in the
background stability of the atmospheric boundary layer
in the KE region.
The MOF-observed potential temperature and salinity
variations due to the diurnal entrainment of deep waterfrom beneath the mixed layer base around the center ofthe ring. The mixed layer potential temperature slowly
decreased at a rate equivalent to the seasonal cooling(∼ 0.1 °C day−1). A freshening event with a magnitude of
up to 0.4 day−1, which is two orders of magnitude greaterthan and opposite to the seasonal variation in salinity,
was observed by the MOF. This suggests that fresh cold
water had been intruded from the north of the KE.
We expect that the mixed layer water convectively
adjusts to the intensive heat loss at the sea surface in the
KE region, particularly intensively outside of the CCR,
and that the spatial contrast in SST and mixed layer
temperature is diminished. The convective adjustmentof the mixed layer water is too rapid for the variation
to be fully detected through conventional temperatureobservations using research vessels, satellites, etc.
Because SST is the only parameter that accounts forthe variation in the ocean state in the estimation of the
turbulent heat fluxes using the bulk flux algorithm,
the calculated variations in turbulent heat fluxes are
considered underestimated. Therefore, additional
appropriate methods such as the eddy correlation flux
measurement technique are required to investigate theair–sea interactions in the KE region.
Abbreviations
CCMP	Cross-calibrated multi-platform
CCR​	Cold-core ring
COARE	Coupled ocean–atmosphere response experiment
CTD	Conductivity–temperature–depth
EOF	Empirical orthogonal function
JAMSTEC	Japan Agency for Marine-Earth Science and Technology

Page 26 of 28

KE	Kuroshio Extension
MOF	Multipurpose observation float
NOAA	US National Oceanic and Atmospheric Administration
OI	Optimum interpolation
RMS	Root-mean-square
R/V	Research vessel
SBE	Sea-Bird Electronics
SSH	Sea surface height
SST	Sea surface temperatureUTC​	Coordinated universal time
XCTD	Expendable conductivity–temperature–depth
Acknowledgements
The authors would like to thank Nippon Marine Enterprises Ltd. (NME) andMarine Works Japan Ltd. (MWJ) for their vessel operations and observation
support, respectively, and scientists onboard the cruise for their assistance.
The authors are grateful to the editor Prof. Akira Oka (Atmosphere and Ocean
Research Institute, The University of Tokyo) and anonymous reviewers forconstructive review comments.
Author contributions
AN proposed the topic, conceived and designed the study, analyzed the data,and constructed the manuscript. MK proposed the topic and conceived anddesigned the study along with the corresponding author (AN). KW designed
the MOF and conducted the observation with MK. IU discussed the results incollaboration with AN and MK. All authors have read and approved the final
manuscript.
Funding
This work was partly supported by the Japan Society for the Promotionof Science (JSPS), Grant-in-Aid for Scientific Research (Grant JP15H04228,
JP17K05660, JP20K04072, JP20H02236, JP20H04349, and JP20KK0097).
Availability of data and materials
Shipboard data used in this study were obtained in the R/V Mirai MR21-06
cruise. Overall information on this cruise and data are provided in the R/V Mirai
MR21-06 cruise report (Kitamura 2022). All data collected in this cruise andthe cruise report have been distributed on the website of the JAMSTEC Data
Research System for Whole Cruise Information (DARWIN, http://​www.​godac.​
jamst​ec.​go.​jp/​ darwin/e). Gridded daily satellite-observed SSH and SST data
are produced by the EU Copernicus Marine Environment Monitoring Service(CMEMS) (ftp://​my.​cmems-​du.​eu/) and NOAA Physical Science Laboratory(https://​psl.​noaa.​gov/​data/​gridd​ed/​index.​html). Gridded multi-platform vector
wind data are produced by Remote Sensing Systems (https://​www.​remss.​com).

Declarations
Competing interests
The authors declare that they have no competing interests.
Received: 2 April 2024 Accepted: 26 July 2024

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