Kuroshio water intrusion into the subarctic region in the western North Pacific Ocean and analyses of the Lagrangian coherent structure

Previous studies have suggested that the quasi-stationary jets, sometimes called the “Isoguchi jets” in the western North Pacific Ocean, regulate the warm and salty conditions in the transition domain between the Subarctic Boundary and the Subarctic Front. Here, we show that mesoscale eddies and interannual/decadal modulations are responsible for the Kuroshio water intrusion into the transition domain. A case study using the Lagrangian coherent structure suggests that the northward shift of the Kuroshio Extension forms a favorable velocity field for the Kuroshio water intrusion around the Subarctic Boundary, while the geometric structure inside the Isoguchi jet is quasi-permanent.


Introduction
Two distinct fronts, the Subarctic Boundary (SAB) and the Subarctic Front (SAF), separate the subpolar region from the subtropical region in the western North Pacific Ocean (Fig. 1a).The surface water in the region bounded by the SAB and SAF (we denote this area as the "transition domain," hereafter) is relatively warm and salty (e.g., Isoguchi et al. 2006;Wagawa et al. 2014;Mitsudera et al. 2018).This "subtropical" condition in the transition domain is essential for the climate system because sea surface temperature (SST) anomalies in this domain are likely to induce anomalous atmospheric circulations in the Northern Hemisphere spanning between the western Pacific Ocean and western Europe (Ma et al. 2015).
There are two quasi-stationary jets along or across these boundaries (see J1 and J2 in Fig. 1a).Previous studies determined that these baroclinic jets are formed due to the low ocean-floor rises, and they regulate the warm and salty conditions of the transition domain (Mitsudera et al. 2018;Miyama et al. 2018).Furthermore, Nishikawa et al. (2021) revealed the Kuroshio water pathways into the transition domain based on particle tracks from the J1.They showed that the Kuroshio water enters upstream of the J1 at the Oyashio Second Branch.The Kuroshio waters are transported northward along the J1, leading to the Kuroshio water intrusion.According to Nishikawa et al. (2021), the eddy components of flow help the Kuroshio water enter the J1.When particle trajectories are calculated using the time-averaged flow, the Kuroshio water rarely enters the J1 and the transition domain; thus, they concluded that eddies were responsible for the Kuroshio water intrusion into the transition domain.
However, the "eddy" described by Nishikawa et al. (2021) contains several components, including mesoscale eddies, seasonal variabilities, and long-term variations such as the Pacific Decadal Oscillation (Mantua et al. 1997).Here, we extend their results of the J1 region using particle tracking based on several temporal-filtered velocity fields.We estimate the subtropical water ratio in the transition domain using each velocity field and identify the time variation responsible for the Kuroshio water intrusion.In addition, we also conducted a case study based on the Lagrangian coherent structure (LCS) (Haller 2015).The LCS can provide robust geometrical features from complex flow fields and has been used to capture tracer distributions in oceanography studies (e.g., Neufeld et al. 1999Neufeld et al. , 2000;;López et al. 2001;Abraham and Bowen 2002;Olascoaga et al. 2006;Beron-Vera and Olascoaga 2009).While particle tracking captures the origin of each particle, the LCS captures the geometrical structures of the flow and those influence on tracer transports.We show that the combination of the particle tracking and the LCS analysis allows us to visualize better the roles of the decadal modulation of the Kuroshio Extension (KE) latitude (e.g., Taguchi et al. 2007;Qiu and Chen 2010;Sasaki and Schneider 2011) related to the Pacific decadal Oscillations (PDOs) (Mantua et al. 1997) or the North Pacific Gyre Oscillations (NPGOs) (Di Lorenzo et al. 2018).According to Qiu and Chen (2010), negative sea surface height anomalies are generated in the eastern North Pacific due to the intensified Aleutian Low during the positive PDO (or negative NPGO) phase.These anomalies propagate westward due to the baroclinic Rossby waves, which results in the southward shift of the KE path.The sequence is opposite to that denoted above during the negative PDO (or positive NPGO).Our LCS analysis highlights that these decadal modulations determine the connectivity between the subtropical and subarctic region and therefore modulates the intensity of the "transport barrier" associated with the SAB.Here, "transport barrier" indicates the region where the particles rarely go across.We also confirm the changes in the transport barrier modulate the particle pathways around the transition domain based on the particle tracking.Furthermore, we discuss the relationship between the LCS and the thermal conditions in the transition domain based on a simple unsupervised machine learning, K-means clustering.An advantage of the unsupervised technique is its objectivity to classify surface waters (Sonnewald et al. 2021).We divide surface waters by K-means clustering into several classes and discuss how the Kuroshio water intrusion influences the SST in the transition domain.

Ocean datasets
We used daily zonal and meridional geostrophic velocities produced from Ssalto/Duacs delayed-time Level 4 sea surface height.The Ssalto/Duacs altimeter products were produced and distributed by the Copernicus Marine and Environment Monitoring Service (CMEMS) (http:// www.marine.coper nicus.eu).The spatial resolution is 0.25 • × 0.25 • .The daily SST with a spatial resolution of 0.25 • × 0.25 • is obtained from NOAA OI SST V2 High-Resolution Dataset data products distributed by Physical Science Laboratory (https:// psl.noaa.gov).OI SST V2 is a blend of in situ ship and buoy SSTs with satellite SSTs derived from the Advanced Very High-resolution Radiometer (AVHRR) (Huang et al. 2021).where x = (x, y) is the position of each particle and u g = u g , v g is the horizontal geostrophic velocity vector at the surface.It has been confirmed that the geostrophic velocity of CMEMS well approximates the speed of the surface buoy recording (Nishikawa et al. 2021).The left-hand side of Eq. (1). is discretized by the fourth-order Runge Kutta method with an integration time-step of three hours.Since the temporal resolution of CMEMS data is daily, the velocity fields are interpolated linearly by every 3 h.Particles are located in our target region by 0.1 • × 0.1 • resolution and tracked for- ward and backward for 360 days.To investigate the roles of mesoscale eddies, seasonal variabilities, and variations longer than interannual variations, we also calculated the particle trajectories using the 91-day moving average velocity field (denoted as the "Seasonal, Interannual and Decadal (SID)" velocity field, hereafter), the monthly climatological velocity field for the years 1995-2020 (denoted as the "Seasonal (S)" velocity field, hereafter), and the 361-day moving average velocity field (denoted as the "Interannual and Decadal (ID)" velocity field, hereafter), respectively.In these cases, the velocity fields are also interpolated linearly by every 3 h.Furthermore, we denote the velocity field without any temporal filters "Mesoscale eddy, Seasonal variabilities, Interannual and Decadal (MSID)" velocity field to emphasize this velocity field includes all the variabilities.Variations that each velocity field includes are summarized in Table 1.
The subtropical water ratio (STR) R (vel)   st is calculated from the backward tracking as follows: (1) where N total is the starting number of particles from each grid, and N st has a value of 1 .if the origin of a particle is south of 34 • N , with a value of 0 used otherwise.The initial time ( t n ) of the particle tracking is every 10 days during the analyzed period of 1995-2020.It is noted that our results are consistent with Nishikawa etl. (2021), where the initial time of the particle tracking was the first day of each month in 1994-2017 and the integration step was 1 day.The superscript vel ∈ {MSID, SID, S, ID} indicates the velocity field used for the calculation.According to Table 1, the differences between R (MSID) st and R (SID)   st emphasizes the role mesoscale eddies have, while a comparison between R (SID) st .with R (ID)  st ( R (S) st ) emphasizes the roles of seasonal variabilities (intannual and decadal variabilities).

Lagrangian coherent structure (LCS)
To obtain the robust geometrical structures of the flow, we utilized the LCS based on the Finite Time Lyapunov Exponent (FTLE) following the work of Shadden et al. (2005) and Haller (2015).The function generated by Eq. (1). is defined as which projects an initial position x 0 at time t = t 0 to its current position x t;t 0 , x 0 at time t 0 + T .This function is referred to as the flow map, hereafter.We estimated the FTLE from the particle tracking using an integrated value of T = 30 days in this study.We confirmed that our results did not change substantially whether we chose T = 15 days or T = 45 days.
Consider the evolution of stretching, i.e., distance between a pair of particles located at x = x 0 and x = x 0 + x t 0 , where x t 0 is infinitesimal.After a time interval of T , the distance becomes This equation means that the growth of stretching fol- dropped.The magnitude of the evolution of stretching is, thus, given by where ⟨⋅, ⋅⟩ is the inner product in ℝ 2 , C is the Cauchy-Green deformation tensor defined as where ⋅ * indicates the adjoint of the tensor.The maximum stretching occurs when x t 0 is chosen to align with the eigenvector associated with the maximum eigenvalue of C T t 0 (x) , max (x): According to Eq. ( 7), the FTLE measures a finite time average of the maximum expansion for a pair of particles advected by the flow map, as described by Eq. ( 1).The ridge of the FTLE for the backward (forward) tracking captures the attracting (repelling) LCS as summarized in Fig. 1b and c (see Shadden et al. (2005) for more detail).The "attracting" means that the trajectories of two particles located across the attracting LCS approach each other along with the attracting LCS as shown in Fig. 1b.In contrast, the trajectories of two particles located across the repelling LCS are separated as shown in Fig. 1c.Therefore, surface waters converge to the attracting LCS, while they diverge from the repelling LCS.In addition, these LCSs are empirically shown to capture the transport barrier (Beron-Vera and Olascoaga 2009;Beron-Vera et al. 2010;Bettencourt et al. 2012).Since the LCSs divide the region two parts, surface waters divided by the LCSs are not stirred.In this sense, the LCSs capture the frontal structure in terms of tracer transports.
One advantage of the FTLE method for the statistical analysis of particle trajectories is its robustness.Since each particle trajectory is sensitive to its initial conditions, the transport barriers inferred from each trajectory might not be robust.In contrast, the FTLE provides robust attracting and repelling structures.Haller (2002) showed that the FTLE is not sensitive to errors in the velocity fields from the mathematical argument.On the other hand, the LCS does not include any information on the origins of each particle.Therefore, the combinational analysis of the particle tracking and the LCS enables us to capture detailed knowledge of the surface water transport and supports the robustness of the results.

K-means clustering
To establish the relationship between the LCS and the thermal conditions of the transition domain, we separate the (6) western North Pacific region (Fig. 1a) into several clusters following the K-means clustering based on the SST.This method is readily available in the scikit-learn library in Python (Pedregosa et al. 2011), and a detailed description of the K-means clustering can be found at https:// scikit-learn.org/ stable/ modul es/ clust ering.html#k-means.The K-means algorithm gives a partition C for n samples into the K disjoint clusters C = C j 1≤j≤K based on the K-means strategy.This algorithm aims to choose the partition that minimizes the error sum of squares: where i is the mean value of the observations belonging to a cluster C i .A choice for the value of K is arbitrary and depends on the problem.To separate our target region into the subtropical region north and south of the KE, the transition domain, and the Oyashio region, we set K = 4 in this study.

Results
The STR obtained from particle tracking can be seen in Fig. 2. The SAB is approximated by the 0.4 m absolute dynamical topography contour in this study.If we use the velocity field without any temporal filters, i.e., MSID velocity, the STR (Fig. 2a) is relatively large in the region between the J1 and the SAB, i.e., the transition domain.The STR is larger than 0.15 on the eastern edge of the J1 and in the area within the transition domain.By contrast, the STR is nearly zero north of 42 • N, except for within the transition domain, suggesting that the J1 regulates the Kuroshio water intrusion, as suggested in previous studies (Wagawa et al. 2014;Mitsudera et al. 2018;Nishikawa et al. 2021).
The differences between the STR values from those obtained using the temporal-filtered velocity fields emphasize the role of time variations.According to Fig. 2b, the anomalies R (MSID)   st − R (SID)   st are positive in the transition domain.With variabilities due to mesoscale eddies, the STR increases at around 150 • E, 39 • N , where the Kuroshio waters are supplied into the entrance of the J1 (Nishikawa et al. 2021).The Kuroshio waters, thus, enter the J1, which is reflected in the positive anomalies along the J1.In addition, the STR also increases along the SAB (Fig. 2b).These anomalies suggest that the mesoscale eddies are responsible for the Kuroshio water intrusion into the transition domain.In contrast, Fig. 2c suggests that the seasonal variabilities are not essential for the Kuroshio water intrusion across the SAB.Although R (SID)   st − R (ID)  st shows large positive values south of SAB between 145 • E and 155 • E , the anomalies are 1 3 smaller than 0.06 in the transition domain except for the region around 160 • E .In particular, the anomalies are smaller than 0.03 along the J1.These results suggest that the exclusion of the seasonal variabilities does not influence on the Kuroshio water intrusion so much.
The anomalies R (SID)   st − R (S)  st shown in Fig. 2d suggest that the interannual/decadal variabilities are important for the Kuroshio water intrusion as well as the mesoscale eddies.The presence of interannual/decadal variabilities dramatically increases the STR along the J1, where the differences exceed 0.08.According to Wagawa et al. (2014), the latitude of the KE (e.g., Taguchi et al. 2007;Qiu and Chen 2010;Sasaki and Schneider 2011) varies the intensity of the J1 over an interannualto-decadal time scale.They showed that the large meander of the KE in a high-latitude state generates more inflow to the J1.
To investigate the relationship between the STR and the decadal modulation of the KE, we calculated the time series of the annual mean value of the STR inside the J1.The interior of the J1 is defined as the region where the amplitude of the SST gradient exceeds the 2 × 10 −5 cm −1 between 42 • N and 45.875 • N .The KE latitude is defined as the latitude of the maximum speed between 30 • N and 40 • N, and averaged between 143 • E and 155 • E .The time series of the normal- ized STR and the SST values inside the J1 are shown in Fig. 3 along with those of the KE latitude.The time series are well correlated before the year 2015.The decrease in the correlation after 2015 may relate to the large meander of the Kuroshio after August 2017 (e.g., Qiu and Chen 2021), but this point is beyond the scope of this study.The correlation coefficient of the STR with KE latitude (the SST) is 0.64 (0.84) between 1995 and 2015.These correlations indicate that the northward shift of the KE latitude increases the STR inside the J1, leading to the warm condition of the transition domain.Therefore, we conclude that the "eddy" transport discussed in Nishikawa et al. (2021) is due to the mesoscale eddies and the interannual/decadal modulations of the KE, while the seasonal variability cannot solely explain the "eddy" transport.

Discussion
We conducted case studies of the LCS on August 1, 2000 and August 1, 2006, when the KE shifted northward and southward, respectively, to determine the roles of interannual/decadal variations of the KE. Figure 4a shows the backward FTLE representing the attracting LCS.There are several ridges of FTLE along the J1, indicating that the edges of J1 are attracting LCS (also see a schematic Fig. 1b).One of the attracting LCSs spans from 148 • E, 39 • N to 153 • E, 43 • N , which likely amassed the Kuroshio waters and supplied them into the J1.To confirm this, we conducted 30-day backward tracking, starting from the region of 148.875 • E − 154.875 • E , 42.375 • N − 42.875 • N (gray-shaded box in Fig. 4a).Fig- ure 4a illustrates that some particles originate from the Oyashio region while the others originate from the upstream region of the KE.In particular, the particles are traced back south of 39 • N across the 0.4 m contour of the absolute dynamic topography associated with the SAB.According to Fig. 4b, the edges of J1 are also the repelling LCS, indicating that the particles located across the J1 are separated in the forward tracking.Indeed, some particles remain in the Oyashio region, while others are transported northward along the J1 or enter the transition domain.Thus, the J1 shields the transition domain from the Oyashio water intrusion while it transports the Kuroshio water, as discussed in previous studies (Nishikawa et al. 2021).
The situation was quite different on August 1, 2006, when the latitude of the KE shifted southward.As shown in Fig. 4c, the ridge connecting the J1 with the KE is absent.Instead, the ridge of the FTLE associated with the SAB is prominent along 41 • N .Since the ridge of FTLE heuristically works as the transport barrier (Shadden et al. 2005;Olascoaga et al. 2006;Beron-Vera and Olascoaga 2009), the SAB possibly divides the subpolar region from the subtropical region.Correspondingly, the particles traced from the J1 (gray-shaded box in Fig. 4c) originate from the Oyashio current and the area near the SAB indicated by the 0.4 m contour of the dynamic topography, markedly different from the case on August 1, 2001 (c.f. Figure 4a, c), and as a result, the Kuroshio waters are not supplied into the J1.Note that regardless of the absence of the Kuroshio water intrusion, the J1 is present (e.g., the northward velocity around 41 • N , 152 • E in Fig. 4b, d), as the J1 is formed by the topography (Mitsudera et al. 2018;Miyama et al. 2018).As can be seen in Fig. 4d, the J1 works as the repelling LCS, as in the case of August 1, 2000.
To establish the relationship between the LCS and the thermal condition of the transition domain, we conducted  5a, b shows that the warm waters shift northward when the KE latitude shifts northward.While the transition domain is included in the same cluster (cluster 02) as the downstream region of the KE on August 1, 2000 (Fig. 5a), it is within the same cluster (cluster 03) as the Sea of Okhotsk on August 1, 2006 (Fig. 5b).As shown in Fig. 4a, some particles of the J1 originate from the KE region when the KE shifts northward, while the SAB avoided the Kuroshio water intrusion on August 1, 2006.Although the J1 always transports the surface waters northward, which the Kuroshio waters or Oyashio waters are transported depends on the latitude of the KE, leading to the transition domain's different thermal conditions.Therefore, we conclude that the thermal condition of the transition domain depends on the geometry and connectivity of the LCS at the SAB and the upstream region of the KE.If the transport barrier associated with the SAB vanishes as in the case in Fig. 4a, the Kuroshio water intrusion is enhanced and results in the warm condition in the transition domain as shown in Fig. 5a.In contrast, the transition domain becomes cool condition (Fig. 5b) if the SAB disrupts the Kuroshio water intrusion as shown in Fig. 4c.

Summary
Our work on particle tracking using the temporal-filtered velocity fields reveal that the mesoscale eddy and the interannual/decadal variations are essential to supply the Kuroshio waters into the J1, while the seasonal variations do not solely explain the Kuroshio water intrusion, extending the results of Nishikawa et al. (2021).Furthermore, the case study, based on the LCS, indicates that the Kuroshio waters are attracted to the entrance of the J1 when the KE is shifted northward.In this case, the attracting LCS spans from the upstream region of the KE to the J1.When the KE shifts southward, the SAB forms the transport barrier along 41 • N and, therefore, separates the subpolar region from the subtropical region.Calculated trajectories of particles also indicate that if the Kuroshio waters are supplied at the entrance of the J1, the jet transports the Kuroshio waters; while if the Kuroshio waters are not supplied at the entrance of the J1, the jet transports the Oyashio waters.Our analysis of the repelling LCS shows that the J1 dynamically separates the transition domain from the Oyashio region regardless of the latitude of the KE.The K-means clustering shows that the SST of the transition domain is included in the same cluster as the subtropical region if the KE shifts northward.The dynamical separation by the J1 shields the transition domain from mixing with the Oyashio waters, which keeps the "subtropical" condition of the transition domain.
While we showed that the interannual/decadal modulations of the KE influence the SST distribution, more detailed studies are necessary.Our study suggests that the SAB sometimes works as a barrier to the Kuroshio water intrusion, while the attracting LCS sometimes penetrates the SAB.We consider the formation mechanism of the SAB and its temporal variations essential to reveal the variations of the thermal condition in the J1 and the transition domain.The dynamics of the SAB should, thus, be addressed in future work.
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Fig. 1
Fig. 1 Schematics for this study.a Our target region.We mainly analyzed the subtropical water intrusion across the SAB into the quasistationary jet named "J1".An orange wavy arrow north of the KE indicates the "eddy" transport suggested by Nishikawa et al. (2021).The transition domain is defined as the region between the SAB and SAF.The SAB and SAF are identified by a salinity of 34.0 psu and a potential temperature of 4 • C at a depth of 100 m, respectively.b The ridge of the Finite Time Lyapunov Exponent (FTLE, defined in Sect.2) (orange line) obtained from backward tracking corresponds to the attracting LCS.The trajectories of two particles (black and gray arrows) are drawn to the attracting LCS.c Same as b but for repelling LCS.Particles located nearby across the repelling LCS are pulled apart from each other and the LCS

Fig. 2 aFig. 3
Fig. 2 a Color shades indicate the subtropical water ratio R (MSID) st value as defined by Eq. (1).Black arrows indicate the square-rooted horizontal geostrophic velocity sign u g√ | | | u g | | | , sign v g √ | | | v g | | | ,where sign(X) returns the sign of X .Velocity vectors whose speeds are less than 10cm s −1 are masked.Green contours indicate the SAB.Each value is averaged from 1995 to 2020.b Same as a but for R(MSID)   st

Fig. 4 a
Fig. 4 a Color shades indicate the FTLE in s −1 calculated from the 30-day backward tracking on August 1, 2000.Values smaller than 0.11 s −1 is masked.Blue triangles represent the origins of particles traced from the gray-shaded box.Black arrows indicate the squarerooted horizontal geostrophic velocity in the same manner shown in Fig. 2. The velocity vectors whose speeds are less than 20 cm s −1 have been masked.Green contours indicate 0.4 m contours of the absolute dynamic topography to represent the SAB.b Color shades are the same as in a but from forward tracking.Blue triangles are endpoints traced from the gray-shaded box.c, d are the same as a and b, respectively, but for August 1, 2006

Fig. 5 a
Fig. 5 a Horizontal distribution of clusters identified by the K-means clustering.Colors indicate each cluster on August 1, 2001.Black contours indicate the SST.b Same as a but for August 1, 2006

Table 1
Summary of variations included in each velocity field