Frontal Waves in the East of the Tsugaru Strait Revealed by the High-Frequency Radar Observation


 Surface velocity observations of the eastern part of the Tsugaru Strait made by the high-frequency radar revealed frequent occurrence of frontal waves along the axis of the Tsugaru Warm Current in 2017–2019. The current axis (maximum of the zonal velocity in the meridional direction) disturbed in the north–south direction with period of ~ 13.7 days that is dominant timescale of tide modulation in the strait, in addition to that of ~ 27.3 days. The amplitude of the axis fluctuation increased in the downstream direction, from the eastern neck of the channel (~ 141.0°E) to the outlet of the strait adjacent to the Pacific Ocean (~ 141.5°E). The propagation speed of the disturbance was slower than that due to surface advection especially in the seasons when the stratification was developed, and agreed well with that estimated from the theory based on the two-layer baroclinic instability model except for winter. The north–south modulation of the axis at the outlet of the strait (~ 141.5°E) could cause short-term (from 20 days to 1 month) variations of an anticyclonic gyre of the Tsugaru Warm Current that is developed in the east of the outlet from summer to autumn reported by the previous studies.

The mean velocity of the TWC in the strait reaches to 1 m s −1 at the axis of the current 90 (e.g., Ito et al. 2003; Matsuura et al., 2007;Saitoh et al., 2008). Its mean volume transport was 91 estimated as about 1.5 Sv (10 6 m 3 s −1 ; Onishi and Ohtani, 1997;Ito et al., 2003) with seasonal 92 variability of about ~0.3 Sv, showing an increase from summer to autumn (Nishida et al., 2003). 93 The outflow from the channel encounters low temperature and salinity water described as the 94 coastal Oyashio water by the previous studies (e.g., Kono  formation of the outflow gyre revealed using high-frequency radar data", hereafter K21). The 105 outflow pattern in the east of the strait (east of ~141.5°E) also changed drastically in summer 106 and autumn, that is, large anticyclonic gyre develops south of Hokkaido (e.g., Conlon, 1982; 107 Kawasaki and Sugimoto, 1984;Kubokawa, 1991;Rosa et al. 2007;K21). 108 In addition to these seasonal changes, shorter variation of TWC was also reported. 109 Whereas the growth of the gyre takes for about 3 months Nof and Pichevin, 110 2001), Yasuda et al. (1988) reported shorter-term variation of the gyre that has 20-30 days 111 period, that is, the direction of the major axis of the elliptical distortion of the gyre rotated 112 clockwise with these fluctuations. As another short-term variation in the strait, based on a 113  Kubokawa (1991) demonstrated that variation of the north-south position of the front 120 at the outlet of the strait could affect rotation of the gyre in a clockwise direction that is resemble 121 with the short-term variation reported by Yasuda et al. (1988), however, the connection of such 122 short-term variation of the gyre and tides are not fully understood, yet. 123 Since remarkable front of the water mass and periodical disturbance due to tide are 124 known in the strait as mentioned above, frontal disturbance related with the tide would be likely 125 to occur in the east part of the strait (from ~141.0 to ~141.6°E, Fig. 1b). Frontal waves that are 126 propagating meander along remarkable front to the downstream direction were reported in other 127 regions including the Kuroshio in the East China Sea (Sugimoto et al., 1988;Qiu et al., 1990;128 waves in the strait are rare although many repeated observations of ships and moorings were 145 conducted there, because of the intense velocity of the TWC and frequent ship traffic through 146 the strait. 147 HFR is one of the effective instruments for investigation of the frontal disturbances 148 including eddies (e.g., Schaeffer et al., 2017). Thus, employing the HFR that includes three 149 antennas installed at the eastern part of the strait (Fig. 1b), we investigated behavior of frontal 150 wave through examination of the axis variation of the TWC. In the present study, the time-series 151 of the surface velocity for three years provided by the HFR, that has horizontal resolution of 152 about 3 km and is temporal resolution of about 30 minutes, was employed. In this paper, as a 153 result, it will be revealed downstream propagation of the disturbance of the axis latitude with 154 increase of the amplitude to the downstream direction. Also, it will be shown that the 155 propagation speed is slower than that of advection due to surface current especially in the 156 seasons of the stratification. Internal stratification and velocity distribution obtained from 157 repeated shipboard observations along the fixed lines across the strait (Shiriya-Esan line, Fig.  158 1b) will be used for the investigation of the frontal waves in order to compare with the baroclinic 159 instability theory. 160 The remainder of the present study is as follows. Following section, we will provide 161 information of observation data and methods including surface velocity observed by the HFR, 162 shipboard observations, and propagation speed of the baroclinic instability waves based on the 163 theories provide by the previous studies. In the result section, first we will demonstrate the 164 seasonal variation of the TWC axis and shorter-term variations. Moreover, vertical distribution 165 of the stratification and velocity would be shown along the transection across the channel. Then, 166 propagation speed will be examined mainly based on the two-layer model concerning baroclinic 167 instability proposed by previous studies (e.g., Pedlosky, 1987;Itoh and Sugimoto, 2008). In the 168 final section, importance of the frontal wave in the strait will be discussed concerning short-169 term variation of the gyre that develops from summer to autumn, and water mass modification. Tecnology (JAMSTEC) has installed the monitoring system using the HFR (CODAR, 176 SeaSonde, 13.9 MHz) that has three antenna stations (Fig. 1c). Two of them are installed in the 177 Shimokita Peninsula, and the other is located at Hokkaido (Esan, Fig. 1c). The HFR provides 178 data whose horizontal resolution of the system is about 3 km, and the coverage of the

Analysis for the Temporal Variation of the Axis of the Tsugaru Warm Current 198
First, we defined twenty-five sub-regions that is long in the north-south direction (Fig. 199 1c; R1-R25), and made spatial mean of zonal velocity in the east-west direction in the 200 subregion. Further, temporal mean of each 6-hour concerning the spatial mean was calculated 201 in each sub-region, to obtain the north-south distribution of the zonal velocity along each sub-202 region. Then, the latitude where mean zonal velocity showed the maximum was defined as the 203 axis of the TWC. We investigated the seasonal mean location of the axis as well as its standard 204 deviation (Figs. 2 and 3). We also focused shorter-term variation of the axis (some examples 205 are shown in Fig. 4), and calculated spectrum of the temporal variation of the latitude of the 206 axis in each sub-grid, using data from 2018 to 2019 ( Fig. 5; there was no missing of the HFR 207 data during the duration, but 2017). Moreover, we obtained low-pass-filtered data using a 5th 208 butterworth filter that has the cutoff timescale of 10-days ( Fig. S1) in order to focus on 209 variations from 10 days to one month , for each three months. Then, we 210 made lag-correlation analysis of the time-series data with the low-pass concerning each sub-211 region in relation to that in the reference sub-region near the eastern neck of the channel (R1; 212 140.96-140.04°E; Fig. 1c), expected as the region where disturbance of the axis would be 213 generated (Fig. 6). The timescale of the correlation peaks was regarded as the lag of arrival of 214 the disturbance, and using the distance between the reference sub-region and each sub-region, 215 propagation speed of the disturbance was estimated in each season (winter: January-March, 216 spring: April-June, summer: July-September, autumn: October-December) for each year (Fig.  217   7). Observations of temperature, salinity, and pressure were made as conductivity-226 temperature-depth (CTD) observation in the cruises, using SBE 911 plus (Sea-Bird Scientific, 227 Inc.). Following the algorithms of UNESCO (United Nations Educational, Scientific and 228 Cultural Organization) (1983), depth was calculated from the value of the pressure and the 229 latitude of the stations. Then, each 1 m mean of temperature, salinity, and pressure was 230 estimated using linear interpolation. The potential density anomaly, σθ, was calculated using the 231 temperature, salinity, and pressure of each 1 m following Gill (1982). Then, an isodepth mean 232 of σθ in each season was calculated again (Fig. 8). After that, geostrophic velocity was 233 calculated following Pond and Pickard (1986) from each seasonal isodepth mean properties 234 between the adjacent stations ( Fig. 9). The reference level was set to the bottom. Sugimoto and . Therefore, it should be treated with caution for assumption of 245 the baroclinicity. In summer, intense pycnocline was reported (e.g., Matsuura et al., 2007;246 Saitoh et al., 2008), which implies an applicability of the two-layer model (e.g., Pedlosky, 1987). 247 On the other hand, in winter, it is well known that surface mixed layer is developed and density 248 is vertically homogeneous (e.g., Sugimoto and Kawasaki, 1984). Thus, it is expected that 249 assumption of baroclinicity probably does not match well in winter, but we included winter in 250 the present investigation for comparison. In spring and autumn, stratification would be weaker 251 than that in summer. For this reason, we also employed the f-plain model that has an assumption 252 of continuous stratification as well as constant vertical shear (Eady, 1949). 253 Using isodepth mean of the seasonal mean density anomaly from station SE3 to SE7, 254 ‹σθ›SE, we defined the depth of the boundary between the upper-and lower-layer as follows: 255 where σ1 and σ2 were potential density anomaly at 10 m and 250 m of ‹σθ›SE, respectively. The 257 depth has the potential density anomaly of σr was defined as H1, that is the upper-layer thickness 258 (2) 262 where K, U1, and U2 are the total wavenumber, the mean velocity of the upper-, and that of the 263 lower-layers, respectively. And 264 where Hn is the thickness of the n-th layer, and g' is the reduced gravity calculated as follows: 266 where g is the gravitational acceleration (we employed it as 9.8 m s −2 ), and ρ1, and ρ2, are mean 268 density in the upper-and lower-layer, respectively. We defined the reference density, ρ0, as 1026 269 kg m −3 . We employed the inertial frequency at 41.5°N (f41.5°N = ~18.1 hour). 270 The instability occurs when K 2 < 2/R1R2. Assuming the wavenumber of the disturbance 271 observed in the strait would be small sufficiently for such instability, we employed the 272 propagation speed of the instability (real part of the Eq. 2), as mentioned in Itoh and Sugimoto 273 (2008), as follows: 274 .

277
The upper-layer thickness, H1, was calculated as mentioned above, and the lower-layer 278 thickness was defined as the difference from 300 m minus H1, assuming that typical water depth 279 in the eastern part of the Tsugaru Strait beneath the axis is about 300 m (Fig. 1b). Then, U1 (U2) 280 was estimated using the spatial mean the geostrophic velocity in the upper-layer (lower-layer) 281 along the SE-line (generally stations SE3-SE7, but SE4-6 in winter; Fig. 10b) in each season. 282 When the horizontal wave number K is sufficiently smaller than 1/Rn, in other words, the 283 wavelength of the frontal wave is far longer than the deformation radii, the Eq. 5 can be further 284 simplified as follows: 285 .
(6) 286 This equation indicates that the propagation speed, c, takes a value between U1 and U2 with 287 1/Rn 2 , as the weighting function. 288 In addition to the two-layer model, for comparison, we calculated the phase speed of 289 the baroclinic instability in the continuous stratification and constant vertical shear of zonal 290 velocity following Eady's theory as follows: 291 where Us is the surface velocity, and = LDK. LD is deformation radius defined by LD = NH/f0 293 (N is Brunt-Väisälä frequency in the continuous stratification as mentioned later; H and f0 are 294 layer thickness and inertial frequency at the reference latitude, respectively). Note that 295 considering occurrence of the instability, we defined the propagation speed in the Eady's case 296 as a real part of the Eq. 7, that is cE = Us/2. Here, Us was calculated as a mean geostrophic 297 velocity for upper 10 m. 298 It should be also noted that in order to determine the wavelength of the disturbance in 299 each season, we employed the maximum growth rate of Eady's case, =1.61. We calculated 300 N as follows: 301 For estimation of LD, H and f were set as 300 m and f 41.5°N, respectively. Using these equations 303 and parameters, we calculated the propagation speed of the baroclinic instability in some cases, 304 and compared them to the propagation speed of the observed disturbance of the TWC's axis in 305 each season (Fig. 7). west of the Shiriya Spur. With respect to the east of the spur, the velocity was slow in winter 319 and spring ( Fig. 2a and b, respectively). In contrast, relatively larger velocity and somewhat 320 straightforward flow pattern in the east-west direction was observed in summer (Fig. 2c). 321 Standard deviation of the axis latitude generally increased to the downstream especially in the 322 region of 141.0-141.6°E, that is west to the Shiriya Spur (Fig. 3). As an exception, in the season 323 of winter the standard deviation showed a small peak at ~141.4°E, at the west-side of the Shira 324 Spur (Fig. 3a). In spring, the standard deviation increased monotonically with increase of the 325 longitude in the region west of 141.8°E (Fig. 3b), while in summer, the standard deviation 326 increased steeply in the range of 141.4-141.6°E (Fig. 3c). Concerning autumn, the distribution 327 of the standard deviation in October (December) was similar with that in spring (winter) (Fig.  328   3d). 329 Besides the seasonal movement of the axis as mentioned above, shorter-term 330 oscillation within several dozen days was observed. We showed some examples of such 331 variation as Fig. 4. In summer of 2017, large amplitude oscillation of the axis in the north-south 332 direction was recognized especially north the Shiriya Spur as ridge-shaped distribution that has 333 one north convex peak with the east-west scale of ~50 km (Fig. 4a). On the other hand, in 334 winter of 2018, short-term variations were also active (Fig. 4b), but multiple peaks of the 335 meander were demonstrated, and the horizontal scale in the east-west direction of the wave-336 like meandering (peak-to-peak) was inferred as ~40 km. The short-term variations were also 337 observed in the other seasons (not shown). 338 We estimated power spectral density concerning the oscillation of the axis in each sub-339 region using data from 2018 (January 1 st ) to 2019 (December 31 st ) when the surface velocity 340 continuously observed (Fig. 5). The spectrum indicated remarkable peaks around timescale of 341 13.66 days as well as that of double of it (27.32 days) in the western regions from the eastern 342 neck of the channel (R1) to the Shiriya Spur (around R12; Fig. 1b and c). Peaks of the timescale 343 of ~13.7 days and ~27.3 days became obscured in the regions east to the spur. The variation 344 with ~13.7 days was consistent with that reported near the eastern neck of the channel (around 345 Esan, Fig. 1b) by Tanno et al. (2005). 346 In order to examine the relationship of the periodical disturbance among each sub-347 region, we defined the sub-region R1 (Fig. 1c) as the reference where the disturbance was 348 expected to be generated, and then, we calculated lag correlation of the time-series of the axis 349 latitude between the reference sub-region and other sub-regions (R2-R25) (Fig. 6). In order to 350 focus the variation that has longer timescale than 10 days , we calculated the 351 low-pass-filtered data using the fifth power butterworth filter that has the cutoff timescale of 352 10-days (Fig. S1). Significant positive peak was recognized in R2-16, showing increase of the 353 lag with the increase of the distance from the reference sub-region (Fig. 6). The lag peaks 354 showed a cyclical characteristic in each sub-region with a cycle of ~14 days (Fig. 6). 355 We plotted the lag-time of the correlation peaks (shown by triangles in Fig. 6) 356 concerning the positive range (y-axis), against the distance from the reference sub-region (x-357 axis) (Fig. 7). Here, in addition to the first cycle, the lag of the second cycle starting at 13.7 358 days, is also shown as the gray plot. The lag-correlation was calculated in four seasons (3 359 months) of each year (2017-2019). We also estimated the timescale of advection estimated 360 from the mean surface velocity U1 from R1 to R25 (gray broken lines with smaller slope in Fig.  361   7). Linear increasing of lag-time of the observed disturbance with increase of the distance 362 (symbol plots in Fig. 7) was clearly demonstrated in spring and summer. The slopes of the 363 disturbance (symbol plots in Fig. 7) indicated seasonal variation, showing the largest angle in 364 spring. We regarded the slope as the propagating speed of the propagation of the axis 365 meandering. That is, it was suggested that the propagation speed of the observed disturbance 366 became slowest in spring. In winter, propagation of the disturbance of the TWC's axis was 367 unclear in 2017 and 2018 (Fig. 7d). To sum up, the results showed that the longer timescale 368 concerning the propagation of the disturbance was frequently recognized than that estimated 369 from the surface advection, especially in the seasons from spring to autumn in the regions west 370 of the SE-line (Fig. 7a-c). 371 The slower propagation speed than that of advection suggested the disturbance of the 372 axis would not be simply advected by the surface current. Thus, we suspected the propagation Introduction. Since meridional range of the frontal disturbance in the strait is relatively smaller 377 (Figs. 3 and 4) than those reported by the previous studies in the western boundaries, thus, it is 378 easy to think that the f-plain assumption seems to be reasonable. Whereas, structure of 379 stratification in the strait was known to be drastically changed in each season as mentioned 380 above (e.g., Nishida et al. 2003;Saitoh et al., 2008). Thus, to examine the application of the 381 two-layer baroclinic instability theory, we would demonstrate the seasonal vertical structure 382 across the strait concerning the density and velocity in the next subsection.  (Table 2). 395 Seasonal mean of the salinity showed that higher salinity water located the southern 396 side of the strait (Fig. 8), indicating a remarkable front around the center of the strait (~41.7°N 397 except for winter; ~41.6°N in winter). The location of the front corresponded well to that of the 398 axis of the TWC (Fig. 2). Moreover, this salinity distribution suggested that high-temperature 399 and high-salinity water of the TWC was distributed along the southern coast, while lower- water of the TWC was highest in summer (Fig. 8b). In autumn, salinity contrast in the north-404 south direction weakened showing a general increase of the salinity (>34.8 psu) in the strait 405 (Fig. 8c). 406 Also, seasonal mean transection along the SE-line of the potential density anomaly, σθ, 407 indicated remarkable variation, showing strong (weak) stratification in summer (winter) (Fig.  408 8). In winter, mean σθ in the channel were estimated as ~26.5 σθ and vertically almost 409 homogeneous. In contrast, steep surface pycnocline at the subsurface, ~50 m, was estimated as 410 a mean distribution in summer, showing that the surface (near bottom) potential density 411 anomaly was ~23.0 (~26.0) σθ. In spring and autumn, although vertical difference of the density 412 was weaker than that in summer, stratification was also developed. 413 Similar as the potential density anomaly distribution, geostrophic velocity distribution 414 along the same transection also showed remarkable seasonal variation (Fig. 9). In winter, the 415 velocity distribution was expected to be vertically homogeneous and the magnitude of the 416 eastward flow was weak. In the other seasons when stratification was developed, remarkable 417 eastward current core (>1 m s −1 ) was calculated near surface. In summer and autumn, opposite  Fig. 10a). The depths, H1, were indicated as magenta horizontal broken lines 429 in Figs. 8 and 9, and the estimation seemed reasonable as the boundary of the upper-and lower-430 layer over the transection. Note that the remarkable two-layer like distribution was 431 demonstrated in summer, but in the other stratified season (spring and autumn), the vertical 432 change in the density seemed somewhat gentle (Fig. 10a). This characteristic was similar 433 regarding seasonal change in the vertical structure of geostrophic velocity (Fig. 10b). Thus, not 434 only the approximation of the two-layer model, but also that of the continuous stratification was 435 also investigated in the present study as mentioned in the next subsection (3.3), using the Eq. 7. 436 437

Investigation of the propagation speed of the frontal disturbance 438
Using the parameters estimated in the previous subsection, and the Eqs. 5 and 7, we 439 calculated the propagation speed of the baroclinic instability in order to compare them to the 440 propagation speed of the disturbance observed by the HFR (Fig. 7). We employed the 441 wavelength of baroclinic instability of each season as 70 km (spring), 145 km (summer), 98 km 442 (autumn), and 43 km (winter), respectively, assuming the maximum growth case in the Eady's 443 model. This wavelength satisfies the instability condition of the two-layer model (e.g., the 444 equation 7.11.10 of Pedlosky, 1987). 445 In spring, the propagation speed of the observed disturbance was similar with that of 446 the two-layer model (0.14 m s −1 ; Fig. 7a) in the distance range of 30-80 km, although outliers 447 were shown in the downstream of the Shiriya Spur in 2018. In contrast, the propagation speed 448 of the Eady's model were somewhat slower than that of the observed disturbance. In summer, 449 the propagation speed of the baroclinic instability ~0.20 m s −1 was also consistent with that of 450 the observed disturbance especially in 2019 (Fig. 7b). It should be noted that, the zonal velocity In the present study, we examined the consistency of the propagation speed of the 474 disturbance of the TWC's axis observed by the HFR with the propagation speed based on the 475 theory of the two-layer baroclinic instability in the f-plane (Fig. 7). Then, close value of the 476 propagation speed of the disturbance of the TWC's axis observed by the HFR with that 477 calculated assuming the two-layer model was indicated in the stratified season, such as spring 478 and summer in a cycle of ~13.7 days (Fig. 7a, and b). In addition to the two-layer model, we 479 also examined the propagation speed based on the Eady's theory. Although the magnitude of 480 the propagation speed based on the Eady's theory was similar with that of the observed 481 disturbance in summer and autumn, however, they were dissociated in the downstream region 482 (>40 km, Fig. 7a) in spring. Also, it should be noted that, considering the characteristic of the 483 internal structure, the two-layer assumption also seemed better than that of continuous 484 stratification especially in summer. The two-layer assumption may be better for the autumn 485 season as well. The geostrophic velocity in the lower layer in autumn may perhaps be 486 overestimated, because some of the observed disturbances seemed slower than that of the 487 Eady's theory. In the SADPC observation, westward velocity was sometimes observed near the 488 bottom between the stations 3-4 (not shown), which may be due to topographic wave 489 propagation from the north related to the wedge-shaped topography in the eastern part of the 490 strait ( Figure 1b). Moreover, we would like to note that more careful investigations are needed 491 for determination of the dominating wavelength in the region, since the dominant wavelength 492 was assumed based on the Eady's theory. 493 The observed propagation speed in summer (0.20 m s −1 ) was similar with that 494 estimated by Itoh and Sugimoto (2008) near the Boso Peninsula ( Fig. 1a; 0 As other issues to be considered, we would like to mention the topography. An impact 505 of the characteristic topography on the instability was not considered in the present study. The 506 steep increase in amplitude over the Shiriya Spur in summer (Fig. 3c), and the bypassing 507 movement of the axis around the spur (Fig. 4a) may suggest the influence of the topography. 508 On the other hand, short-term variation of the axis also indicated a riding up of the TWC over 509 the spur sometimes (Fig. 4a). The outliers in Fig. 7a around the spur in 2018 (with lag of ~10 510 days) may be also related with the topographic effect. Y21 suggested that the TWC tends to 511 flow over the spur with increase of inertia in winter. Thus, the relationship between the 512 topographic effect and the path of the TWC should be also investigated as an issue to address 513 in relation to intensification of the inertia of the TWC. 514 515 Figure 4 implies that the length-scale of the frontal disturbance in the east-west 517 direction seemed smaller in winter than that in summer. In winter, as estimated LD was small, it 518 might occur the scale of the instability become smaller. However, as mentioned above, the 519 accuracy of the application of the baroclinic instability is suspicious for the homogenous density 520 distribution (Fig. 10a). Instead, barotropic disturbance along the shelf might be plausible. In 521 relation with the barotropic phenomena, using idealized topography, Ohshima (1994) pointed 522 out scattering of the Kelvin wave to the higher mode shelf waves at the eastern outlet of the 523 strait (northeast corner of the Shimokita Peninsula) based on a numerical model. Although there 524 is difference in the topography between the idealized one of Ohshima (1994) and reality, similar 525 scattering might be caused by the topography in the eastern neck of the channel (~141.1°N), 526 because the mouth of the strait becomes wider there in the eastward direction (Fig. 1b). These 527 shelf waves might affect the short-term disturbance of the TWC's axis along the north coast of 528 the Shimokita Peninsula in winter (Fig. 4). Especially higher mode of the shelf waves might 529 cause slow propagation of the disturbance of the axis (Fig. 7d, that in the range of 0-40 km of 530 2019). Moreover, the eastward propagation of the disturbance, which was more pronounced in 531 winter (Fig. 7d, 2018), may imply the influence of topographic trapping waves from north to 532 east associated with the wedge-shaped topography in the eastern part of the strait as mentioned 533 above (Fig. 1b). Wintertime behavior of the TWC should be examined using the HFR and 534 numerical model in future. 535 536

Impact of the Disturbance on the Short-term Variation of the Tsugaru Gyre 537
As mentioned in the Introduction, observational studies by Yasuda et al. (1988) have 538 reported short-term fluctuations of the large anticyclonic gyre which timescale was 20-30 days 539 (the direction of the major axis of the gyre's elliptical distortion rotated clockwise with these 540 fluctuations). Kubokawa (1991) showed in his numerical experiment that such clockwise 541 variations along the gyre can be successfully reproduced by varying the volume transport of the 542 TWC that has relatively lower potential vorticity by changing the latitude of the front of the 543 TWC at the outlet of the strait in the north-south direction. Therefore, it is quite possible that 544 the north-south frontal disturbances observed in this study could influence such short-term 545 variations of the large anticyclonic gyre. At the eastern outlet of the strait (e.g., R12; 141.42-546 141.50°E), a peak of ~27.3 days was also demonstrated in the spectrum of the frontal 547 disturbance (Fig. 5), which is consistent with the periodicity reported by Yasuda et al. (1988). 548 On the other hand, although the period of ~13.7 days was also recognized at the outlet of the 549 strait, the period is a little shorter than the timescale reported by Yasuda et al. (1988). Thus, it 550 is necessary to examine whether the shorter-term variability of the gyre at this timescale also 551 occurs, as a future work. Since the period of the frontal disturbance is in good agreement with 552 the ~13.7 days cycle (and its double length) that prevails in the Tsugaru Strait and the Soya 553 specific processes are involved between them. This is another issue that needs to be continued 556 to be examined. The short-term variability of the large anticyclonic gyre (gyre mode) is 557 considered to be closely related to changes in the fishing grounds of pelagic fishes around the 558 Shimokita Peninsula (e.g., Sato 1974, and thus, the elucidation and 559 forecasting of the excitation process is an important issue in terms of contributing to the 560 prediction of fishing grounds. If the relationship between the tide and the short-term variability 561 of the gyre is clarified, there is a high possibility that it will eventually contribute to the 562 prediction of the fishing grounds. 563 564

Tsugaru Strait 566
As pointed out by the many previous studies, the development of the frontal wave 567 could affect water mass exchange in the direction across the front (e.g., Yanagi et al., 1998;568 Kouketsu et al. 2005). In the region of the frontal disturbance was observed by the HFR, the 569 low temperature and salinity water called as the coastal Oyashio Water sometimes juts from 570 north (e.g., Kuroda et al. 2012;Wakita et al., 2021). Thus, the development of the disturbance 571 may contribute to the transport of such cold (warm) water to the northern coast of the Shimokita 572 Peninsula (coastal area of Hokkaido). Actually, the north-south contrast of salinity in the strait 573 rapidly weakened in autumn (Fig. 8c), the after season of summer when the remarkable 574 occurrence of the instability would be expected. Also, although it is a case in winter, coastal 575 monitoring conducted by the MIO revealed that intense negative anomaly from the annual mean 576 (about 4 °C lower) in 2014 around the northern coast of the Shiomokita Peninsula. In this year, 577 landing of the yellow goosefish (Lophius litulon) was poor, which brought large social impact 578 around the fisheries communities along the northern coast of the peninsula. Thus, investigation 579 of the mechanisms of such water exchange and subsequent forecast are important not only for 580 science but also for the society. 581 In addition, the instability may also affect vertical mixing of the waters through some 582 mechanisms such as local intensification of the vertical shear. Kouketsu et al. (2007) suggested 583 that intrusion of the denser water at the mid-depths could occur in the region of the crest to the 584 trough of the upper frontal wave in the Kuroshio Extension due to the baroclinic instability. 585 Thus, local enhancement of the turbulence associated with such intrusions could be also 586 expected, which might contribute to the characteristic distribution of the turbulence intensity 587 along stream direction. The grasp of the along stream structure of the turbulence and fluxes 588 would bring more accurate estimation of them in the frontal region as a progress study of the 589 previous understanding such as Kaneko et al. (2012;. The observations of the turbulence 590 and fluxes including low pH water will be conducted in near future. Moreover, these studies of 591 water mass exchanges and vertical mixing (including the present study) would also contribute 592 to improve understanding of the mechanism of the faster acidification the Tsugaru Strait than 593 that in the open ocean (Wakita et al., 2021).  We appropriacies the technical support staff from Marine Work Japan. We also thank T. Yasui, 650 T. Hashimukai, T. Nakayama, and S. In for their helpful comments. We refereed following 651 preprint studies in the present study; 1) H. Kaneko               Examples of lag-correlation (r) of some sub-regions in relation to the reference sub-region (R1) in 2017.
Triangles show peaks of the lag correlation. Thin lines denote 95 % con dence interval.

Figure 10
Typical vertical structure in each season of (a) potential density anomaly, σθ, and (b) zonal velocity in the Esan-Shiriya-line. Note that whereas (a) is the seasonal isodepth mean of σθ, from the station SE3 to SE7, (b) is the seasonal isodepth mean of the geostrophic velocity for the stations SE3-SE7 (as an exception, SE4-SE6 in winter). Triangles are the upper-layer depth, H1, in each season.

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