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Oyashio Southward Intrusion and Cross-Gyre Transport Related to Diapycnal Upwelling in the Okhotsk Sea

HIROAKI TATEBE AND ICHIRO YASUDA Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo,

(Manuscript received 3 March 2003, in ®nal form 5 April 2004)

ABSTRACT The intrusion of western boundary currents (WBC) across the wind-driven gyre boundary and associated cross-gyre transport are examined using layered numerical models with realistic topography and annual mean wind stress, with special emphasis on the Oyashio southward intrusion and North Paci®c Intermediate Water (NPIW) formation. Diapycnal transport due to strong tidal mixing around the in the North Paci®c Ocean is modeled by source/sink thickness restoring terms in the continuity equation to form the deep pycnocline observed in the Okhotsk Sea. About 3 Sv (Sv ϵ 106 m3 sϪ1) of the model diapycnal upwelling occurring along the Kuril Islands induces a meridional±diapycnal overturning circulation, and the transport is consistent with the estimates from recent observations with chemical tracers, GCM results, and the present study using observed density ®elds with enhanced diapycnal diffusivity around the Kuril Islands. The model with the diapycnal transport reproduced the realistic Oyashio southward intrusion, cross-gyre transport, and current dis- tributions in the ``Mixed Water Region.'' These features can be simply explained by a linear 2.5-layer reduced- gravity analytical model composed of a Sverdrup interior and WBC in geostrophic balance with the source/sink distribution. In this analytical model, the southern limit of the Oyashio can be de®ned as the latitude where the

coastal equivalent depth along the Japan coast (Dc) is equal to the depth at the western edge of the interior

(Dw). Here, Dc at an arbitrary latitude y can be written as a function of total amount of the diapycnal transport from the deeper layer through the pycnocline in the whole area north of y and total meridional

across y; Dw is mainly determined by Ekman pumping velocity at the sea surface based on the linear Sverdrup

relation. As the diapycnal transport becomes larger, Dc and the net cross-gyre transport increase, compensating vertical convergence of the diapycnal transport; the Oyashio can cross the wind-driven gyre boundary and intrude

more southward because the difference between Dc and Dw at the latitude of the wind-driven gyre boundary causes southward geostrophic transport along the east coast of Japan. These results explain the observed features that about 3±5 Sv of the cross-gyre Oyashio transport along the western boundary participates in the formation of NPIW.

1. Introduction subarctic front (e.g., Favorite et al. 1976) and intrudes into the subtropical gyre, conserving the properties on The Oyashio is the western in the its pathway in the vicinity of the east coast of Japan. North Paci®c Ocean subarctic gyre, and Oyashio water Then, Oyashio water ¯ows eastward along the Kuroshio is known to feed North Paci®c Intermediate Water Extension, being strongly modi®ed by the mixing with (NPIW) that is characterized by a salinity minimum and the warm and saline Kuroshio water to form new NPIW is one of the most remarkable features in the North that widely spreads in the ``Mixed Water Region'' Paci®c subtropical gyre (e.g., Sverdrup et al. 1942; Reid (MWR), de®ned here as the area between the Oyashio 1965; Talley 1993; Yasuda et al. 1996; Yasuda 1997). front and the northern edge of the Kuroshio Extension One of the major sources of Oyashio water and thus and the subtropical gyre. Along the east coast of Japan, NPIW is Okhotsk Sea Mode Water (OSMW; Kitani recent observations using direct current measurements 1973; Alfultis and Martin 1987; Talley 1991; Yasuda suggests that Oyashio water of about 3±5 Sv (Sv ϵ 106 1997; Yasuda et al. 2002). 3 Ϫ1 m s ) in the density range of 26.7±27.4 ␴␪ is supplied As reported by Yasuda (1997), Oyashio water that to the MWR (Yasuda et al. 2001; Hiroe et al. 2002; has OSMW characteristics ¯ows southward as a cross- Masujima et al. 2003). gyre ¯ow beyond the wind-driven gyre boundary and The origin of NPIW, namely, OSMW, has a low± potential vorticity signature in the density range of 26.6± 27.2 ␴ . Thick OSMW corresponds to deep pycnocline Corresponding author address: Dr. Hiroaki Tatebe, Department of ␪ Earth and Planetary Science, Graduate School of Science, University depths along the western boundary in the areas south of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. of the southern Kuril Islands and in the Okhotsk Sea. E-mail: [email protected] The depth of the isopycnal surface at 27.2 ␴␪ (Fig. 1)

᭧ 2004 American Meteorological Society

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a large amount of heat is released from the ocean to the overlying atmosphere (e.g., Nitta and Yamada 1989; La- tif and Barnett 1994; Nakamura et al. 1997; Qiu 2002). Noto and Yasuda (1999) showed that the population of the Japanese sardine is signi®cantly related to winter± spring sea surface temperature in the Kuroshio Exten- sion. Thus, modeling current variabilities and water properties in the MWR and the Kuroshio Extension is necessary to investigate possible impacts of the ocean on climate changes, ecosystem, and ®sheries. However, previous numerical simulations have not well repro- duced the observed current and hydrographic structure in the MWR and the Kuroshio Extension region. The most serious problem in modeling these regions is that typically the modeled Oyashio does not extend as far southward as in the real ocean. The long-term- averaged southern limit of the Oyashio is about 40ЊN (Yasuda 2003). The modeled Oyashio tends to separate from the western boundary around the wind-driven gyre boundary determined by the Sverdrup balance (42Њ± 47ЊN depending on wind dataset). Such premature sep- aration in numerical models is often accompanied by a northward bifurcation of the Kuroshio Extension along the Japan coast with unrealistic northward heat trans- port, causing the formation of unrealistic water masses FIG. 1. Observed depth of the 27.2-␴␪ isopycnal surface of Itoh et al. (2003). The areas with values larger (smaller) than 800 (600) m (e.g., Kobayashi 1999). Improvement of horizontal res- are heavily (lightly) shaded. The contour interval is 50 m. olution (⅛Њϫ⅛Њ or ®ner) has not solved the problem of the coastal intrusion of the Oyashio (Hurlburt et al. 1996). near the east coast of the is less Recent studies suggested that restoring model tem- than 600 m, while it is about 800 m near the Bussol' perature (T) and salinity (S) to observed ®elds in the Strait. Around the Kuril Islands, there exists a strong Okhotsk Sea can encourage the modeled Oyashio to tidal current through the straits that connect the Okhotsk cross the wind-driven boundary. In a GCM with hori- 1 Sea and the North Paci®c (e.g., Katsumata et al. 2001; zontal resolution of ¼Њ lon ϫ ⁄Њ lat including T/S re- 2004). The large change of the pycnocline depth along storing in the Okhotsk Sea and , the location the coast implies diapycnal transport due to turbulent of the Oyashio front and the distribution of NPIW are vertical mixing. Using two- and three-dimensional non- successfully reproduced (Ishizaki and Ishikawa 2004). hydrostatic models, Nakamura et al. (2000; Nakamura In a relatively coarse-resolution model (2Њ lon ϫ 1Њ lat) and Awaji 2002, manuscript submitted to J. Geophys. with subgrid-scale mixing parameterization, the realistic Res.) showed that the strong diurnal over the sills Oyashio intrusion is not reproduced, while the modeled between the Kuril Islands can cause a maximum dia- NPIW density range was close to the observed in the pycnal diffusivity greater than 103 cm2 sϪ1. Yamamoto case where T/S restoring in the Okhotsk Sea and Bering et al. (2001, 2002) showed the existence of the diapycnal Sea was included. (Yamanaka et al. 1998). Using a re- upwelling for the formation of OSMW using oxygen gional model based on the Princeton Ocean Model fo- isotopes (␦18O). cused on the Kuroshio±Oyashio con¯uence, Mitsudera Potential vorticity (PV) is an essential factor in ro- et al. (2004) emphasized the importance of restoring in tating geophysical ¯uid dynamics, and thus low-PV the Okhotsk Sea. In their numerical experiment where OSMW may alter the current structures and variabilities the T/S restoring in the Kuril Basin of the Okhotsk Sea in the MWR and the subtropical/subarctic gyre in the was included, the Oyashio realistically extends south- North Paci®c. For example, using an idealized numer- ward. In the case where the Okhotsk Sea was closed, ical model of the region, Spall (1996a,b) the Oyashio unrealistically retreats. suggested that the deep western boundary current, which Instead of the T/S restoring in the Okhotsk Sea, en- transports low-PV water southward in the intermediate hanced diapycnal mixing around the Kuril Islands and layer, could shift the Gulf Stream and lead to self-sus- sea ice formation can also yield a more southern Oyash- tained oscillations with interdecadal time scales in the io intrusion in a GCM with 1Њϫ1Њ resolution (Naka- current system. mura et al. 2004). With enhanced diapycnal diffusivity Many researchers have suggested the importance of (200 cm2 sϪ1) parameterizing the strong tidal mixing the MWR and the Kuroshio Extension as the areas where around the Kuril Islands, diapycnal upwelling of about

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e 4 Sv from the deeper layers is induced around the velocitywi , which prevents a layer thickness from be- e Okhotsk Sea, compared with the control experiment coming extremely thinner. The formula forwi follows without the enhanced diapycnal diffusion around the McCreary and Lu (1994): Kuril Islands. Nakamura et al. (2004) suggested the im- max(0, H Ϫ h )2 e ei portance of the diapycnal upwelling in the Okhotsk Sea wi ϭ , (1) in reproducing realistic dense shelf water, OSMW, and tHee distribution of NPIW. where He is a prescribed threshold and te is a speci®ed Although the modeling of the Oyashio intrusion, relaxation time. Following McCreary and Lu (1994) and

MWR, and the Kuroshio Extension have been recently Qiu and Miao (2000), we choose He ϭ 75 m and te ϭ improved in GCMs, the previous studies argued only 1 day. If hi becomes smaller than He, upward entrain- the importance of the T/S restoring or the enhanced ment velocity brings a water mass from the layer just vertical mixing in/around the Okhotsk Sea. The physical below and keeps hi greater than He. The upward en- mechanism that connects the existence of OSMW and trainment velocity occurs mainly in the subarctic region the Oyashio southward intrusion are far from clear. where Ekman pumping is upward. In the present study, we try to answer why the Oyashio The second type of diapycnal velocity is a restoring extends southward beyond the wind-driven gyre bound- process through mass exchange between the second lay- ary with a corresponding net cross-gyre transport and er and the deepest layer in the Okhotsk Sea. As noted how the southern limit of the Oyashio is determined, with in section 1, strong diapycnal mixing around the Kuril special emphasis on the diapycnal upwelling through the Islands can force the Oyashio intrusion to be more pycnocline from the deeper layers along the Kuril Islands southward in the GCM (Nakamura et al. 2004) where and emphasis on the large pycnocline depths correspond- low-PV water around the Kuril Islands is successfully ing to OSMW. In order to understand the questions clear- simulated due to the enhanced diapycnal mixing. In ly, we use simple numerical layered models as described terms of the meridional circulation cell, this enhanced in section 2. In section 3, we show the results from the mixing leads to greater upward ¯ux from the deeper numerical experiments and interpretation of the Oyashio layer to the intermediate layer around the latitude of the intrusion and the associated cross-gyre transport is at- Kuril Islands. tempted with a simpli®ed analytical model. In section 4, The layer model used in this study cannot include our results are compared with observations and the information about temperature and salinity as variables GCMs, giving reasons why both T/S restoring and en- of vertical strati®cation. Only isopycnal thickness can hanced diapycnal mixing around the Kuril Islands can be considered. As shown in Fig. 1, the depth of 27.2 lead to the realistic Oyashio intrusion. We summarize our ␴␪ in the Okhotsk Sea differs greatly from its depth in results brie¯y in section 5. the North Paci®c. This thick intermediate layer might be related to enhanced tidal mixing around the Kuril 2. Model description Islands and dense shelf water formation in the north- western shelf region of the Okhotsk Sea (e.g., Kitani The numerical model used in this study is a three- 1973; Alfultis and Martin 1987; Talley 1991; Yasuda layer primitive equation model on a sphere. The model 1997; Yasuda et al. 2002). Nakamura et al. (2002) sug- domain is the North Paci®c from 5Њ to 60ЊN and from gested that vertical diffusivity due to strong could 120ЊEto100ЊW. Isopycnal layers represent the surface be over 103 cm2 sϪ1 in the area shallower than 1000 m layer above the main thermocline, the intermediate layer around the Kuril Islands. Instead of enhanced diapycnal that corresponds to NPIW, and the deepest layer where mixing or T/S restoring to observations adopted in currents directly interact with bottom topography. The GCMs, vertical velocity wr is employed to form the thick model has realistic coastline geometry and bottom to- intermediate water in our model: wr is written as pography. In specifying these boundaries, we use the wr Ϫ1( h h ), (2) ETOPO-05 dataset of the National Oceanic and At- ϭ ␥ ␣ obsϪ 2 mospheric Administration. The model ocean, initially where ␥ is a restoring time scale (1 month), hobs is the at rest, is spun up for 30 years by the long-term mean observed layer thickness in the second layer, and h 2 is wind stress of National Centers for Environmental Pre- the second layer thickness at each time step. Using the diction±National Center for Atmospheric Research hydrographic datasets of Itoh et al. (2003) and the World (NCEP±NCAR) reanalysis data from 1979 to 1998 until Ocean Atlas of Levitus and Boyer (1994) and Levitus statistically steady state is attained. After the spinup, we et al. (1994, henceforth WOA94), hobs is estimated as integrate the model for an additional ®ve years. In the the isopycnal thickness between the potential densities following analysis, 5-day-averaged data in this period of 26.6 ␴␪ and 27.2 ␴␪ in the Okhotsk Sea. In Eq. (2), are used. See also the appendix, which describes details ␣ is set at 1.0. In the studies to elucidate the in¯uence on the model con®gurations. of OSMW on surface circulation described in section

In the present model, diapycnal velocity wi, de®ned 3, we control the given thickness by changing ␣. at the lower interface of ith isopycnal layer, is composed Using the above two kinds of the diapycnal velocity, e of two kinds of velocity. The ®rst is an entrainment the total diapycnal velocity is written as w1 ϭ w1 and

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e r w 2 ϭϩw2 w . After wi is obtained, its area-averaged different between the real ocean and the present model. value in the entire model basin is subtracted from a local In our model, the mass in the deepest layer is entrained value at each model grid point so that total mass in each into the middle layer through the process of thickness layer is conserved. restoring in the Okhotsk Sea. In the model basin ex- cepting the Okhotsk Sea, the same amount of mass re- turns to the deepest layer in order to conserve the total 3. Results mass in each layer. As a result of the vorticity input due a. Modeled Oyashio pathway and net cross-gyre to the diapycnal velocity through the upper interface of transport related to meridional diapycnal the deepest layer, the anticyclonic circulation in the in- overturning circulation terior basin and corresponding northward WBC are pro- duced in the deepest layer. On the other hand, in the The southward intrusion of the Oyashio across the real ocean the northeastward deep WBC along the Ja- wind-driven gyre boundary is realistically reproduced pan±Kuril±Kamchatka Trench is considered to be one when the second-layer thickness is restored to observed branch of the deep ocean circulation extending from the thickness in the Okhotsk Sea (left panels of Fig. 2). The Southern Ocean. wind-driven gyre boundary is located at around 42ЊN, Figure 4 shows the mean potential vorticity distri- namely, the location of the contour of zero Sverdrup bution in the second layer. Here, PV in the second layer transport (Fig. 3). In the upper two layers, the Oyashio is de®ned as ( f ϩ ␨ 2)/h 2, where ␨ 2 is relative vorticity ¯ows southward until it meets the northward branch of in the second layer. In the case with thickness restoring the Kuroshio Extension along the east coast of Japan in the Okhotsk Sea, relatively low PV is seen in the (Figs. 2a,c). The southern limit of the Oyashio intrusion MWR at 35Њ±45ЊN, where PV Ͻ 1.7 ϫ 10Ϫ7 mϪ1 sϪ1 is located at about 39.5ЊN, which is similar to the ob- is shaded. Low-PV water is also found in the Okhotsk served latitude (Yasuda 2003). In the present model, the Sea and along the east coasts of the southern Kuril Is- southern limit of the Oyashio is not especially variable lands and Japan. The areal average of PV from 30Њ to because the location of the limit is distant from the 45ЊN and from 145ЊE to 180Њ is about 1.8 ϫ 10Ϫ7 mϪ1 Kuroshio Extension where variations due to mesoscale sϪ1. In the case in which the Okhotsk Sea is closed (Fig. eddies are quite large. 4b), the area-averaged PV is 2.0 ϫ 10Ϫ7 mϪ1 sϪ1, which When the Okhotsk Sea is closed (right panels of Fig. is higher than in the restoring case. Clearly the water 2), the southern limit of the Oyashio is located at around properties in the subtropical region and MWR are al- 41ЊN and ¯ows more or less along the wind-driven gyre tered by the thick water that originates from the Okhotsk boundary. The northward branch along the east coast Sea. of Japan extending from the Kuroshio Extension is more Zonally integrated meridional±diapycnal circulation remarkable in this case than in the case of thickness patterns are shown in Fig. 5. We assume that the wind- restoring in the Okhotsk Sea. An anticyclonic cen- driven gyre boundary is located at 42ЊN because the tered at (38ЊN, 144ЊE), accompanied by the branch, can gyre boundary determined from the wind stress ®eld is be seen in Fig. 2b. In the case of thickness restoring in around this latitude (Fig. 3). In the case with the re- the Okhotsk Sea (Figs. 2a and 2c), the branch and eddy storing process in the Okhotsk Sea, the mean diapycnal are weaker. transport is upward (downward) in the subarctic (sub- In the deepest layer with thickness restoring (Fig. 2e), tropical) region. The upward transport from the deepest a relatively strong northward deep western boundary layer to the middle layer in the subarctic region mostly current (WBC) along the Japan±Kuril±Kamchatka occurs in the Okhotsk Sea through the restoring process. Trench and slow southward ¯ow in the interior forms As a result, the southward cross-gyre transport occurs an anticyclonic circulation. In contrast, when the in the upper two layers (Ϫ1.6 Sv in the ®rst and Ϫ1.7 Okhotsk Sea is closed, such northward deep WBC is Sv in the second layer). In the deepest layer, the cross- very weak (Fig. 2f). Using two years of moored current- gyre transport of 3.3 Sv ¯ows northward. In the case meter data from southeast of , Owens and War- where the Okhotsk Sea is closed, the upward transport ren (2001) showed that the mean ¯ow at depths deeper from the deepest layer and the meridional±diapycnal than 2000 m is directed northeastward, is relatively swift overturning circulation are much weaker and not sig- (0.08 m sϪ1) above this trench, and has a transport of ni®cant (Fig. 5b). 20 Sv. In our model, the northward transport across To examine whether the above cross-gyre transport 40ЊN in the deepest layer reaches 10 Sv from 144Њ to occurs in the western boundary region or the interior, 145ЊE, The northward velocity is about 0.05 m sϪ1. we illustrate the meridional transport distribution across Owens and Warren (2001) noted that the transport of 42ЊN, which is integrated from the western boundary 20 Sv might be exaggerated by 10 Sv due to broad (Fig. 6). As a boundary between the subtropical water mooring spacing. and the subarctic water, we use the potential vorticity The relatively strong northward deep WBC seen in front in the middle layer located at 165ЊE and 42ЊN our model agrees well with the observations. However, (Fig. 4a). The integrated transport at the front is about generation mechanisms for the deep current might be Ϫ1.5 Sv in each of the upper two layers. This value

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FIG. 2. Mean pressure ®eld representing the geostrophic ¯ow streamlines in the (top) ®rst, (middle) second, and (bottom) third layer. In the left panels, the second-layer thickness is restored to the observed thickness in the Okhotsk Sea. In the right panels, the Okhotsk Sea is closed. The contour intervals are 1.0, 0.5, and 0.1 kPa from the top to bottom panels. Negative values are denoted by dashed contours.

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FIG. 3. Sverdrup transport streamfunction (Sv) calculated using NCEP±NCAR mean wind stress. The shaded region denotes the sub- arctic gyre. agrees well with the meridional transport induced by the convergence of the upward transport in the subarctic region (viz., ␷1 and ␷ 2 in Fig. 5a). The net cross-gyre transport mainly consists of the advection of the mean layer thickness by the mean ¯ow. Contribution from time-dependent motions is negligible. The net south- ward transport in the upper two layers tends to occur in the Oyashio near the east coast of Japan, compen- sating the upward transport from the deepest layer in the subarctic region. Recent observations suggested that Oyashio water of about 3±5 Sv in the intermediate layer crosses the sub- arctic front and directly intrudes into the subtropical gyre along the east coast of Japan (Yasuda et al. 2001; Hiroe et al. 2002; Masujima et al. 2003). Talley (1997) FIG. 4. Mean potential vorticity distribution in the second layer for also reported that zonal transport of subarctic water in the cases in which (a) the thickness restoring is included in the the subtropical gyre across 152ЊN is estimated to be Okhotsk Sea and (b) the Okhotsk Sea is closed. The contour interval about 3 Sv. As compared with these observations, the is 1.0 ϫ 10Ϫ7 m Ϫ1 sϪ1. The areas where PV Ͻ 1.7 ϫ 10Ϫ7 are shaded. modeled Oyashio transport in the second layer (1.5 Sv) Areas with PV Ͼ 3.0 ϫ 10Ϫ7 are not contoured. is somewhat small. As shown in Fig. 5a, there exists upward diapycnal transport (w1) of 1.6 Sv from the sec- ond to ®rst layer in the subarctic region. This transport (2002) suggested that at least 1.0 Sv of surface water e comes from the entrainment velocityw1 in Eq. (1), sinks to intermediate depth through sea ice formation. which works to prevent the ®rst-layer thickness from This formation process could make the net Oyashio becoming extremely thin. If the isopycnal interface out- transport be 2.5 Sv (1.0 of DSW ϩ 1.5 of the modeled crop were included in our model or surface buoyancy transport in the second layer), which is comparable to ¯ux were given, this arti®cial diapycnal transport in the the observations (3±5 Sv). subarctic gyre might not occur; consequently the dia- From the results described in this section, the south- pycnal transport of 3.3 Sv from the deepest layer could ward intrusion of the Oyashio across the wind-driven ¯ow southward as net cross-gyre transport in the second gyre boundary reproduced in our model might be ex- layer. Since the net southward transport of the modeled plained as the meridional-diapycnal overturning circu- Oyashio tends to compensate the upward transport, it lation. Although the diapycnal upwelling in the Okhotsk might be expected that the Oyashio in the intermediate Sea and around the Kuril Islands that forces the over- layer transfers about 3 Sv of subarctic water. Dense shelf turning circulation has not yet been completely evident, water (DSW) formation in the northwestern shelf region recent observations (Yamamoto et al. 2001, 2002) seem of the Okhotsk Sea might be another reason for the small to support the existence of upwelling of deep water to cross-gyre transport in the second layer. Yasuda et al. the middle layer. The comparison between our model

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FIG. 6. Northward transport integrated from the western boundary across 42ЊN. The thick solid line represents the longitude of the PV front in the second layer. The solid, dashed, and dotted lines denote the transport in the ®rst, second, and third layer, respectively.

thickness by the mean ¯ow, since the location of the FIG. 5. Meridional±diapycnal overturning circulations and transport limit is distant from the Kuroshio Extension with active (Sv) for the cases in which (a) the thickness restoring is included in mesoscale eddies, and contribution from time-dependent the Okhotsk Sea and (b) the Okhotsk Sea is closed. In (a) the values motions is negligible. In fact, around the southernmost written in parentheses are the diapycnal transport in the Okhotsk Sea. latitude of the Oyashio the eddy horizontal advection of eddy PV is much smaller than mean horizontal ad- vection of mean PV (details are not shown here). In and the observations/GCM will be discussed again in addition, although the deep northeastward WBC, with section 4a. magnitude of 0.05 m sϪ1, is produced along the Japan± Kuril±Kamchatka Trench near the east coast of Japan, b. Analytical model for the Oyashio intrusion and deep ¯ows in the interior are quite weak and negligible cross-gyre transport when compared with the upper-layer ¯ows. Isostacy is thus achieved in the broad range of the model basin. In section 3a, we showed the results of the three-layer These suggest that the RG-2.5-layer model without me- numerical model the thickness restoring in the Okhotsk soscale eddies is appropriate for the present attempt to Sea. The three-layer numerical model is used because interpret the Oyashio southward intrusion and cross- it can take into account the effects of bottom topography gyre transport. and time-dependent motions that could affect the be- In the ocean as depicted in Fig. 7a, the ocean cir- havior of the western boundary current. Based on the culation is assumed to be composed of two parts. One results, the annual-mean southward intrusion of the is the geostrophic western boundary current region from Oyashio and associated net cross-gyre transport of sub- the western boundary at x ϭ xc to the eastern edge of arctic water are caused by the diapycnal upwelling in WBC region at x ϭ x . The other is the Sverdrup interior the Okhotsk Sea. w from x ϭ xw to the eastern boundary at x ϭ xe. The Next, we attempt to relate the Oyashio southward governing equations are written as intrusion and associated cross gyre transport to the dia- pycnal upwelling, based on a reduced-gravity 2½-layer Interior: analytical model (henceforth RG-2.5 layer). ␶ (h ϩ h ) ϩ , (3)١ ١h Ϫ g In the analytical model, mass exchange between the f k ϫ u111212ϭϪg upper layers and the motionless deepest layer is per- ␳ 01h mitted. (Thus, the model is described as a source/sink (h u ) ϭ w , (4)´ ١ model.) 11 1

(h ϩ h ), (5)١ As explained in the previous section, the Oyashio f k ϫ u2212ϭϪg southern limit is not variable and the cross-gyre trans- (h22u ) ϭϪw 1ϩ w 2, (6)´ ١ port mainly consists of the advection of the mean layer

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FIG. 7. Schematic view of the analytical model explained in the text. The thick solid arrows indicate the pathway of cross-gyre transport through the western boundary current (WBC) region. The zonal dashed line denotes the latitude of the southern limit of the Oyashio intrusion (y ϭ

yc), and the dash±dotted line the latitude of the wind-driven gyre boundary (y ϭ yGB). In the

Okhotsk Sea, the upward diapycnal transport (3) from the deepest layer occurs. At y ϭ yGB, there is no meridional wind-driven transport in the interior. Since the WBC must ¯ow southward

across y ϭ yGB to compensate for the diapycnal upwelling in the subarctic region, VWBC Ͻ 0. The

equivalent depth Dc(y ϭ yGB) at the western boundary is larger than the depth Dw(y ϭ yGB)

determined from the Sverdrup relation. On the other hand, at y ϭ yc (the southern limit of the

WBC), Dc(y ϭ yc) ϭ Dw(yc) and VWBC ϭ 0.

WBC: including the in¯uence of the diapycnal velocity w 2 (see the appendix): (h ϩ h ), and (7)١ f k ϫ u1ϭϪg 11212١h Ϫ g 2 f 2 xe 2 2 (h ϩ h ), (8) D(x, y) ϭϪ (wEkϪ w 2) dxЈϩDe (12)١ f k ϫ u2212ϭϪg ␤g2 ͵ x where the notation is the same as Eqs. (A1) and (A2). In the WBC, the depth-integrated (®rst ϩ second layer) and northward geostrophic transport V is written as WBC ␶ (ϫ , (13 ١ ´ wEk ϭ k 2 Dץ g2 V ϭ h ␷ ϩ h ␷ ϭ and (9) ΂΃␳ 0 f xץ WBC11222 f where De is the value of D at the eastern boundary x g 221 2 ϭ xe, ␤ the meridional gradient of the Coriolis parameter D ϭ (h12ϩ h ) ϩ h 1. (10) g2 f, and wEk Ekman pumping velocity. Thus, the offshore depth D at each latitude is given by Henceforth we call D an equivalent depth or, simply, w depth. Integration of Eq. (9) from x ϭ x to x ϭ x yields 2 f 2 xe c w 2 2 the total transport of the WBC at each latitude as Dw ϭϪ (wEkϪ w 2) dxЈϩDe . (14) ␤g2 ͵ xw g 2 22 On the other hand, the coastal depth D can be de- TWBC ϭ (DwcϪ D ), (11) c 2 f termined from mass balance. At an arbitrary latitude y, total Sverdrup transport across y can be written as where Dw (Dc) is the value of D at x ϭ xw (xc). The transport TWBC is dependent on the two depths: Dc is the xe coastal depth and D the other is the offshore depth. 1 ␶ (ϫϪfw2 dx. (15 ١ ´ w TSv ϭ k ␤␳͵ 0 Because T should vanish at the southern limit of the x ΂΃ WBC w [] WBC, we can de®ne the limit as the latitude where D c The total amount of the diapycnal ¯ux north of the ϭ D . Next, we will see how the two factors, D and w c latitude y is Dw, can be determined for given ®elds of wind stress and diapycnal velocity. yN Following Pedlosky (1996), within the framework of W ϭ w dS, (16) 2 ͵͵ 2 linear theory, we can obtain D in the interior region y

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where yN represents the latitude of the model northern boundary. The mass transports north of y must balance:

TWBCϩ T Svϩ W 2 ϭ 0. (17) Combination of Eqs. (11), (14), (15), (16), and (17) yields the equation for the coastal depth Dc as 2 f xe ␶ x 22 Dceϭ D ϩ W2 Ϫ dx , (18) g20͵ ␳ f x ΂΃ []w where ␶ x is zonal wind stress. Equation (18) shows that the coastal depth Dc at an arbitrary latitude y is deter- mined by meridional Ekman transport across y and the total diapycnal transport W2 north of y. Note that Dc is related to the total diapycnal transport W 2 and is not directly dependent on where the diapycnal velocity w 2 occurs in the area over which we integrate. Using Eqs. (11), (14), and (18), we can also obtain the equation for the transport of WBC, TWBC as 1 xxeef FIG. 8. Comparison of the coastal equivalent depth Dc at 42ЊN . ϫ ␶ dx ϩ wdx22Ϫ W ١ ´ TWBC ϭϪ k ␳␤0 ͵͵ ␤ (vertical axis) derived from the RG-2.5-layer model experiments (o) xx wwand based on the analytical model (*). The horizontal axis denotes (19) the amount of the diapycnal transport from the deepest layer north of 42ЊN. The modeled D (⌬) from the three-layer model and the Based on the above analytical model, we can explain c predicted Dc (ϩ) are also plotted. what determines the southern limit of the Oyashio and how the associated cross-gyre transport could be in- duced, associated with the diapycnal upwelling in the Figure 8 shows the comparison of Dc obtained from Okhotsk Sea. At the latitude of the wind-driven gyre the numerical model and evaluated using Eq. (18): Dc boundary (y ϭ yGB), the ®rst and second terms of the from the RG-2.5-layer numerical experiment and the rhs of Eq. (19) are zero. In the case where the diapycnal analytical model are in good agreement. Applying the upwelling transport W 2 is present, TWBC Ͻ 0aty ϭ analytical model to the three-layer numerical model re- yGB. This means that Dc becomes larger than Dw ,as sult, both the modeled and predicted Dc also have similar predicted by Eqs. (11) and (19) (Fig. 7b). Southward values (⌬ and ϩ). As Eq. (18) implies, the coastal depth geostrophic transport is induced in the WBC region at Dc becomes larger with the increase of W 2. Since the y ϭ yGB. Southward intrusion of the WBC and asso- Ekman transport is known a priori, the variation of Dc ciated cross-gyre transport beyond the wind-driven is dominated by W 2. gyre boundary must be present. Since the distribution The southern limit of the Oyashio predicted by the of Dw is regulated by wek in Eq. (14), the southernmost analytical model is con®rmed as follows: First, we cal- latitude, y ϭ yc , shifts more southward as Dc becomes culate the offshore depth Dw using Eq. (14). Then, the larger, corresponding to an increase of W 2 as predicted coastal depth Dc is estimated along the western bound- by Eq. (18). With regard to the cross-gyre transport ary using Eq. (18). In these procedures, w 2, W 2, and

TCGT across y ϭ yGB in the WBC, TCGT can be evaluated the wind stress distribution are given as external con- from Eq. (19) as ditions from the output of numerical experiments. As described before, D is equal to D at the southern limit T W . (20) c w CGTϭϪ 2 of the Oyashio. Therefore, the latitude corresponds to

The cross-gyre transport TCGT joins the subtropical gyre the intersection point of Dc and Dw at the western bound- circulation after subarctic water enters into the subtrop- ary x ϭ xc (Fig. 9). Here, Dw is calculated not at x ϭ ical gyre, as indicated by the thick solid curves with xw but at x ϭ xc. This is a good approximation because arrows in Fig. 7. On the other hand, in the case without the zonal integration of Eq. (14) from x ϭ xw to xc has the diapycnal transport, TWBC ϭ TCGT ϭ 0, namely, Dc a negligible effect on Dw. ϭ Dw at y ϭ yGB. Next, we compare the southern limit of the Oyashio To con®rm the above analytical model, numerical ex- derived from the numerical experiments to that pre- periments using the RG-2.5-layer model are carried out dicted by the analytical model. Since contours of equiv- using the same boundary conditions as the three-layer alent depth correspond to streamlines of the geostrophic model. In these experiments, the prescribed thickness transport integrated in the ®rst and second layer in unit in the Okhotsk Sea is varied by changing ␣ in Eq. (2) length [Eq. (9)], the modeled southern limit of the from 1.0 to 1.5. The experiment where the Okhotsk Sea Oyashio is determined to be the southernmost latitude is closed is also performed. of the indicator, which is the contour of the coastal

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FIG. 9. The coastal depth Dc (solid) and the offshore depth Dw (dashed) along the western boundary, which are evaluated by the analytical model described in the text. As an example, the values estimated using the output from RG-2.5-layer numerical model ex- periment (␣ ϭ 1.0) are plotted. The intersection point of the lines indicates the southernmost latitude of the Oyashio. equivalent depth starting at 43ЊN near Hokkaido. For example, the thick dashed line in Fig. 10a is the indi- cator, and its southernmost latitude, 40ЊN, shows the southern limit of the Oyashio.

Figure 11 tells us that as W2 becomes larger (viz., Dc becomes larger), the southern limit of the Oyashio moves farther southward. Quantitatively, the latitudes derived from the numerical model and from the ana- FIG. 10. Mean equivalent depth distributions derived from the RG- lytical model are in good agreement for the cases W 2 Ͻ 8 Sv. In the cases ␣ ϭ 1.4 and 1.5 where W Ͼ 8 2.5-layer experiments where (a) ␣ ϭ 1.0 and (b) ␣ ϭ 1.5. In this 2 ®gure, the thick dashed curve represents the indicator of Oyashio Sv, there are discrepancies; the Oyashio extends farther water at the coast of 43ЊN. The southern limit of the Oyashio (denoted southward in the numerical models than when predicted by dots) is taken to be the southernmost point of this curve. The from the analytical model. In these two cases, the contour intervals are 50 m. Oyashio extends beyond 35ЊN and reaches the eastward Kuroshio Extension (e.g., see Fig. 10b). The southern- most latitude of the Oyashio intrusion is found at the thickness restoring. Hence the northward branch of the same latitude where the swift Kuroshio Extension ¯ows Kuroshio Extension becomes weaker. eastward. In this situation, the Sverdrup relation be- It seems appropriate to mention the series of processes comes invalid because of the relatively strong nonlin- that lead to the southward intrusion of the modeled earity of the current ®elds. Oyashio. First, the diapycnal ¯ux from the deepest layer As described in section 3a, the northward WBC along makes the equivalent depth thicker in the Okhotsk Sea. the east coast of Japan branching from the Kuroshio Correspondingly, the coastal equivalent depth, Dc, along Extension is weaker in the case with thickness restoring the east coast of the Kuril Islands and Japan becomes in the Okhotsk Sea than when the Okhotsk Sea is closed. larger than in the purely wind-driven case. Assuming This weakening of the northward WBC can also be geostrophy, the Oyashio can ¯ow southward with the explained based on the analytical model. According to thickened coastal water until Dc ϭ Dw, where Dw is the Eq. (19), the transport of WBC is directed northward at interior thickness regulated by the Sverdrup relation. an arbitrary latitude in the subtropical gyre where the To explain the deep-ocean circulation, Stommel and wind stress curl is negative, and thus the northward Arons (1960) presented an idealized ocean composed branch of the Kuroshio Extension exists. The total up- of the Sverdrup interior with horizontally uniform dia- ward diapycnal transport north of the latitude W 2 works pycnal velocity and the deep WBC. The analytical mod- to decrease the northward transport in the case with el proposed in this section is a modi®ed version of Stom-

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FIG. 11. Comparison of the southernmost latitude of the Oyashio (ЊN; vertical axis) derived from the RG-2.5-layer model experiments and the ones based on the analytical model: horizontal axis and sym- bols as in Fig. 8. FIG. 12. Distribution of mean diapycnal velocity from the deepest layer in the three-layer numerical experiment with thickness restoring. mel and Arons (1960) with the effect of wind stress The contour interval is 5.0 ϫ 10Ϫ6 msϪ1; negative values are denoted ®elds. The model suggests that a simple system of typ- by dashed lines. The areas with values larger than 1.0 ϫ 10Ϫ5 msϪ1 ical Sverdrup dynamics in the interior and the WBC as are shaded. compensation of interior ¯ow can also explain the Oyashio southward intrusion and the associated cross- gyre transport in relation to diapycnal transport from Nakamura et al. (2004) reproduced the southward in- the deep layer. It should be noted that this analytical trusion of the Oyashio using a global GCM by setting 2 Ϫ1 model explicitly explains the effects of diapycnal trans- the diapycnal diffusivity coef®cient K␳ to 200 cm s port on the WBCs, which is also the main result of the around the Kuril Islands, based on the result of the present study. nonhydrostatic tidal model (Nakamura et al. 2000; Nak- amura and Awaji 2002, manuscript submitted to J. Geo- phys. Res.). According to the meridional±diapycnal 4. Discussion overturning circulation in their GCM experiment, the a. Upward diapycnal transport from the deep layer enhanced diapycnal mixing leads to 3 Sv of additional around Kuril Islands and its validity upward diapycnal transport in the North Paci®c sub- As described in the previous section, the diapycnal arctic region as compared with the control experiment transport from the deepest layer to the middle layer without the enhanced diffusivity. The additional dia- induced by thickness restoring generates the meridio- pycnal transport in the GCM is comparable to our three- nal±diapycnal overturning circulation where the dia- layer model result (3.2 Sv). pycnal transport between the deepest layer and the mid- Using the enhanced diapycnal diffusivity coef®cient 2 Ϫ1 dle layer is upward (downward) in the subarctic (sub- K␳ ϭ 200 cm s in the range of 1Њ centered at the tropical) region. In this section, we discuss the validity Kuril Islands, we estimate diapycnal velocity across the of such upward transport in the Okhotsk Sea in com- 27.2-␴␪ isopycnal surface. The annual-mean climato- parison with the results from the GCM and observations. logical hydrographic data of WOA94 are used in this Figure 12 shows the diapycnal velocity distribution estimate. The governing equation in this procedure is from the deepest to middle layer in the three-layer nu- the advection±diffusion equation on the isopycnal sur- merical experiment. Around the Kuril Islands, relatively face in steady state (similar to McDougall 1984): 2␳ץ ␳ץ ,large upward velocity of over 2.0 ϫ 10Ϫ5 msϪ1 is seen while it is small in the central the Okhotsk Sea. As w ϭ K␳ . (21) z2ץ zץ shown in Fig. 5a, the diapycnal transport is about 3.3 ss Sv in the area north of 42ЊN, including 3.2 Sv in the Note that Eq. (21) is not a one-dimensional equation, Okhotsk Sea. The diapycnal upward transport mostly but is reduced from the equation described on the iso- occurs around the Kuril Islands. pycnal surface

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␳ Based on the analytical model proposed in the present 2ץ ␳ 2␳ץ (ϩ u ´ ٌ ␳ ϩ w ϭ K ϩٌ ´(K ٌ ␳), (22 z2 shs study, the occurrence of the southward intrusion largelyץ z ␳ץ t sץ ss depends on the coastal depth of the pycnocline. Since where Kh represents the isopycnal diffusivity coef®cient both the T/S-restoring method and enhanced diapycnal -١s horizontal gradient operator along the isopycnal mixing method can reproduce OSMW, which is char and surface. The tendency, horizontal advection, and hori- acterized by a deep pycnocline, and its out¯ow to the zontal diffusion terms must be zero independently be- North Paci®c in the GCMs, the pycnocline depths along cause ␳ is constant on the isopycnal surface. Although the the east coast of Japan become larger than the ones zs is the coordinate axis normal to the isopycnal surface, determined by the linear Sverdrup vorticity balance. As here we regard this axis as vertical, assuming that the a result, the Oyashio can extend southward past the horizontal variation of zs is negligible. Based on Eq. wind-driven gyre boundary. (21) with the isopycnal depth data from WOA94, 4.4 Sv On the other hand, water mass exchanges between of upward diapycnal transport is obtained around the the subtropical and subarctic regions must be quite dif- Kuril Islands. This diapycnal transport is consistent with ferent between the two methods. The enhanced diapyc- the results of our numerical experiment and the GCM. nal mixing can lead to diapycnal transport through the Although observational knowledge of the upward dia- pycnocline, and the diapycnal transport converges in the pycnal transport has been quite limited in the Okhotsk surface and intermediate layers. Oyashio water thus di- Sea and around the Kuril Islands, recent observations rectly intrudes southward as cross-gyre transport so as support its existence. Based on chemical tracers ␦18O, to compensate the diapycnal convergence in the sub- Yamamoto et al. (2001, 2002) suggested that the dia- arctic region. This process is expected from the ana- pycnal transport in producing OSMW could be about lytical model in the present study. 2±3 Sv. This estimate is similar to the result of our In the case where the T/S restoring is applied, the model. deep pycnocline of OSMW is maintained by perpetual The upward diapycnal transport from the deep layer sources added to advection±diffusion equations of T/S along the Kuril Islands discussed above leads to the as forcing terms. If the diapycnal transport through the pycnocline would not occur in the T/S-restoring case, thickening of the intermediate isopycnal thickness and no cross-gyre Oyashio transport would occur. In the the ability to increase the coastal thickness along the GCM of Ishizaki and Ishikawa (2004) with the T/S re- western boundary as expressed in Eq. (18). Therefore, storing, the cross-gyre transport of the Oyashio is mostly the upward diapycnal transport is suggested to be an accomplished by small-scale eddies and the role of the important factor that determines the southern limit of mean ¯ow through the western boundary current region the Oyashio and the cross-gyre western boundary trans- is not signi®cant. The lesser importance of the mean port as explained by the analytical model. ¯ow in transporting Oyashio water into the subtropical In the North Paci®c, deep northward currents extend gyre might be explained by the lack of the diapycnal from the South Paci®c (e.g, Talley and Joyce 1992; transport through the pycnocline. Johnson and Toole 1993; Owens and Warren 2001). Although upwelling regions of the deep currents have c. Dependence of the Oyashio southern limit on wind not been clear, a part of the transport might be upwelled stress ®eld around the Kuril Islands through diapycnal mixing, and the diapycnal transport is likely to join the Oyashio as In the present study, the annual-mean NCEP±NCAR indicated by the present study. We can speculate that wind stress is used to spin up the numerical model. For the southward intrusion of the Oyashio and the corre- the separation of the western boundary current, distri- sponding cross-gyre ¯ow in the real North Paci®c are bution of the wind stress ®eld (especially the location related to the global thermohaline circulations. of zero wind stress curl) is known to be a crucial factor (e.g., Hurlburt et al. 1996). Therefore, not only the in- formation of low-PV water in the Okhotsk Sea en- b. Remarks on methods of T/S restoring and courages the southward intrusion of the Oyashio, but enhanced diapyncal mixing used in GCMs also the wind stress ®eld could alter the Oyashio. Figure 13 shows the mean pressure ®eld in the surface In order to force the Oyashio near the east coast of layer from the model driven by the annual-mean wind Japan to intrude more southward beyond the wind-driv- stress of Hellerman and Rosenstein (1983, hereinafter en gyre boundary, two methods have been proposed in HR) where the Okhotsk Sea is closed. It is obvious that previous studies using GCMs, as introduced in section the pathway of the Oyashio differs from the one driven 1. One is the T/S-restoring method where temperature by the NCEP±NCAR wind (Fig. 2b). The Oyashio seems (T) and salinity (S) in the GCMs are restored to obser- to intrude more southward along the coast of Japan for vations in the Okhotsk Sea (Mitsudera et al. 2004; Ish- the NCEP±NCAR wind, as compared with the HR wind. izaki and Ishikawa 2004). The other is the method of Also after the separation, the current structures are not enhanced diapycnal mixing, where diapycnal diffusivity similar between the two cases. For the NCEP±NCAR coef®cient K␳ is set to be large around the Kuril Islands wind, the Oyashio immediately loops back to the north (Nakamura et al. 2004). around 146ЊE. For the HR wind, it ¯ows eastward up to

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Hiroe et al. 2002; Masujima et al. 2003). Our model results might explain the observed direct intrusion that feeds NPIW as compensation of the diapycnal upwelling along the Kuril Islands. Using the numerical RG-2.5-layer model, we have ex- amined the sensitivity of the Oyashio southern limit to the prescribed thickness in the Okhotsk Sea. As the thick- ness becomes larger, so does the coastal equivalent depth along the east coast of Japan, and the Oyashio can intrude more southward. To explain how the limit is determined, we proposed an analytical model where the ocean is com- posed of the geostrophic WBC region and the Sverdrup interior. Based on the analytical model, the Oyashio ex- tends to the latitude where the coastal equivalent depth,

Dc, at the latitude of the Oyashio southern limit is equal

to the depth at the western edge of the interior, Dw. Here, FIG. 13. The mean pressure ®eld in the surface layer for the model Dw is determined by the linear Sverdrup relation [Eq. driven by the annual-mean wind stress of Hellerman and Rosenstein (14)], and Dc can be written as a function of the total (1983). The Okhotsk Sea is closed. The contour interval is 1.0 kPa. amount of the diapycnal transport W2 from the deeper layer in the entire area north of its latitude and the total 152ЊE. In terms of the velocity along the Kuril Islands, meridional Ekman transport at that latitude [Eq. (18)]. the Oyashio is stronger for the NCEP±NCAR wind than Generally the above results are valid for changes of the for the HR wind, whereas the Kuroshio and the Kuroshio Okhotsk Sea pycnocline depth, and the Oyashio south- Extension seem to be weaker for the NCEP±NCAR wind. ward intrusion and the cross-gyre transport through WBC

Thus the annual-mean southern limit of the Oyashio is are enhanced with the increase of Dc, corresponding to sensitive not only to the pycnocline depths along the the increased thickness and diapycnal transport in the Japan coast but also to wind stress ®elds. Okhotsk Sea. These results indicate that the diapycnal transport around the Kuril Islands is essential to the 5. Concluding remarks Oyashio southward intrusion. The annual-mean Oyashio southward intrusion and the cross-gyre transport that In the present study, we have investigated the south- feeds NPIW observed near the east coast of Japan are ward intrusion of the Oyashio using simple layered suggested to be directly connected with the diapycnal models with realistic topography driven by annual-mean upwelling around the Kuril Islands. wind stress of NCEP±NCAR and an analytical model. Fundamental understanding of the cross-gyre transport through the western boundary current (WBC) beyond Acknowledgments. This study was partly supported the wind-driven gyre boundary, which is essential to the by KAKEN (#13440139) from Ministry of Education, formation of North Paci®c Intermediate Water (NPIW), Culture, Sports and Technology, and by research pro- has been attempted. gramme DEEP from the Agriculture, Forestry, and Fish- Diapycnal ¯ux introduced in the present model to eries Research Council, and by funds from Center for reproduce the deep pycnocline in the Okhotsk Sea re- Climate System Research at the University of Tokyo. ¯ects recent observations (Yamamoto et al. 2001, 2002), We thank Dr. M. Itoh for providing data of isopycnal GCM results (Nakamura et al. 2004), and the present depth in the Okhotsk Sea and Dr. L. D. Talley (editor) diagnostic estimate described in section 4a with en- and an anonymous reviewer for their valuable comments hanced diapycnal diffusion. The diapycnal ¯ux occurs and English grammatical suggestions. We are grateful mostly around the Kuril Islands and the total amount in to Drs. Awaji and Nakamura at Kyoto University for the Okhotsk Sea is 3.2 Sv. In the real ocean, the above their comments on the present manuscript. The ®gures transport is considered to be induced by strong tidal in this paper were prepared with the GFD-dennou li- mixing along the Kuril Islands. brary and numerical experiments were carried out on The vertical convergence of the diapycnal transport the HITACHI SR8000/MPP at the Information Tech- in the upper layers leads to a net cross-gyre transport nology Center, University of Tokyo. of 3.0 Sv, which is accompanied by the southward in- trusion of the Oyashio across the wind-driven gyre APPENDIX boundary. The cross-gyre transport through the WBC agrees well with the total diapycnal transport around the Details of the Three-Layer Numerical Model Kuril Islands (3.2 Sv). Recent observations suggest the Oyashio crosses the subarctic front into the subtropical The governing equations of the present model are gyre along the east coast of Japan (Yasuda et al. 2001; written as follows:

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ui 1 ␶ interface between upper and intermediate layers is setץ ١p iϩ ١u ϩ f k ϫ u iϭ ´ϩ uii .t ␳␳h at 26.6 ␴␪ and the density of lower interface is 27.2 ␴␪ץ 00i The potential density of each layer is 25.1, 26.9, 27.7

١u ) ␴␪, and the initial thicknesses of the upper two layers A)´ ١ Ϫ ruihiϩ are 350 and 400 m. From the above parameters, the (uiiϪ u ϩ1) Ϫ reduced-gravity g1 and g 2 are set at 0.018 and 0.009 m Ϫ2 hi s , respectively. Along the model horizontal boundaries, no-normal max (0, w ) ϫ i and no-slip conditions are applied. The model grid has (u Ϫ u ) the horizontal resolution of 0.25Њ by 0.25Њ. The reso- ϩ iϪ1 i lution is necessary to ensure that the Kuroshio Extension h i separates at the Boso Peninsula and to permit existence of unstable eddies. Time step for the model integration ϫ max (0, ϪwiϪ1) is about 1200 s, satisfying the Courant±Fredrichs±Lewy (A1) condition. and Of the straits along the Kuril Islands, which connect the Okhotsk Sea and the North Paci®c, only two straits, h the Bussol' and the Kruzenshterna, are included in theץ . h u ) ϭ w Ϫ w)´ ١ i ϩ t ii iϪ1 i model because in the real ocean, water exchange acrossץ the Kuril Islands is considered to occur mainly through (A2) these two straits (e.g. Katsumata et al. 2001, 2004). In the model, width of the Bussol' (Kruzenshterna) Strait In the above equations, ui is the horizontal velocity vec- is about 1.25Њ (0.75Њ), and is set to be somewhat broader tor, hi is the layer thickness, pi is the pressure in the ith layer, k is a unit vector in the vertical direction, f is than the one in the real ocean so as to be resolved within the horizontal resolution of the present model. the Coriolis parameter, Ah is the coef®cient of the hor- izontal eddy viscosity, r is the coef®cient of the bottom drag, ␶ is the surface wind stress, ␳ is the reference 0 REFERENCES .is a horizontal gradient operator ١ water density, and Surface wind stress acts only on the ®rst layer, and the Alfultis, M. A., and S. Martin, 1987: Satellite passive microwave bottom drag works only in the deepest layer; wi denotes studies of the ice cover and its relation to oceanic the diapycnal velocity de®ned at the lower interface of processes. J. Geophys. Res., 92, 10 313±13 028. the ith layer. At the sea surface and bottom, the dia- Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical processes of the UCLA general circulation mod- pycnal velocity is set at zero. el. Meth. Comput. Phys., 17, 173±265. ١pi is calculated based Favorite, F., A. J. Dodimead, and K. Nasu, 1976: Oceanography of The pressure gradient term on the hydrostatic equation as the subarctic Paci®c region 1960±1971. Bull. Int. North Paci®c Comm., 33, 1±187. iϪ1 j Hellerman, S., and M. Rosenstein, 1983: Normal monthly wind stress over the world ocean with error estimates. J. Phys. Oceanogr., (h , (A3 ١p Ϫ ␳ 0 gjk١ ١pisϭ ͸͸jϭ1 ΂΃kϭ1 13, 1093±1104. Hiroe, Y., I. Yasuda, K. Komatsu, K. Kawasaki, T. M. Joyce, and F. Ϫ1 where gi ϭ (␳iϩ1 Ϫ ␳i)g␳ 0 (␳i is the ith-layer density) Bahr, 2002: Transport of North Paci®c Intermediate Water in the is the reduced gravity at the lower interface of the ith Kuroshio±Oyashio interfrontal zone. Deep-Sea Res., 49B, 5353± layer, g the acceleration due to gravity, and p is the 5364. s Hurlburt, H. E, A. J. Wallcraft, W. J. Schmitz Jr., P. J. Hogan, and surface pressure under the rigid-lid approximation. E. J. Metzger, 1996: Dynamics of the Kuroshio/Oyashio current The governing equations are solved in ®nite-differ- system using eddy-resolving models of the North Paci®c Ocean. ence form using the potential enstrophy±conserving J. Geophys. Res., 101, 941±976. scheme on an Arakawa staggered C grid (Sadourny Ishizaki, H., and I. Ishikawa, 2004: Simulation of formation and 1975; Arakawa and Lamb 1977). For the eddy viscosity spreading of salinity minimum associated with NPIW using a high-resolution model. J. Oceanogr., 60, 463±485. coef®cient Ah, the formula of Smagorinsky (1963) is Itoh, M., K. I. Ohshima, and M. Wakatsuchi, 2003: Distribution and used and written as formation of Okhotsk Sea Intermediate Water: An analysis of isopycnal climatological data. J. Geophys. Res., 108, 3258, doi: 2221/2 Ah ϭ max{A0, c⌬x⌬y[uxyxyϩ 0.5(u ϩ ␷ ) ϩ ␷ ]}. 10.1029/2002JC001590. (A4) Johnson, G. C., and J. M. Toole, 1993: Flow of deep and bottom waters in the Paci®c at 10ЊN. Deep-Sea Res., 30B, 371±394. 2 Ϫ1 where A 0 is a constant 300 m s , c is a nondimensional Katsumata, K., I. Yasuda, and Y. Kawasaki, 2001: Direct current values 0.05, and ⌬x and ⌬y are the grid spacing. The measurements at Kruzenshterna Strait in summer. Geophys. Res. bottom drag coef®cient r is 1.0 ϫ 10Ϫ7 sϪ1. Lett., 28, 319±322. ÐÐ, K. I. Ohshima, T. Kono, M. Itoh, I. Yasuda, Y. Volkov, and The potential density and layer thickness at rest are M. Wakatsuchi, 2004: Water exchange and tidal current through determined using WOA94. In this study the second layer the Bussol' Strait revealed by direct current measurements. J. is considered as the NPIW layer, so the density at the Geophys. Res., in press.

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