A numerical study of the Kuroshio-induced circulation in Tosa Bay, off the southern coast of Japan

Continental Shelf Research 53 (2013) 50–62

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Research papers

A numerical study of the Kuroshio-induced circulation in Tosa Bay, off the southern coast of Japan Hiroshi Kuroda a,b,n, Takashi Setou b, Kazuhiro Aoki b, Daisuke Takahashi c, Manabu Shimizu b, Tomowo Watanabe b a

Hokkaido National Fisheries Research Institute, Fisheries Research Agency, 116 Katsurakoi, Kushiro-shi, Hokkaido 085-0802, Japan National Research Institute of Fisheries Science, Fisheries Research Agency, 2-12-4 Fukuura, Kanazawa-ku, Yokohama-shi, Kanagawa 236-8648, Japan c Graduate School of Agriculture Science, Tohoku University, 1-1 Amamiya-machi, Tsutsumidori, Aoba-ku, Sendai-shi, Miyagi 981-8555, Japan b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 February 2012 Received in revised form 13 September 2012 Accepted 18 December 2012 Available online 26 December 2012

We performed a numerical experiment for the circulation in Tosa Bay using a triply-nested 1/50-degree model. This study revisits the climatological features of the Kuroshio-induced circulation in Tosa Bay by comparison with previous studies based on hydrographic observations. The model well reproduces the climatological features previously reported and reveals the following new findings: long-term mean circulation in Tosa Bay is characterized by an anticlockwise circulation (AC) spreading over the bay. The AC exhibits a cold-dome structure with deep baroclinic velocity shears. The velocity shears can be accounted for mainly by geostrophic shear. In this regard, however, the gradient wind balance is maintained because an ageostrophic velocity attributed to the momentum advection is caused by the state where the AC is intensified. The primary condition for controlling the development and decay of the AC is the mesoscale onshore–offshore movement of the Kuroshio axis; the secondary condition is a high-frequency submesoscale variation such as a Kuroshio frontal wave, which can be regarded as noise for the primary condition. Sequential development and decay of the AC is frequently simulated when the Kuroshio takes a nearshore path, and the frontal waves propagate eastward and interact with coastal water in Tosa Bay. That is, the horizontal advection of relative vorticity due to the frontal wave propagation plays an important role in controlling the sequential response. & 2012 Elsevier Ltd. All rights reserved.

Keywords: ROMS Tosa Bay Anticlockwise circulation Ageostrophic velocity Kuroshio and frontal wave Mesoscale and submesoscale

1. Introduction The continental shelf along the southern coast of Japan is characterized by a narrow shelf width typically less than 50 km and an irregular coastal topography composed from several capes and open-type bays (e.g., Fig. 1b). The western boundary current of the subtropical gyre in the North Pacific, namely, the Kuroshio with a large velocity ( a few knots) and strong horizontal shear flows along the southern coast. Since the northern part of the Kuroshio comes into intermittent contact with the coast through the narrow shelf, coastal waters are seriously affected by the Kuroshio (e.g., Kuroda et al., 2007, 2008, 2010). Although some studies such as Nishimura et al. (1984) regarded coastal waters between the Kuroshio and coastline as the ‘‘turbulent boundary layer’’, physical structure and dynamics there have not been sufficiently understood.

n Corresponding author at: Hokkaido National Fisheries Research Institute, Fisheries Research Agency, 116 Katsurakoi, Kushiro-shi, Hokkaido 085-0802, Japan. Tel.: þ 81 154 92 1723; fax: þ 81 154 91 9355. E-mail address: [email protected] (H. Kuroda).

0278-4343/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.csr.2012.12.005

This study focuses on circulation in Tosa Bay as a candidate of open-type bays facing the Kuroshio southwest of Japan, which exhibits semicircular shelf-slope topography between Capes Ashizuri and Muroto off Shikoku (Fig. 1b). The Kuroshio flows eastward south of this bay, basically taking a nearshore path, and occasionally the Kuroshio axis is displaced largely southward due to the generation and eastward propagation of a small meander (Nitani, 1975; Nagano and Kawabe, 2004). There are many studies investigating the sea surface current in Tosa Bay. Using long-term, regular geomagnetic electrokinetograph (GEK) measurements, Fujimoto (1987) divided spatial patterns of the surface current into five classes based on Yamashige’s (1979) findings. The most dominant current pattern is an anticlockwise circulation (AC) which can account for 23% of the total measurements. The appearance of the AC seems to be related to a nearshore path of the Kuroshio on the basis of his schematic view. The AC appears during the non-large-meander period more frequently than during the large-meander period because the Kuroshio tends to take an offshore path during the latter period. Awaji et al. (1991) performed barotropic numerical experiments and pointed out that the formation and disappearance of the AC can be induced by the combined effect of the

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131° 30’ 132° 30’ 133° 30’ 134° 30’ 135° 30’ 136° Fig. 1. Model domains. The 1/2-degree model domain corresponds to the whole region of (a). The 1/10-degree model domain is surrounded by a dashed square in (a). The 1/50-degree model domain is the whole region of (b). CTD data analyzed by KU08 were obtained from Stns. A and B, denoted by closed squares in (b).

onshore–offshore movements of the Kuroshio axis and the irregular topography of the continental margin. The time scale of the axis movement in their study is a few months. As for the Kuroshio disturbances with shorter time scales, using satellite thermal images, Toda (1993) showed that the Kuroshio frontal eddy generated near Cape Ashizuri propagates eastward and affects the sea surface temperature and thermal front in Tosa Bay. Yoshida and Sugimoto (2004) investigated the effects of Kuroshio frontal waves on circulation in a coastal water south of Japan using rotating tank experiments. They proposed that the spatial patterns of the surface current, as in Fujimoto (1987), can be explained as a sequential response of the coastal water to the frontal-wave propagation. However, since their study simplified some conditions, such as topography, stratification and the Kuroshio, further studies are desirable under more realistic conditions. To examine the relationships between current and temperature variations on the slope in Tosa Bay, Kuroda et al. (2008) (hereafter, ‘‘KU08’’) analyzed monthly regular ADCP and CTD measurements in the years from 1991 to 2004. The results from KU08 can be summarized as follows: when there is a strong along-isobath southwestward current on the slope, associated with the northwestern part of the AC, isotherms below the main thermocline on the slope are displaced upward. The acrossisobath gradient of isotherms seems to be related to thermal gradient balance. In this case, the Kuroshio also takes a nearshore path south of the bay. As a result, KU08 inferred that these results

can be interpreted by formation of the AC interacting with a cold eddy with deep baroclinic velocity shears, such as in the snapshots of CTD and ADCP measurements by Saito (1994). Several results from KU08 must be reexamined, because the datasets analyzed are limited temporally and spatially. For instance, the interval of regular hydrographic observation is roughly monthly. This means that high-frequency variation with time scales less than a month, such as induced by the Kuroshio frontal disturbances, cannot be resolved. Moreover, their CTD data is limited to two stations on the slope with a water depth of 650 m (Stn. A in Fig. 1b), and the shelf edge with a water depth of 200 m (Stn. B in Fig. 1b). Across-isobath thermal gradients below 200 m between the stations cannot be captured. In this study we perform a numerical experiment by developing a high-resolution shelf-slope model with a grid size of 1/50 degree, capable of resolving submesoscale variability near the Kuroshio front (Isobe et al., 2010, 2012; Sugimatsu and Isobe, 2011). The model is triply-nested to incorporate realistic mesoscale Kuroshio variability from the lateral boundary. Three models are forced by climatological monthly mean fluxes at the sea surface. The purpose of this study is to reproduce the climatological circulation in Tosa Bay induced by the Kuroshio and to revisit the climatological features of the circulation by comparison with the results from KU08. This paper is organized as follows: detailed designs of the numerical experiment are explained in Section 2. Overviews of the Kuroshio simulated in the 1/10-degree model are described in

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dynamics are parameterized by a K-profile parameterization (KPP) scheme (Large et al., 1994). The 1/50-degree model was driven by fluxes at the sea surface, the restoring force of tracers, and forcings on the lateral boundary. For sea surface fluxes, a climatological monthly mean of metrological elements was estimated from reanalysis products in the years 2003 to 2008. Wind velocity, air temperature, sea surface pressure, and relative humidity were derived from GPV/MSM (Saito et al., 2006), and net shortwave and downward longwave radiations were from JRA25/JCDAS (Onogi et al., 2007). In our model run, every internal time step, the sea surface fluxes are computed via the COARE bulk formula from the climatological monthly mean of the metrological elements and simulated sea surface temperature. The fluxes are then corrected with VAM proposed by Hanawa and Toba (1987). The correction coefficients adjusted for our model domain and bulk formula were estimated prior to the model run. For the restoring force of tracers, climatological monthly mean temperature and salinity were estimated for the model domain (Fig. 1b). The climatological monthly mean in the Seto Inland Sea (gray area in Fig. 1b) was computed from temperature and salinity data obtained at the Japan Oceanographic Data Center and the Ministry of Land, Infrastructure and Transport. The climatological monthly mean excluding the Seto Inland Sea was derived from WOA2001 (Conkright et al., 2002). Sea surface salinity in the model domain is restored with a 30-day time scale to the monthly climatology. In addition, the Seto Inland Sea is treated as a buffer region, where temperature and salinity are restored with a 30-day time scale to the monthly climatology. Total 20-year simulation is implemented using three models. The 1/50-degree model is integrated for the last five years from the 16th to 20th year. The initial value is created by bi-linear interpolation from output of the 1/10-degree model at 1 January in the 16th year. The lateral boundary value was extracted from daily mean output of the 1/10-degree model. Barotropic tidal height and current of four major tidal constituents (Matsumoto et al., 2000) are added to the daily lateral boundary value. However, we confirmed that tidal effects are almost completely

Section 3. In Section 4, we compare simulated results with observed results from KU08 and revisit the circulation in Tosa Bay in terms of long-term mean circulation, dynamical balance, and spatio-temporal variability. Findings from this study and discussion are given in Section 5.

2. Model configuration We developed a triply-nested high-resolution model using a Regional Ocean Modeling System (ROMS) (Shchepetkin and McWilliams, 2003, 2005; Haidvogel et al., 2008). The ROMS is a free-surface, terrain-following, S-coordinate, primitive equation ocean model widely used by many scientific communities in the world (e.g., Haidvogel et al., 2000; Ezer et al., 2002; Marchesiello et al., 2003). Three models with different resolutions (1/2, 1/10 and 1/50 degree) are connected by one-way nesting (Guo et al., 2003; Penven et al., 2006) (Fig. 1). The 1/2- and 1/10-degree models are necessary to simulate the realistic Kuroshio south of Tosa Bay and incorporate it into the 1/50-degree model. The 1/2-degree model covers almost the entire North Pacific, and the 1/10-degree model is limited to the western North Pacific around Japan, including the Kuroshio–Oyashio regions (Fig. 1a). All the models are forced by climatological monthly mean fluxes at the sea surface; however, the fluxes are different between these models. Numerical schemes, parameterization, parameter values, and integration schedules are also different. Configuration of the 1/2- and 1/10-degree model is summarized in Appendix, and that of the 1/50-degree model is explained below. The 1/50-degree model domain is shown in Fig. 1b. The vertical resolution is 21 levels. As tracer and momentum advection, third-order upstream-biased and fourth-order centered schemes are applied for the horizontal and vertical direction, respectively. A harmonic operator is adapted for horizontal mixing. Smagorinsky-type viscosity with a constant coefficient of 0.1 is used for momentum along the S-surface. Mixed layer

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negligible for our analysis and results (not shown). Hence, the tidal height and current are not filtered out in the subsequent analysis. We analyze the last 4-year simulation; 12-hourly snapshots of temperature and velocity, and 12-hourly means of individual terms in momentum equations. In the subsequent section the reference time of the model integration, above the 16th to 20th years, is changed and referred to as the 1st to 5th years.

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33° 3. The Kuroshio axis simulated by the 1/10-degree model

In this section we focus on three climatological features of the circulation in Tosa Bay simulated by the 1/50-degree model: longterm mean circulation (Section 4.1), dynamic balance (Section 4.2), and current–temperature variability together with the Kuroshio variability south of the bay (Section 4.3). Each subsection is separated into two parts: simulated results are compared with results from KU08 in the first, while several new findings from the simulation are demonstrated in the second.

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Before demonstrating simulated results of the 1/50-degree model, we firstly show the reproducibility of the Kuroshio axis variability south of Tosa Bay in the 1/10-degree model. Fig. 2a shows a spaghetti diagram of the Kuroshio axis in the 1/10-degree model. The axis is estimated by a method of Ambe et al. (2004) from a 3.8-day mean velocity at the sea surface in the 2nd to 5th years. The simulated Kuroshio is limited to the non-large-meander path throughout the period analyzed. For comparison, Fig. 2b shows the Kuroshio axis position during the non-large-meander period (1992–2003), derived from Quick Bulletin of Ocean Conditions published weekly or bi-weekly. Frequency distribution for a fixed longitude is overlaid. It can be recognized that the Kuroshio axis positions and all of the frequency distributions are very similar between Fig. 2a and b. The Kuroshio takes a nearshore path south of Tosa Bay in most cases, and occasionally the axis is largely displaced southward. To understand the frequency of such a large displacement, associated with the generation and propagation of a small meander, Fig. 3 shows the simulated axis distance averaged from Capes Ashizuri and Muroto. Intermittent large southward displacements exceeding one standard deviation, indicated by downward arrows, can be detected. The occurrence frequency of the large displacement is a few times per year in our simulation. This frequency is consistent with the report of Nitani (1975) that mesoscale disturbances of the Kuroshio axis are generated about twice or three times a year. Accordingly, the 1/10-degree model can sufficiently simulate the climatological features of the Kuroshio axis variation south of the bay and give realistic lateral boundary values to the 1/50-degree model.

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Fig. 4. (a) Long-term mean current velocity at the sea surface estimated from historical ADCP and GEK data by KU08, and (b) 4-year mean current velocity at the sea surface simulated by the 1/50-degree model. Current stability is categorized by four types of velocity vectors.

4.1. Long-term mean circulation 4.1.1. Validity of simulation Fig. 4a shows the long-term mean velocity and stability of sea surface current estimated from historical ADCP and GEK data by KU08, and Fig. 4b shows the 4-year mean current velocity and stability in the simulation. The stability is defined as the ratio of the magnitude of a mean current vector to a scalar mean current velocity (e.g., Egawa et al., 1993). The most remarkable feature of the circulation (that is, the AC) is successfully simulated. The spatial scale, central position, and southwestward current speed ( 0.2 m/s) of the AC are quite consistent between observation and simulation. The southwestward current of the AC also exhibits the maximum velocity trapped against the shelf-slope region, where the stability is relatively larger (0.5–0.7 for the observation (Fig. 4a) and 40.7 for the simulation (Fig. 4b)). These consistencies suggest that our simulation reasonably reproduces the mean circulation over Tosa Bay. It should be noted that there are a few discrepancies between observation and simulation. The simulated northeastward flows related to the Kuroshio are stronger. The simulated current stability tends to be larger over the whole of the model domain. This is partly because the simulated Kuroshio is restricted to the non-large-meander path (Fig. 4b), whereas the observed mean field (Fig. 4a) includes not only the non-large-meander but also the large-meander state, when the Kuroshio keeps taking an offshore path south of the bay (e.g., Kawabe, 1995). The larger

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current stability in the simulation may be also attributed to the simplified monthly mean fluxes at the sea surface.

4.1.2. New findings from the simulation Using the 4-year mean output, we describe the three-dimensional structure of the mean circulation over the bay, which has not been demonstrated from observations because of lack of enough hydrographic data.

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Fig. 5 shows the 4-year mean temperature at the 200-m depth. The local minimum temperature (o13 1C) can be detected around the center position of the AC (Fig. 4b), associated with a cold-dome or cold-eddy structure. This pattern is similar to snapshots of 100-m density observed by Saito (1994) when the AC developed. As for horizontal temperature gradients normal to the closed isotherm of 13 1C, the gradient seem to be larger near the bottom on the shelf-slope region in the northwest inshore side of the AC than the southeast offshore side facing the Kuroshio. To illustrate the inshore-side structure more clearly, Fig. 6 shows the vertical section of the 4-year mean east velocity and temperature on the meridional line in Fig. 5. On the whole, isotherms (thicker lines) tend to slope downward in the direction of the coast. Particularly large inclinations of isotherms are detected near the bottom on the shelf-slope region, where there are strong vertical shears of westward velocity (background color with thin line), as pointed out in Fig. 5. This temperature–velocity structure is associated with the thermal wind relation. For the region between the slope and shelf edge indicated by the double headed arrow, isotherms above 200 m are nearly parallel to the horizontal level, while isotherms below 200 m moderately slope downward toward the coast. Moderate velocity shears of westward velocity are also found below 200 m, suggesting a deep baroclinic structure of the AC. The vertical shear of along-isobath velocity and dynamic balance on the slope are further examined in the next section.

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4.2.1. Validity of simulation We initially examine the dynamical balance of the along-isobath current velocity on the slope in terms of geostrophic balance, as KU08 assumed. The meridional line denoted by the double-headed arrow in Fig. 6 is refocused on and referred to as ‘‘Line-AD’’. According to our simulation and KU08, the along-isobath east and northeast velocities at the sea surface averaged over Line-AD and Line-AB (a transect between Stns. A and B in Fig. 1b), respectively, are available as indexes of the intensity of the AC. The along-isobath velocities averaged over Line-AD and -AB are also referred to as ‘‘surface slope current velocities.’’ Although the locations of Line-AD and -AB are not identical, subsequent results are hardly sensitive to this difference (not shown). An absolute geostrophic velocity normal to Line-AD (Fig. 6) is estimated from 12-hourly mean of pressure gradient force term in the meridional momentum equation. Fig. 7 shows the 12-hourly time series of the simulated surface slope current velocity (thick gray line) and absolute geostrophic velocity (thin dashed line) at the sea surface which is averaged over Line-AD. These time series are highly correlated (r¼ 0.986) and exhibit a relatively small mean difference of 4.68 cm/s and a root mean squared difference

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(rmsd) of 7.20 cm/s. This indicates that the dynamic balance of the along-isobath velocity on the slope is controlled primarily by geostrophic balance, which supports the validity of the geostrophic assumption in KU08. To demonstrate quantitative validity of the simulated absolute geostrophic velocity, vertical profiles of an absolute geostrophic velocity averaged between the slope and the shelf edge are compared between the simulation (Line-AD) and observation (Line-AB) (Fig. 8). The vertical profiles are ensemble-averaged for ‘‘AC case’’ and ‘‘Non-AC case’’, which are classified according to the normalized surface slope current velocity ( ¼ ðuuÞ=su , where u is the surface slope current velocity, u the time mean, and su the standard deviation). The AC case is defined as when the normalized velocity is less than 0.5, associated with AC development, whereas the Non-AC case is when the normalized velocity is greater than 0.5, associated with AC decay. Three profiles are illustrated for each case (Fig. 8a,b), namely, the observed absolute geostrophic velocity from KU08 (thickest gray line), simulated absolute geostrophic velocity (thick black line) and east velocity (thin black line). As explained in the caption of Fig. 8, the estimation method of absolute geostrophic velocity is not identical between the model and observation. Nevertheless, the speed and vertical shear structure of the geostrophic velocity above 200 m are similar for both the AC case (Fig. 8a) and Non-AC case (Fig. 8b). Errors of mean velocity at each depth between the model and observation are 4 cm/s at a maximum. This suggests that the model properly simulates the density structure as well as the absolute geostrophic velocity on the slope.

4.2.2. New findings from the simulation Several new findings can be recognized from Fig. 8. The most important point to be emphasized is that the simulated geostrophic velocity shear below 200 m is more significant for the AC (Fig. 8a) than the Non-AC case (Fig. 8b), indicating a deep baroclinic structure when the AC develops. Our simulation thus supports the inference of KU08 that there is a strong geostrophic shear below 200 m when the AC develops. A geostrophic velocity shear can be also recognized for the 4-year mean (Fig. 8c), which mainly determines the vertical shear of westward velocity (thin line in Fig. 8c), as expected from a thermal-wind-like relation in Fig. 6. It should be noted that there

are differences between the east velocity and absolute geostrophic velocity, which increase toward the sea surface (Fig. 8c). The velocity difference is more remarkable for the AC case (Fig. 8a) than the Non-AC case (Fig. 8b). This means that not only geostrophic but also ageostrophic velocity becomes important for dynamical balance in the mean state, which is accompanied by the state where the AC develops. To clarify the cause of the ageostrophic velocity, Fig. 9 shows the vertical section of ensemble-averaged velocity for the AC case; the east velocity (Fig. 9a), absolute geostrophic velocity (Fig. 9b), their difference (Fig. 9c), and ageostrophic velocity (Fig. 9d) estimated from advection terms in the meridional momentum equation. To compute the ageostrophic velocity, 12-hourly mean of the advection terms is divided by the inertial frequency and ensemble-averaged for the AC case. The absolute geostrophic velocity (Fig. 9b) is larger than the east velocity (Fig. 9a) as well as Fig. 8. Their difference (Fig. 9c) is compensated by the ageostrophic velocity attributed to momentum advection terms (Fig. 9d). Moreover, it was confirmed that ageostrophic velocity from the other terms (e.g., vertical eddy viscosity and horizontal eddy viscosity) is about 1 cm/s at most and smaller than one from the momentum advection terms (Fig. 9d). As a result, the gradient wind balance is maintained on the slope when the AC is intensified. The source of the momentum advection will be discussion in terms of an eddy momentum flux in Section 5. Note that the zonal momentum balance differs from the meridional momentum balance. The meridional ageostrophic velocity estimated from the zonal momentum equation ( 2 cm/s at a maximum for the AC case) tends to be intensified near the bottom boundary layer (BBL) on the slope (not shown), about a half of which arises from the vertical eddy viscosity due to the bottom friction. The BBL may be also modified by replacing the KPP scheme with another turbulence model or by increasing the vertical resolution of the model. 4.3. Current and temperature variability on the slope 4.3.1. Validity of simulation In the Sections 4.1 and 4.2, we described the mean or the ensemble-mean state in Tosa Bay. In fact, however, the circulation in this bay is not static but responses dynamically to the Kuroshio variation south of the bay.

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Fig. 9. Vertical sections on the meridional line denoted by thick line in Fig. 5, such as (a) east velocity, (b) absolute geostrophic velocity, (c) their difference ((a) minus (b)), and (d) ageostrophic velocity attributed to momentum advection terms. Each velocity is ensemble-averaged for the AC case.

The simulated current and temperature variation on the slope in Tosa Bay is investigated together with the Kuroshio axis variation. In addition to the surface slope current velocity, we take up temperature at Stn. A (Fig. 6) which is averaged vertically from 200 m to 450 m. According to KU08, the vertical-mean temperature, referred to as ‘‘subsurface slope temperature,’’ can be utilized as an index of the vertical displacement of isotherms which are hardly affected by seasonal mixed layer. Fig. 10a shows the scatter plots of surface slope current velocity versus the Kuroshio axis distance averaged from Capes Ashizuri and Muroto. Fig. 10b is the same as Fig. 10a, except for the subsurface slope temperature. The Kuroshio axis distance was determined from 12-hourly snapshots of current velocity at the sea surface by the maximum velocities south of the capes. Quadratic regression curve based on the least-square method, mean (open circle) and standard deviation (vertical bar) for individual classes are overlaid by the red line for the simulation and the green line for the observation (KU08). Many features of these statistical values are consistent between the simulation and observation. The mean and quadratic regression curve indicate that as the Kuroshio axis approaches the bay, east velocity and subsurface temperature tend to decrease (Fig. 10a,b). The standard deviation also tends to decrease gradually, as the axis

distance decreases. The quadratic curves from the simulation and observation are quite similar, except for the 5- to 10-km bias of the mean axis distance. These results indicate that the simulated current and temperature on the slope in Tosa Bay respond realistically to the Kuroshio axis variation south of the bay. Fig. 11a and b shows the time series of the surface slope current velocity and subsurface slope temperature, respectively. The time series of 12-hourly snapshots and the time series low-passed by 30-day running mean filter are denoted by a thin and thick line, respectively. The current and temperature variations are correlated with each other, as reported by KU08. For the 12-hourly snapshot time series, a correlation coefficient of 0.59 from the simulation is almost equal to that of 0.53 from the observation (KU08). This correlation, which is statistically significant but is not robust compared with Fig. 7, indicates the decrease tendency of the subsurface temperature near the center of the AC when the AC is intensified.

4.3.2. New findings from the simulation This section initially takes up the 30-day low-pass time series (Fig. 11), which cannot be filtered out from the monthly data in KU08. Fig. 10c is the same as Fig. 10a, except for the low-passed time series. Compared with Fig. 10a, there are much smaller

H. Kuroda et al. / Continental Shelf Research 53 (2013) 50–62

0 mean axis position

axis distance (km)

50 R =0.23 P =1.74Q +11.78Q +40.15

100 150

AC case

200

normalized velocity 250

-3

-2

-90

-1

0

-30

-60

1

2

0

3

30

60

east velocity (cm/s) 0 mean axis position

axis distance (km)

50 100 R =0.46 P =6.32Q +14.73Q +38.37

150 200

normalized temperature 250

-3

-2

-1

7

8

0

9

1 10

2 11

3 12

temperature (C) 0

axis distance (km)

50 100

R =0.74 P =11.8Q +19.46Q +36.30

150 200

normalized velocity

250

-3 -90

-2 -60

-1

0

1

2

-30 0 30 east velocity (cm/s)

3 60

Fig. 10. (a) Scatter plots of surface slope current velocity versus the Kuroshio axis distance averaged from Capes Ashizuri and Muroto. (b) Same as (a), except for the subsurface slope temperature at Stn. A. (c) Same as (a), except for the time series low-passed by 30-day running mean filter. The horizontal thin line in each panel corresponds to the mean axis distance. Red and green lines denote quadratic regression curves from the simulation and observation (KU08), respectively. Binaveraged axis distance and its standard deviation are depicted by an open circle and a vertical bar, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

deviations of data points from the regression curve. The curvatures of the regression curves in Fig. 10a and c are different, but both regression curves qualitatively exhibit the same relationship between axis distance and surface slope current velocity. The 74% variance can be accounted for by the regression model. It was also confirmed that the 30-day time width of the low-pass filter

57

almost maximizes determination coefficient values of the two regression models in Fig. 10a,b. Let us focus on the low-passed time series of the Kuroshio axis distance (thick line) in Fig. 11c. The low-passed time series is characterized by intermittent large southward displacements of the Kuroshio axis lasting typically one to a few months. A similar feature can be identified in the Kuroshio axis position in the 1/10degree mesoscale model (Fig. 3). This indicates that the quadratic regression models (Fig. 10) express responses of the current and temperature in Tosa Bay (i.e., the AC) to the mesoscale onshore– offshore shifts of the Kuroshio axis. Hence, the mesoscale axis variations can be considered as the primary condition for controlling the AC variation. High-frequency variations can be thus regarded as a noise for the primary condition. The notable point is that, according to distribution of data points (closed circles) in Fig. 10a, the AC case is seldom found when the Kuroshio takes an offshore path south of the mean axis position (horizontal line in Fig. 10a), whereas the AC case is not necessarily detected even when the Kuroshio takes a nearshore path north of the mean axis position. This implies that high-frequency submesoscale variations play an essential role in the development and decay of the AC particularly under the nearshore Kuroshio condition. To illustrate a typical pattern of the AC variation when the Kuroshio takes a nearshore path, Fig. 12 shows daily snapshots of the sea surface temperature from 4 to 9 February in the third simulation year. The Kuroshio axis distance averaged from Capes Ashizuri and Muroto changes in a range of 11–37 km for the case of Fig. 12. This range is much smaller than the intermittent southward displacement of the axis (Fig. 3). Warm water (420 1C) around the Kuroshio is emphasized by the gray area. A thermal front is formed between the Kuroshio and coastal waters, and appears like a wavy structure. The crest and trough of the frontal waves, indicated by several types of arrows, propagate sequentially eastward. One of the crests comes into contact with Cape Muroto (Fig. 12c), so that warm water (420 1C) spreads from the vicinity of the cape into Tosa Bay anticlockwisely (Fig. 12d,e). Similar water spreading is also found at the western side of Cape Ashizuri. Fig. 13 shows daily snapshots of velocity at the sea surface. Strong velocities greater than 75 cm/s are emphasized by the gray area. Open circles denote the axis positions south of Capes Ashizuri and Muroto. A contour line depicts depth-integrated and closed stream function (0.5-Sv interval). The snapshots in Fig. 13d and e corresponds to the AC case. In this case, the duration of the AC case is 1.5 days. The current velocity in Tosa Bay changes drastically with the eastward propagation of frontal disturbances. In Fig. 13a, a single small cyclonic eddy is located in the eastern part of the bay. In Fig. 13b, another cyclonic eddy appears near the frontal trough in the western part of the bay (Fig. 12b). In Fig. 13c, the western cyclonic eddy propagates eastward, developing rapidly, and coalesces with the eastern eddy. In Fig. 13d, a combined cyclonic eddy develops and forms a typical AC spreading over the bay. Then, the AC decays rapidly and returns to a similar state to that in Fig. 13a (f). To clarify properties of the frontal waves sequentially inter¨ acting with circulation in Tosa Bay, Fig. 14 shows Hovmoller diagram of the meridional position anomaly of the Kuroshio front from January to February in the third-year simulation, when the Kuroshio keeps taking a nearshore path (Fig. 3). The frontal position is defined by the northern edge of a strong current area ( 475 cm/s) near the Kuroshio (gray area in Fig. 13). The meridional amplitude of the frontal waves is in a range of 0.1–0.31 (  10–30 km). The period is 4–6 days, the propagation speed is about 0.4 m/s, and the wavelength of 140–200 km. The orders of the magnitude are comparable to those of the frontal waves reported by Kimura and Sugimoto (1993).

58

H. Kuroda et al. / Continental Shelf Research 53 (2013) 50–62

east velocity (cm/s)

60 30 0 -30 -60 -90

1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112

2nd year

5th year

4th year

3rd year

temperature (°C)

13 12 11 10 9 8 7

1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112

axis distance (km)

2nd year

5th year

4th year

3rd year

0 50 100 150

1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112

2nd year

5th year

4th year

3rd year

Fig. 11. Time series of (a) surface slope current velocity, (b) subsurface slope temperature, and (c) the Kuroshio axis distance averaged from Capes Ashizuri and Muroto. Thin and thick lines indicate 12-hourly snapshot time series and time series low-passed by 30-day running mean filter, respectively. The horizontal dotted line in the upper part of each panel represents the period of the AC case. Downward arrows are the same as in Fig. 3.

Cape Muroto

30’

30’

Cape Ashizuri

33°

33°

30’

30’

132°

30’

133°

30’

134°

30’

135°

30’

30’

132°

30’

133°

30’

134°

30’

135°

30’

132°

30’

133°

30’

134°

30’

135°

30’

132°

30’

133°

30’

134°

30’

135°

30’

30’

33°

33° 30’

30’

132°

30’

133°

30’

134°

30’

135°

30’

30’

30’

33°

33°

30’

30’

132°

30’

133°

30’

134°

30’

135°

30’

Fig. 12. Daily snapshot of sea surface temperature. Upward and downward arrows indicate the crest and trough of the thermal front, respectively.

Note that the cyclonic eddies rather than the anticyclonic ones sequentially propagate in our model (Fig. 13), which makes the Kuroshio front wavy, like a frontal wave. The cyclonic eddies

(negative anomaly in the right panel of Fig. 14) tend to begin to propagate from the upstream and just the east of Cape Ashizuri, which can be thought as the generation area of the eddies.

u=0.36

59

>

>

H. Kuroda et al. / Continental Shelf Research 53 (2013) 50–62

axis dis.=34km

u=-1.45 (AC)

axis dis.=16km

1 m/s

1 m/s 30’

30’

33°

33°

30’

30’

133°

30’

134°

30’

135°

30’

132°

axis dis.=11km

u=0.80

30’

133°

30’

134°

>

30’

>

132°

135°

30’

axis dis.=27km

u=-1.19 (AC)

1 m/s

30’

1 m/s

30’

30’

33°

33°

30’

30’

133°

30’

134°

u=1.24

30’

135°

30’

132°

30’

133°

30’

134°

>

30’

>

132°

u=-0.07

axis dis.=37km

30’

135°

30’

axis dis.=24km

1 m/s

1 m/s

30’

30’

33°

33°

30’

30’

132°

30’

133°

30’

134°

30’

135°

30’

132°

30’

133°

30’

134°

30’

135°

30’

Fig. 13. Daily snapshot of sea surface current velocity. Open circles denote the Kuroshio axis position south of Capes Ashizuri and Muroto. The contour line denotes the closed stream function of volume transport integrated from the sea surface to bottom.

Jan. in the 3rd year Time

Feb. in the 3rd year

Cape TOSA Cape Ashizuri BAY Muroto

28

28

21

21

14

14

7

7

28

28

21

21

14

14

7

7

Cape Shiono

>

u

ð1Þ      where J ðA,BÞ ¼ @A=@x @B=@y  @A=@y @B=@x , curlZ ðAÞ ¼ @Ay =@x R0 R0 @Ax =@y and w ¼ g=r0 H zrdz. Moreover, u ¼ 1=H H ðui þvjÞdz is the depth-averaged velocity, H the water depth, f the Coriolis parameter, g the gravity acceleration, r the water density, r0 the reference water density, ta the wind stress, and ta the bottom stress. D¼DxiþDyj and A¼AxiþAyj represent the depth-averaged horizontal mixing and momentum advection terms, respectively. According to Eq. (1), the tendency of the vorticity on the left side is governed by the beta effect (first term on the right side), the topographic vortex stretching (second), the JEBAR (third), the sea surfacing forcing (fourth), the bottom damping (fifth), the horizontal mixing (sixth), and the advection (seventh). Fig. 15 shows major four term values in Eq. (1) averaged over Tosa Bay, such as the tendency, stretching, JEBAR and advection, which are denoted by subscripts of (i), (ii), (iii) and (iv) in Eq. (1), respectively. The sign of the tendency is reversed. Correlation and neutral regression analysis (Garrett and Petrie, 1981) showed that the largest correlation (r ¼0.92) is detected between the JEBAR and stretching, the second largest (r ¼0.84) is found between the tendency and advection, but gradients of the neutral regression line for each correlated pair are 0.79 and 0.59, which is not to equal 1. These indicate that the tendency (JEBAR) is roughly 

contour int. 0.05 degree

-2 -1 0 1 2

equation for depth-averaged momentum equations (e.g., Guo et al., 2003), which is likely reasonable for describing variations of the AC with a relatively large depth-average velocity accompanied by deep baroclinic velocity shears (Fig. 8a).   @ f curlZ ðuÞ ¼ uUrf þ ðuUrHÞ þ J w,H1 @t H ðiiiÞ ðiiÞ ðiÞ     ta tb curlZ þcurlZ ðDÞcurlZ ðAÞ ðivÞ þ curlZ r0 H r0 H

133

134

135

136

longitude (east)

Fig. 14. (Left panel) Time series of the normalized surface slope current velocity (thin line) and the surface current vorticity (dotted line) averaged over Tosa Bay (1303 300 –1343 E, 323 500 –333 300 N). The gray area represents the period of the AC ¨ case. (Right panel) Hovmoller diagram of an anomaly of the meridional position of the Kuroshio front, which is defined by the northern edge of a strong current region (475 cm/s) near the Kuroshio. The gray area represents a negative anomaly. The contour interval is 0.05-degrees latitude (  5.6 km).

The former and latter generation areas are consistent with reports from Akiyama and Saitoh (1993) and Toda (1993), respectively. To dynamically discuss the sequential development-decay process of the AC, we analyze the term balance of vorticity

60

H. Kuroda et al. / Continental Shelf Research 53 (2013) 50–62

Time

Jan. in the 3rd year 7

14

21

28

7

14

21

28

7

14

21

28

term value in the vorticity eq. (10-10s-2)

>

-2 -1 u 0 1 2

Feb. in the 3rd year

4

2

0

-2

advection

JEBAR

tendency

stretching

-4 7

14

21

28

Fig. 15. Upper panel is the same as the left panel in Fig. 14. Lower panel shows major term values in the vorticity equation for vertically-averaged velocity (Eq. (1)). Each term is averaged over Tosa Bay (1303 300 –1343 E, 323 500 –333 300 N).

balanced with the advection (stretching). Consequently, the sequential development and decay of the AC can be controlled mainly by the horizontal advection of relative vorticity induced by the eastward propagation of the frontal waves/eddies when the Kuroshio takes a nearshore path.

5. Summary and discussion We performed a numerical experiment for circulation in Tosa Bay using a triply nested 1/50-degree model capable of resolving submesoscale variability. The model successfully simulates climatological features of the Kuroshio-induced circulation in the bay which KU08 reported. New findings from this study are summarized as follows. Long-term mean circulation in Tosa Bay is characterized by the AC spreading over the bay. The AC is accompanied by a cold-dome structure with deep baroclinic velocity shears. The velocity shears can be explained mainly by geostrophic shear. In this regard, however, an along-slope ageostrophic velocity attributed to the momentum advection, which is intensified when the AC develops, contributes significantly to the across-slope momentum balance; namely, the gradient wind balance is maintained. The primary condition for controlling the development and decay of the AC is the mesoscale onshore–offshore movement of the Kuroshio axis. As the secondary condition, we propose a highfrequency submesoscale variation (roughly speaking, time scale o30 days) such as the Kuroshio frontal wave, which can be regarded as noise for the primary condition. The high-frequency variations play an essential role in the development and decay of the AC particularly under the nearshore axis condition. The sequential development and decay of the AC was frequently simulated when the Kuroshio took a nearshore path. In this case the Kuroshio frontal waves/eddies propagate eastward and interact with coastal water in Tosa Bay. The simulated frontal eddies are generated at the just east of Cape Ashizuri and the upstream of the cape. The generation areas are consistent with reports by the previous studies. Vorticity-equation analysis showed that the sequential development and decay of the AC can be controlled mainly by the horizontal advection of relative vorticity due to the propagation of the frontal waves when the Kuroshio takes a nearshore path. The above formation mechanism of the AC is partly similar to that proposed by Awaji et al. (1991). They studied the response of

Tosa Bay to the onshore–offshore movement of the Kuroshio with a time scale of a few months using a barotropic model. According to their study, the Kuroshio path moves shoreward, the northern part of the Kuroshio comes into contact with Cape Ashizuri, positive relative vorticity is generated near the cape, and the positive vorticity advected toward the downstream (i.e., the direction of Cape Muroto) develops the AC. Similarly, in our model, one of the generation areas of positive relative vorticity is near Cape Ashizuri, the positive vorticity is then advected to the downstream and develops the AC (Fig. 13a–d). A crucial difference from Awaji et al. (1991) is that the AC in our model hardly reaches a quasi-steady state even when the Kuroshio stably takes a nearshore path (Fig. 15). Under the quasisteady state in Awaji et al. (1991), the positive relative vorticity stably supplied from the cape is advected to the bay and balanced primarily with beta and horizontal viscosity (ref. Eq. (1)). In contrast, the supply and advection of the relative vorticity vary with time in our model due to generation and propagation of the submesoscale frontal waves (Figs. 12–15). It should be borne in mind that the duration of the AC cases in Figs. 14 and 15 is in a range of 0.5–5 days, while some of the simulated AC cases last longer than 20 days. In such cases, remarkable sequential development and decay of the AC is not simulated even though the Kuroshio takes a nearshore path. Vorticity–equation analysis using Eq. (1) (not shown) demonstrated that the magnitude of relative vorticity advected to/from the bay is smaller in the case of such a long duration than in the case of a sequential development and decay (Figs. 14 and 15). The tendency of the vorticity also fluctuates with a smaller variance. As a result, a relatively strong AC which is initially developed by the supply of positive relative vorticity is maintained, although the intensity of the AC changes with time. In addition, on the basis of our preliminary analysis (not shown), the magnitude of relative vorticity advection, affecting the AC duration, seemed to depend on the meridional scale of the frontal waves or the presence and intensity of the frontal waves propagating from the upstream of Cape Ashizuri. The mechanism to control the magnitude of the relative vorticity advection is an interesting issue but beyond the scope of this article, which will be the focus of future work. Next, we discuss the source of ensemble-mean momentum advection (e.g., Fig. 9d) in terms of eddy momentum flux, that is, to what extent high-frequency variations such as the Kuroshio frontal waves can contribute to the ensemble-mean momentum advection. Three-dimensional velocity at every internal time step (u) was separated into mean (u), and low-frequency (uL) and high-frequency (uH) components. The uL and uH components are divided by 30-day running mean filter, though it cannot completely decompose them. Using the separated velocities, the ensemble-mean advection terms in the momentum equation for the north velocity (v) can be decomposed into six terms: ð7Þ 1 1 ð1Þ ð2Þ ð3Þ rUðvuÞ ¼ rUðvu Þ þ rUðvL u þvuL Þ þ rUðvH u þ vuH Þ f f  ð4Þ ð5Þ ð6Þ þ rUðvL uL Þ þ rUðvH uL þ vL uH Þ þ rUðvH uH Þ ð2Þ where the longer upper bar indicates the ensemble mean. The above seven advection terms expressed as the flux form were computed on the meridional transect in Fig. 5, divided by the inertial frequency to convert ageostrophic velocity, ensemble-averaged for the AC case and the entire period of the 4 simulation years. The eddy momentum flux in Eq. (2) is shown in Fig. 16 as ageostrophic velocity averaged over the transect. For the 4-year mean (white bar), the largest eddy momentum flux arises from the mean velocity, (1), which accounts for 55% of the total momentum flux (7). The high-frequency eddy momentum flux (6) accounts for

H. Kuroda et al. / Continental Shelf Research 53 (2013) 50–62

21% of the (7). The (6) is comparable to the low-frequency eddy momentum flux (4). Since the ageostrophic velocity for the 4-year mean is 5 cm/s at the sea surface on the slope (Fig. 8c), the high- or the low-frequency eddy momentum flux accounts for 1 cm/s out of the 5 cm/s. The magnitudes of the (4) and (6) for the AC case (black bar) are also almost consistent with those for the 4-year mean (white bar). Meanwhile, the ratio of the (6) to the (7) for the AC case is 5%, which is smaller than the 4-year mean (21%) because the magnitude of the (7) becomes greater for the AC case. Finally, it should be remembered that our model was forced by monthly mean fluxes at the sea surface to simplify meteorological disturbances. We performed an additional experiment without sea surface fluxes. In this experiment seasonal stratification and mixed layer depth during winter in Tosa Bay could not be properly reproduced, but major features of the bay circulation shown in this study were retained (not shown). This implies that the lateral boundary forcings affect the circulation in Tosa Bay more significantly than the sea surface forcings. Meanwhile, some of large storm surges have been reported to occur occasionally around the bay (Ueno, 1981). Such higher-frequency meteorological disturbances, which are neglected in our model, may work 0.05

ageostrophic velocity (m/s)

0.04 0.03 0.02 0.01 0.00

(1)

(2)

(3)

(4)

(5)

(6)

(7)

-0.01 -0.02 -0.03

Fig. 16. The value of eddy momentum flux. A numeral in parenthesis corresponds to the term in Eq. (2). Each term value is divided by the inertial frequency, ensemble-averaged for the AC case (black bar) and 4 simulation years (white bar), and averaged over the meridional transect denoted by thick line in Fig. 5.

as a noise for the AC variation, the details of which should be clarified in future work.

Acknowledgments We would like to deeply thank the Agriculture, Forestry and Fisheries Research Information Technology Center for the computation resource of high performance cluster and vector computing systems. This study was supported by an expenses Grants project of Fisheries Research Agency and a SKED project of Ministry of Education, Culture, Sports, Science and Technology. Our grateful thanks are also extended to the editor and anonymous two reviewers for many constructive and helpful comments.

Appendix The 1/2- and 1/10-degree model configurations are briefly summarized. The model domains are shown in Fig. 1a. The 1/2degree model covers almost the entire North Pacific, and the 1/10-degree model covers the Kuroshio–Oyashio region around Japan in the western North Pacific. All the lateral boundaries in the 1/2-degree model are closed by an artificial wall, near which temperature and salinity were restored to climatological monthly mean values of WOA2001. The two models were forced by climatological monthly mean fluxes at the sea surface. Prior to the model run, fluxes were estimated from JRA25/JCDAS and GHRSST in the years of 1986– 2006 on the basis of the COARE bulk formula. The salinity at the sea surface was restored to WOA2001’s monthly mean value with a time scale of 30 days. Additionally, since a sea ice model was not coupled with the 1/2- and 1/10-degree model, temperature and salinity in the Okhotsk and Bering Seas were restored to WOA2001’s monthly mean values with a time scale of 30 days. Table A1 lists numerical schemes, parameter values, and so on for the 1/2- and 1/10-degree models. One of the notable points is that a hybrid-type lateral viscosity is adapted for the 1/10-degree model. This lateral viscosity is essential for reproducing a realistic Kuroshio path variability south of Japan in the 1/10-degree model. Many types of lateral viscosity parameterizations were tested (e.g., zero viscosity, harmonic or biharmonic viscosity, and some

Table A1 Parameterization, parameter value, and numerical scheme in the 1/2- and 1/10-degree model. 1/21 model

1/101 model

Vertical level Vertical coordinate parameters

48

48

yS yb

5 0 20 m

5 0 10 m

3rd-order upstream-biased 4th-order centered

3rd-order upstream-biased 4th-order centered

3rd-order upstream-biased 4th-order centered

MPDATA

Harmonic Along S surface Smagorinsky scheme (constant ¼0.1) –

Hybrid (harmonic plus bi-harmonic) Along S surface 0.005(m/s)  grid-diagonal length (m) Smagorinsky scheme (constant ¼ 0.2)

Harmonic Along isopycnal surface 200 m2/s

Harmonic Along Z surface 5 m2/s

Hc Momentum advection scheme Horizontal Vertical Tracer advection scheme Horizontal Vertical Lateral viscosity Formulation Direction Viscosity coefficient: harmonic Viscosity coefficient: bi-harmonic Lateral diffusion Formulation Direction Viscosity coefficient

61

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hybrid-type viscosity schemes applied for MICOM (Chassignet and Garraffo, 2001), MRI.com (Tsujino et al., 2006), HYCOM (Kelly et al., 2007), and POP (Hecht et al., 2008)). It was found that, for our 1/10-degree model, the superposition of a grid-size dependent harmonic viscosity and a bi-harmonic viscosity with the Smagorinsky parameterization (Griffies and Hallberg, 2000) provides the best performance. Harmonic viscosity plays an important role in stabilizing the Kuroshio path, and bi-harmonic viscosity in adjusting the intensity of mesoscale eddies and reducing subgrid-scale noise (Chassignet and Garraffo, 2001). A harmonic viscosity velocity of 0.005 m/s is used to express Munk layer at the middle latitude (  30 1N) with a few grids. The 1/2-degree model was integrated for 8 years from initial values based on WOA2001’s monthly mean value in January (Conkright et al., 2002). After the 8-year spinup, the 1/10-degree model was integrated for 12 years together with the 1/2-degreee model. The total integration time was 20 years. An initial value of the 1/10-degree model was prepared by bi-linearly interpolating the 1/2-degree model output on 1 January in the ninth integration year onto grid points of the 1/10-degree model. Daily mean output from the 1/2-degree model is imposed on the lateral boundary in the 1/10-degree model. References Ambe, D., Imawaki, S., Uchida, H., Ichikawa, K., 2004. Estimating the Kuroshio axis south of Japan using combination of satellite altimetry and drifting buoys. Journal of Oceanography 60, 375–382. Akiyama, H., Saitoh, S., 1993. The Kyucho in Sukumo Bay induced by Kuroshio warm filament intrusion. Journal of Oceanography 49, 667–682. Awaji, T., Akitomo, K., Imasato, N., 1991. Numerical study on shelf water motion driven by the Kuroshio: barotropic model. Journal of Physical Oceanography 21, 11–27. Chassignet, E.P., Garraffo, Z.D., 2001. Viscosity parameterization and Gulf Stream separation. In: Muller, P., Henderson, D. (Eds.). Proceedings of the ‘Aha Huliko’a Hawaiian Winter Workshop, U. Hawaii, pp. 367–374. Conkright, M.E., Locarnini, R.A., Garcia, H.E., O’Brien, T.D., Boyer, T.P., Stephens, C., Antonov, J.I., 2002. World Ocean Atlas 2001: Objective Analysis, Data Statistics, and Figures, CD-ROM, DocumentationNational Oceanographic Data Center, Silver Spring, MD17 pp. Egawa, T., Nagata, Y., Sato, S., 1993. Seasonal variation of the current in the Tsushima Strait deduced from ADCP data of ship-of-opportunity. Journal of Oceanography 49, 39–50. Ezer, T., Arango, H.G., Shchepetkin, A.F., 2002. Developments in terrain-following ocean models: intercomparisons of numerical aspects. Ocean Modelling 4, 249–267. Garrett, C.J.R., Petrie, B., 1981. Dynamical aspects of the flow through the Strait of Belle Isle. Journal of Physical Oceanography 11, 376–393. Griffies, M.S., Hallberg, R.W., 2000. Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Monthly Weather Review 128, 2935–2946. Guo, X., Fukuda, H., Miyazawa, Y., Yamagata, T., 2003. A triply nested ocean model for simulating the Kuroshio—roles of horizontal resolution on JEBAR. Journal of Physical Oceanography 33, 146–169. Fujimoto, M., 1987. On the flow types and current stability in Tosa Bay and adjacent seas. Umi to Sora 62, 127–140. (in Japanese with English abstract). Haidvogel, D.B., Arango, H.G., Hedstrom, K., Beckmann, A., Malanotte-Rizzoli, P., Shchepetkin, A.F., 2000. Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates. Dynamics of Atmospheres and Oceans 32, 239–281. Haidvogel, D.B., Arango, H., Budgell, W.P., Cornuelle, B.D., Curchitser, E., Di Lorenzo, E., Fennel, K., Geyer, W.R., Hermann, A.J., Lanerolle, L., Levin, J., McWilliams, J.C., Miller, A.J., Moore, A.M., Powell, T.M., Shchepetkin, A.F., Sherwood, C.R., Signell, R.P., Warner, J.C., Wilkin, J., 2008. Ocean forecasting in terrain-following coordinates: formulation and skill assessment of the Regional Ocean Modeling System. Journal of Computational Physics 227, 3595–3624. Hanawa, K., Toba, T., 1987. Critical examination of estimation methods of longterm mean air–sea heat and momentum transfers. Ocean–Air Interactions 1, 79–93. Isobe, A., Guo, X., Takeoka, H., 2010. Hindcast and predictability of sporadic Kuroshio-water intrusion (kyucho in the Bungo Channel) into the shelf and coastal waters. Journal of Geophysical Research 115, C04023, http://dx.doi.org/ 10.1029/2009JC005818.

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