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A Triply Nested Ocean Model for Simulating the Kuroshio—Roles of Horizontal
Resolution on JEBARXINYU GUO
Center for Marine Environmental Studies, Ehime University, Matsuyama, and Institute for Global Change Research,
Yokohama, JapanHISASHI HUKUDA AND YASUMASA MIYAZAWA
Institute for Global Change Research, Yokohama, JapanTOSHIO YAMAGATA
Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, Tokyo, and Institute for Global
Change Research, Yokohama, Japan(Manuscript received 1 October 2001, in final form 25 June 2002)
ABSTRACTA triply nested ocean general circulation model was used to examine how the model horizontal resolution
influences the Kuroshio in the East China Sea (ECS) and the sea level variability. As the model resolution
increases from 1⁄28 to 1⁄188 the path, current intensity, and vertical structure of the model Kuroshio and the variabilityof sea level become closer to observations. In general, the higher-resolution model improves the baroclinic aswell as barotropic component of the Kuroshio and thus reproduces more realistic density and current fields. This
improvement, in addition to better representation of topography, results in better reproduction of the interaction
between baroclinicity and bottom topography, that is, JEBAR (joint effect of baroclinicity and bottom relief )in a high-resolution model. Modeling the Kuroshio in the ECS provides an ideal example of such improvement.
In particular, the Kuroshio veering phenomenon at (308N, 1298E) southwest of Kyushu is discussed, together
with the seasonal meridional migration of the path. It is shown that JEBAR and advection of the geostrophic
potential vorticity are two major contributions to the vorticity balance in this area. The summer intensificationof JEBAR resulting from the intensified stratification yields a strong offshore volume transport across the shelf
break, thereby leading to the southward shift of the veering latitude. In winter, the weakened JEBAR, combinedwith the increased wind stress curl, decreases the offshore volume transport in a considerable amount, explaining
the northward shift of the veering latitude. The present reproduction of seasonal migration of the Kuroshio axis
at 1298E is in good agreement with observation.

1. Introduction
The Kuroshio, one of the major western boundary
currents, influences not only global ocean climate variations but also the regional climate system in East Asia.
It originates in the northward branch of the bifurcatedNorth Equatorial Current off the Philippine coast (Nitani1972), enters the East China Sea (ECS) east of Taiwan,
and flows northeastward along the continental slope in
the ECS. After passing through Tokara Strait south of
Kyushu, the Kuroshio intensifies its speed and continues
to flow along the southern coast of Japan, where it shows
the well-known bimodal paths: the straight path and theCorresponding author address: Xinyu Guo, Center for Marine Environmental Studies, Ehime University, 3 Bunkyo-cho, Matsuyama
790-8577, Japan.
E-mail: guoxinyu@dpc.ehime-u.ac.jp

meandering path. Then, it leaves Honshu (the main island of Japan) off the Boso Peninsula and enters thedeep Pacific Ocean as the Kuroshio Extension.
Up to now, studies of the Kuroshio using basin-scaleocean models have mainly focused on the variation of
the volume transport (Greatbatch and Goulding 1990;
Sekine and Kutsuwada 1994; Kubota et al. 1995; Kagimoto and Yamagata 1997). Because of the limitationin model resolution, only the work of Kagimoto andYamagata (1997) paid attention to the vertical structureof the Kuroshio. Using a 1⁄ 38 Pacific Ocean model, Kagimoto and Yamagata (1997) emphasized the importance of high resolution in simulating the Kuroshio, particularly in capturing JEBAR (joint effect of baroclinicity and bottom relief ). Recently, Smith et al. (2000)
also showed the importance of high resolution in simulations of the Gulf Stream. Their Atlantic Ocean modelwith 1⁄108 resolution reproduced the sea level variability

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147

FIG. 1. Surface mean currents in the East China Sea derived from GEK data from 1953 to
1984 (after Qiu and Imasato 1990).

observed by the TOPEX/Poseidon altimeter, whereas
their model with 1⁄58 resolution failed to do so.
The Kuroshio in the ECS is largely controlled by thebottom topography. For example, as shown by Qiu andImasato (1990), the long-term GEK observation data
(Fig. 1) demonstrate that the Kuroshio in the ECS approximately flows along the continental slope (see also
Fig. 3 for the topography of ECS). However, there areat least two phenomena that cannot be explained by the
topographic control. One is the Kuroshio around 308N,
1288–1298E where it becomes free from the control ofbottom topography and leaves the continental slope.
This phenomenon is referred to as the Kuroshio veering.
Another is the seasonal meridional migration of the Kuroshio path at 1298E (Sun and Su 1994). In this article,
we will give an explanation of these two phenomena—that is, why the Kuroshio veers east at 308N in the ECS
and why the Kuroshio path shows the seasonal meridional migration at 1298E.
Since the continental slope in the ECS has a gradientof as much as 800 m in 20–30 km, a numerical modelneeds to have a grid size less than 10 km to resolve it.
Also, we prefer a basin-scale model to a regional model
to avoid the open boundary problem. To meet these two
conflicting requirements, we adopt a one-way nested
model. Figure 2 shows the three ocean models designedwith a triply nested structure for the Pacific Ocean.
These models, called NEST1, NEST2, NEST3, havegrid sizes that decrease with a ratio of 1/3 in increasingorder and are linked through their lateral interface where
the coarser grid model results are used to specify theboundary conditions for the finer grid model. This way,
we can satisfy the requirement of high resolution in thecontinental slope region and also circumvent the open
boundary problem for the regional model. We did not
adopt a two-way nested model in the present work because of complications that make it difficult to conserve
some properties and because of excessive computer resources requirements.
In the next section, we give a brief description on theabove three models, used for a hindcast experiment for
the years 1992–98. In section 3, results of these models

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FIG. 2. Domain of triply nested models: NEST1, NEST2, and NEST3.

are compared with each other to demonstrate the importance of model resolution in simulating the Kuroshio
and the related sea level variation. In section 4, we
describe how the Kuroshio path in the ECS is affectedby the model resolution, showing the important role
played by JEBAR in determining the Kuroshio veering
latitude west of Kyushu. Last, conclusions are given in
section 5.
2. Numerical model
The Princeton Ocean Model (POM) is a three-dimensional primitive equation ocean model. It includes
thermodynamics and the level-2.5 Mellor–Yamada turbulence closure and uses a sigma coordinate in the vertical to resolve the variation of bottom topography(Blumberg and Mellor 1987; Mellor 1998). Originally,
the POM was designed for coastal waters since the sigma-coordinate system can well resolve complex topography in the coastal region. However, it has also successfully simulated large-scale ocean circulations in recent years. For example, the POM has been used tosimulate the Kuroshio in the Pacific Ocean basin model(Kagimoto and Yamagata 1997) and the Gulf Stream in
the Atlantic Ocean basin model (Ezer and Mellor 1997).
For our purpose to investigate the open ocean–coastal
sea interactions, both the open ocean and coastal sea,
are of equal importance; to choose the POM as our basicmodel seems natural.
The grid ratio between a coarse model and a finemodel is an important factor in constructing a nested
model. Spall and Holland (1991) suggested that gridratios of 3:1 and 5:1 should be used in nested model

calculations, based on their estimate of the root-meansquare errors. Although their suggestion is based on a
two-way nested model, it is likely to remain true in ourcase as well and is followed in this study. To achieve
high resolution in the Kuroshio region, we use the 3:1
grid ratio twice to decrease the grid size from 1⁄28
(NEST1) to 1⁄ 188 (NEST3). We use the same sigma levels
for all three models (see Table 1) since our main concern
is the effect of changing the horizontal resolution.
The model topography of the Pacific Ocean is based
TABLE 1. Values of sigma coordinates used in the NEST1, NEST2,
and NEST3.
Layer

Sigma coordinate

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

0.000
20.00220.00420.01020.02020.04020.06020.08020.10020.12020.14020.17020.20020.30020.40020.50020.65020.80020.90020.95021.000JANUARY 2003

GUO ET AL.

on Digital Terrain Model 5 [DTM5: Geophysical Exploration Technology (GETECH) 1995], which covers
the global ocean with 59 3 59 resolution. In coastal
waters of Japan that cover three areas (348–468N, 1358–
1488E; 308–388N, 1288–1448E; and 248–308N, 1228–
1328E), the topography data with 500 m 3 500 m resolution prepared by the Japan Oceanographic Data Center (JODC) are used. Two modifications are done to theoriginal topography data: 1) setting the minimum (10m) and maximum (6500 m) depths in the model and 2)
smoothing the topography data to satisfy the following
criteria (Mellor et al. 1994):|H i11 2 H i |# a,(H i11 1 H i )(1)where, H i11 and H i are the depths at two adjacent grids
and a is a slope factor set as 0.2.
Each model depth mapped in the NEST3 domain isshown in Fig. 3. The main differences between eachpanel of Fig. 3 are manifested in the shelf break regionof the ECS and also around some seamounts. The
smoothing changes the NEST1 topography rather drastically from realistic features. The NEST2 model topography is much improved but not enough, as seen in
the difference of the spaces between the 200- and 1000m isobaths in NEST2 and NEST3. The NEST3 topography is almost the same as that on charts of the ECS.
The models are driven by wind stresses, heat fluxes,
and salt fluxes applied at the sea surface. The heat andsalt fluxes are of a Haney type [see (26) in Barnier(1998)]. The coefficient used in the retroaction term is
35 W m 22 K 21 for the heat flux and 10 m month 21 forthe salt flux.
Figure 4 shows a designed schedule of model runs
and the sources of each forcing data. The NEST1 andNEST2 models are both forced to run from rest statewith the annual mean temperature and salinity of
WOA94 (Levitus et al. 1994; Levitus and Boyer 1994),
while the NEST3 model starts from the initial conditioninterpolated from the NEST2 results. During their spinup phase, NEST1, NEST2, and NEST3 are integrated
for 20, 15, and 3 years, respectively; they are forced by
the monthly wind stresses (Hellerman and Rosenstein1983), the monthly heat fluxes (da Silva et al. 1994),
zero salinity fluxes, the monthly sea surface temperature(SST), and the monthly sea surface salinity of WOA94.
During their hindcast phase from September 1991 to
December 1998, the weekly wind stresses from the satellite data of ERS-1 and ERS-2 (CERSAT: see more
information online at http://www.ifremer.fr/cersat), andthe weekly SST data blended with the ship, buoy, andbias-corrected satellite data (Reynolds and Smith 1994)
are used instead of the monthly wind stresses and themonthly SST data.
The lateral boundary condition of NEST1 is treatedas a solid boundary for simplicity. This simplicity is
acceptable because its southern boundary is located at

149

408S, far from the Kuroshio region. As for NEST2 andNEST3, the boundary condition is treated in the following manner. First, the depths of the fine grids along
the boundary are set equal to those of the corresponding
coarse grids. Next, along the boundaries of NEST2 andNEST3, the unknown variables, that is, elevation, velocity, temperature and salinity, are obtained by spatial(bilinear) interpolation of the NEST1 and NEST2 model
variables saved during their runs every 3h and every
1h, respectively. The turbulent kinetic energy and a macroscale length of turbulence at the open boundaries areboth set to a small value (10 210 ) as in the POM.
Since bilinear interpolation does not conserve volume
flux through the interface between the fine and coarse
grid model, the normal external velocity is modified sothat the net flux through the interface is conserved (seethe appendix). These spatially interpolated variables arethen used to specify the boundary conditions for eachnested model in which temporal (linear) interpolationof the saved variables is made to fit data to the fine gridmodel at each time step. Table 2 summarizes the model
domain and physical parameters of all three models.
3. Resultsa. Mean sea level and velocity distributions
The mean sea level calculated by each model for the
NEST3 domain and averaged over the years 1994–98
is shown in Fig. 5; data for the first two years, 1992–
93, are not used because of the influence of switchingfrom monthly to weekly forcing.
One of the most obvious differences among threemodels is the Kuroshio path in the ECS. The gradientof sea level across the Kuroshio, which measures theintensity of the Kuroshio surface current, becomes larger as the model resolution becomes finer. The Kuroshio
main path, as remarked in the introduction, is estimatedby tracing the steepest gradients of sea level in Fig. 5,
for example, the contour lines of 30 cm in NEST1 andthose of 20 cm in NEST2 and NEST3. The Kuroshio
in NEST1 flows farther north than observed (Fig. 1) and
its retroflection latitude is about 328N. This overshooting of the veering latitude is improved a little by NEST2.
Only the NEST3 model reproduces the correct eastward
veering of the Kuroshio at 308N. Other obvious differences in models are seen in the Japan Sea and east of
Honshu; the Tsushima Warm Current and the Kuroshio
Extension become more realistic as resolution increases.
The model mean currents at depth 20 m for the same
domain and period are shown in Fig. 6. The region
where velocity amplitudes exceed 50 cm s 21 is hatchedrather than arrowed. This figure illustrates the importance of horizontal resolution to simulate the strong
ocean currents such as the Kuroshio and the Tsushima
Warm Current. Comparison with the observed current
data (Fig. 1) shows that the Kuroshio reproduced by
NEST1 is much weaker and wider in the ECS. To the

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FIG. 3. Model depths (m) mapped for the NEST3 domain: PN denotes the observationalhydrographic line in the East China Sea (known as the PN line).

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b. Variability of sea surface height
Here we calculate the square root of the standard
deviation in order to see how the sea surface heightvariability changes with increasing the model resolution.
It is defined as

O

!

N
1
(h 2 h ) 2 ,N 2 1 i51 i

FIG. 4. Schedule for model run and data sources. Schematic ofmodel runs (top rows); units of spinup and hindcast phases are inyears and calendar years, respectively; slanted and vertical arrows
show how initial and boundary conditions of nested models are obtained (see text for explanations). Data sources used to drive models(bottom rows) are HR: Hellerman and Rosenstein wind stress data,
SST: sea surface temperature data, SSS: sea surface salinity data, andNet HF: heat flux data.

south of Japan, it is also weaker than the realistic one
and cannot form a jetlike current, particularly in the
Kuroshio Extension region. The Kuroshio reproducedby NEST2 is much stronger than that of NEST1, but
the retroflection (veering) latitude in the ECS is too far
northward. Also, after leaving the eastern coast of Honshu, the Kuroshio overshoots to the north. However,with increasing resolution, the NEST3 model with aresolution of 1⁄ 188 resolves the Kuroshio in a realistic
way, both in strength (larger than 1 m s 21 ) and path.
There are many other improved features in NEST3.
These are 1) the shelf circulation in the ECS, 2) the
currents in the Yellow Sea, 3) the Tsushima warm current flowing into the Japan Sea, 4) the southward current
along the west coast of Kyushu, 5) the Kuroshio countercurrent west of the Ryukyu Islands, 6) the warm recirculation eddy south of Japan, and 7) the Tsugaru
warm current along the Sanriku coast.

where h i and h denote the sea surface height of the ith
data in a time series and the average of h i over all data
N of that time series, respectively (e.g., Emery andThomson 1998). We simply refer to this quantity as rms(root mean square). Figure 7 shows this distribution
reproduced by each model for the NEST3 domain andduring the years 1994–98. Also shown on the bottom
right, marked T/P, is the rms distribution calculated fromthe satellite TOPEX/Poseidon data [World Ocean Circulation Experiment (WOCE) global data from the Jet
Propulsion Laboratory (JPL)].
It is clearly seen that the rms changes remarkably
with the model resolution. In the NEST1 results, wefind three separate regions with rms values over 8 cm,
each located around the Ryukyu Islands, south of Japan,
and east of Honshu. With increasing resolution, theseregions are merged into one large area with enhanced
rms amplitudes. Such change is related to the more realistic resolution of mesoscale eddies in the finer gridmodels.
One noticeable area that is strongly sensitive to themodel resolution is the Kuroshio Extension region. The
satellite altimeter gives a maximum rms of about 40 cm
there. The rms variability in this area produced by
NEST1 and NEST2 shows a maximum of about 10 and
24 cm, respectively; these values are much smaller thanthose observed. The variability reproduced by NEST3
shows a maximum of about 32 cm, a value much closer
to the observed value. However, its distribution east of
Honshu differs a little from that of TOPEX/Poseidon.
The influence of the eastern boundary, where the NEST2
results are fixed, may be inevitable in this region. One
obvious point is that the overshooting of the Kuroshio
Extension in NEST2 leads partly to a more northward
position of the Kuroshio Extension in NEST3, whichmight alter the rms distribution of sea level in NEST3

TABLE 2. Domain and parameters used in the triply nested model. The meanings of SLMIN, HORCON, TPRNI, DTE, and DTI can befound in the users guide of POM (Mellor 1998).
Model

DomainNEST1

408S–708N
1008E–708W
0–638N
1108–1758E
248–448N
1188–1508E

NEST2
NEST3

Grid size
(deg)

SLMIN

HORCONTPRNIDTE (s)DTI (min)

1/2

0.2

0.1

0.5

36

18

1/6

0.2

0.1

0.5

12

12

1/18

0.2

0.1

0.5

6

6

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FIG. 5. Mean sea levels of three models for the NEST3 region; values on contour lines represent
those of hindcast results averaged over the years 1994–98.

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FIG. 6. As in Fig. 5 but for the mean velocity at depth 20 m; regions where current speeds
are over 50 and 100 cm s 21 are hatched with shallow and deep tones, respectively, rather thanarrowed; arrows for NEST2 and NEST3 are drawn every two and six grid points, respectively.

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FIG. 7. As in Fig. 5 but for rms of sea surface height (see text for definition); T/P in the bottom-right picture represents rms calculated from TOPEX/Poseidon data (contour interval
is 2 cm). Because of tidal correction problem, data in the Yellow Sea and a part of ECS are not included in T/P dataset.

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to be different from that of TOPEX/Poseidon data. Thisis a weak point of the one-way nested model. To solve
this, we must use a two-way nested method. An alternative is to shift the eastern boundary of the NEST3
model farther east of the Kuroshio Extension region.
c. Vertical structure and volume transport across PN
line
As a typical transect in the ECS, the PN line (see Fig.
3 for its position) provides a good location to compare
our model results with the observed data; it also enables
us to demonstrate how model results are sensitive tochanges in grid size.
In Fig. 8 we show the vertical section of the alongshelf velocity component, potential temperature, and salinity distributions on the PN line reproduced by eachmodel. In general, all three models simulate a strong
current core, that is, the Kuroshio, in the surface layer
just above the shelf break. Since the shape of the shelf/
slope is improved with model resolution, the geographical location of the Kuroshio core is also improved withresolution. We see that the area and intensity of the core
and the vertical shear of the alongshelf current are allvery sensitive to model resolution. For example, thesurface speed changes from 40 cm s 21 in NEST1 to 110
cm s 21 in NEST3. This is associated with the changeof the vertical shear of the Kuroshio. In contrast to these
local features, the total volume transport through the PN
line changes little as shown in the left three panels of
Fig. 8. The total transport must be determined by thelarger scale dynamics (Kagimoto and Yamagata 1997).
The water temperature and salinity distributions
change gradually as the model resolution increases.
With increasing Kuroshio core speed, however, the isotherms and isohalines around the core become slanted.
This means that the horizontal gradient for both watertemperature and salinity increases. The distribution of
the density field is similar to that of the temperaturefield in this area (e.g., see Fig. 17).
The above features of the alongshelf velocity, watertemperature, and salinity along the PN line are explainedin terms of the thermal wind relation, which relates thehorizontal density gradient with the vertical shear of thealongshelf velocity component. As already remarked,
there is not much change in the volume transport among
the three models because the driving forces (wind stresses and heat fluxes) are the same in all three models.
Thus, in order to conserve the volume transport, thesurface (bottom) current must become larger (smaller)
as the vertical shear of the current increases.
Using hydrographic data for the years 1988–94 andassuming a level of no motion at depth 700 m, Oka andKawabe (1998) calculated the geostrophic current acrossthe PN line for four seasons. Compared with the annual
mean distribution of geostrophic currents, potential temperature, and salinity fields at this section (Fig. 9), theresults of NEST3 are consistent with these observed

155

data. In particular, the vertical shear of current is well
reproduced by NEST3.
When compared with the NEST3 result, the velocity
distributions in NEST1 and NEST2 are more barotropic
in the vertical profile. Kagimoto and Yamagata’s (1997)
result of a 1⁄ 38 model also shows the weaker vertical shearof currents compared to the NEST3 result. Increasing
the horizontal resolution also leads to a water temperature distribution close to the observed one associatedwith the large horizontal gradient across the Kuroshio.
Thus we conclude that the model Kuroshio becomes
more baroclinic as the model horizontal resolution increases.
The volume transport across the PN line is often used
to represent the Kuroshio transport typical in the ECS.
Based on the hydrographic data observed along the PN
line from 1973 to 1993, Hinata (1996) suggested, assuming a reference depth of no motion at a depth of
700 m, that the mean geostrophic volume transport
through the PN line is 25.4 Sv (Sv [ 10 6 m 3 s 21 ) witha little decrease in autumn. By assuming no motion at
700 m artificially in our model and integrating verticallythe alongshelf velocity across the PN line, we can compare the model transport with Hinata (1996)’s result.
Besides this estimate, we give another estimate of thevolume transport integrated from 700 m to the surface,in which the velocity at depth 700 m is not zero. The
difference between these two transports is the barotropic
component of the Kuroshio transport defined at depth
700 m. In Table 3, we show these two volume transports
calculated from the results as shown in Fig. 8.
Though the values in Table 3 are a little smaller thanthat given by Hinata (1996), the volume transport from
700 m to the surface does increase as the model resolution is increased. The interesting feature in Table 3 isthe trend among the three models toward decreasing thebarotropic component of the Kuroshio transport withincreasing resolution (i.e., 7.6, 3.5, and 2.2 Sv in theorder of NEST1, 2, and 3). This trend is consistent withthe reduction of the bottom velocity on the slope withincreasing the resolution. This aspect is important inmodeling the Kuroshio path correctly since the presenceof bottom velocity on the slope enables the interaction
between the bottom topography and ocean current,
keeping the Kuroshio path along isobaths (Warren1963).
4. The Kuroshio veering at 308N in the ECS
a. Effects of model resolution on JEBAR
As is observed, the Kuroshio flowing to the northeast
along the shelf break of the ECS suddenly turns to theeast at 308N west of Kyushu. The existence of Kyushu
and Tokara Strait is the primary cause for this turn because the ocean current is expected to flow, at first approximation, along the f /H contours ( f and H being the
Coriolis parameter and the water depth, respectively)

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FIG. 8. Vertical distribution of model results at PN line: (left) alongshelf velocity, (middle) potential temperature, and (right) salinity. Regions with negative values of alongshelf velocity
are shaded; model-calculated volume transports are shown in left panels (VT-pos and VT-neg are volume transports calculated with positive and negative alongshelf velocity, respectively;
VT-net represents a sum of VT-pos and VT-neg).

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when the relative vorticity is much smaller than theplanetary vorticity. However, notice that the contours at
200 and 500 m in Fig. 3, which correspond to the shelf
break in the ECS, extend up to 328N west of Kyushu,
28N farther north of the veering latitude. Therefore, theKuroshio does not exactly follow the f /H contours, so
there should be some other mechanisms deflecting theKuroshio from the f /H contours.
To see this more clearly, we show in Fig. 10 thevertically integrated current field (from surface to adepth of 1000 m) for the three models, along with thef /H contours. The Kuroshio in the NEST3 model flows
along the f /H contours in the ECS until it reaches westof Yakushima located near 308N, 1308E. Then the Kuroshio crosses the f /H contours to enter Tokara Strait.
Apart from this feature, the NEST3 model also shows
the presence of the Ryukyu Current, the current flowing
northeastward along the eastern offshore of the Ryukyu
Islands (Yuan et al. 1995). This is the advantage of using
a high-resolution model that can resolve the small-scaleseamounts such as the Ryukyu Islands.
Concerning the Kuroshio veering, three models produced the following features: three eastward branch currents located at 288, 308, and 328N in NEST1; a wide
eastward current ranged from 308 to 328N in NEST2;
and a coherent jetlike current that turns, as in the observation, to the east at 308N in NEST3. From theseresults, we see that the deflection of the Kuroshio fromthe f /H contours becomes more prominent as model
resolution is improved.
To analyze the Kuroshio veering, we consider theoffshore/onshore volume transport across the shelf
break. If we decompose the Kuroshio currents into thevelocities parallel and perpendicular to the f /H contours, the Kuroshio veering may be regarded as a phenomenon in which the offshore transport exists and ismaintained by some mechanism.
To make this idea concrete, we start from the primitive equations. After vertically averaging the momentum equations and then taking a curl, we obtain thefollowing vorticity equation:

1 2

12
t
t
5 J(x, H ) 1 curl 1
2 curl 1
r H2
r H2

]
M
f
curlz
1 M·=
]t
H
H
21

a

z

b

z

0

1 curl z

1H2 2 curl 1H2 .
DAz

In (2), two operators are defined as
FIG. 9. Vertical distributions of observed data at PN line for (top)alongshelf geostrophic velocity with reference depth of no motion at
700 dbar, (middle) potential temperature, and (bottom) salinity. Regions with negative values of alongshelf velocity are shaded.

J(A, B) 5

]A ]B
]A ]B
2
and
]x ]y
]y ]x

curl z (A) 5

]A y
]A x
2
;
]x
]y

0

(2)

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TABLE 3. Volume transport through the PN line calculated fromthe results of three models shown in Fig. 8: VTtotal is defined as #00(# 700m V dz) dl, and VTref is # (# 700m (V 2 V 700m dz) dl, where dl expresses
the integrating along the PN line.
Model

VTtotalVTref

VTtotal 2 VTref

NEST1
NEST2
NEST3

22.2
25.6
25.7

14.6
22.1
22.8

7.6
3.5
2.9

0
also, M 5 #2H(ui 1 y j) dz is a volume transport vector,
021
J(x, H ) the JEBAR term with x 5 #2H
zgr/r 0 dz being
the potential energy, t a the wind stress, and t b the bottom stress. Two other vectors D 5 D xi 1 D y j and A 5
A xi 1 A y j are the vertically integrated horizontal diffusion term and the nonlinear advection term, respectively.
When one considers a mean state of the Kuroshio
such as shown in Fig. 10, the first term in (2) is neglected. The second term on the left-hand side of (2)represents the advection of the geostrophic potential
vorticity f /H (hereinafter referred to as APV). This termis also interpreted as giving a transport across the f /H
contours and should be balanced by the right-hand side(rhs) terms of (2) in a steady state. Then, three cases
are possible depending on the sign of rhs. If APV 5 0,
the transport is exactly along the f /H contours. If APV. 0, the transport is in the onshore direction and theKuroshio tends toward the continental shelf of the ECS.
But if APV , 0, the transport is in the offshore direction
and the Kuroshio tends toward the deep ocean. Thus,
the Kuroshio veering must be associated with the caseof APV , 0.
Using the model data averaged over the years 1994–
98, we calculated all terms in (2) except for the time
variation term and mapped their values. Figure 11 is for
APV. Comparing Fig. 11 with Fig. 10, we find that alarge positive value exists from the northeast of Taiwan
through the west of Kyushu in the NEST1 model. Thisagrees well with the transport distribution of the NEST1
model in Fig. 10, which shows the general tendency of
currents ascending the shelf region. As the model resolution is increased, the map of APV changes drastically. The large elongated area with a positive value
along the shelf break splits into many small patchlike
areas with alternate signs. The Kuroshio veering area
west of Kyushu corresponds to the area with a large
negative value around 328N in NEST2 and that around308N in NEST3.
The next problem is to identify contribution to thisoffshore transport across the f /H contour. As we willsee, it is mainly due to the JEBAR term. Figure 12 shows
maps of JEBAR, the first term on the rhs of (2), for thethree models. The JEBAR shows a pattern similar tothat of APV for all three models, particularly along theshelf break of the ECS and at the southern coast ofJapan. This suggests that the offshore advection of f /H is mainly balanced by JEBAR, regardless of the model

VOLUME 33

resolution. Away from the shelf break, however, thedistribution pattern is different between Fig. 11 and Fig.
12. For example, the distribution of APV over the shallow sea area northeast of Taiwan Strait and over the
Chinese coastal sea area cannot be explained only by
the JEBAR forcing.
Three curl terms of wind and bottom stresses andnonlinear advection in (2) are shown in Fig. 13 for the
NEST3 model. Interestingly, the curl of the nonlinear
advection term shows a very fine structure similar to
those in Figs. 11 and 12, while the wind and bottom
stress curls show more definite patterns. The curls of
nonlinear advection and bottom stress both give a dominant balance against the APV term only over the shallow sea area northeast of Taiwan Strait extended to the
ECS continental shelf, where the JEBAR term is small.
Along the Chinese east coast and the shelf break, thecurl of wind and bottom stresses dominates and showsa definite sign; such features are simply interpreted interms of the Ekman flux divergence (convergence) andthe associated vortex stretching (shrinking) in the wholewater column, which in turn pushes the fluid with f /H
towards onshore (offshore; e.g., Hukuda et al. 2001).
The remainder is very difficult to interpret in a simple
way because of its fractal-like feature as seen in eachmap of APV, JEBAR, and the nonlinear advection termfor NEST3. These features are caused by higher order
spatial derivative terms augmented with increasing theresolution of bottom topography and flow nonlinearity.
As clearly seen in Fig. 12, we note that the amplitude
and sign of the JEBAR term depend strongly on themodel resolution. As discussed before, both horizontal
density gradient and bottom topography approach therealistic observed feature as the model resolution is increased. Thus, a high-resolution model is necessary tocorrectly reproduce the JEBAR term, which in turn influences the path of the Kuroshio in the ECS.
To quantify the above discussion on the Kuroshio
veering at 308N, we checked the values of all terms in(2) over the block enclosed by 288–308N, 1268–1288E
as indicated in Figs. 10–13. This area is located just
upstream of the Kuroshio veering location, and thus thevorticity balance in this area is directly responsible forthe Kuroshio veering. Table 4 shows the values of allterms in (2) integrated over the area. As expected, both
NEST1 and NEST2 models give positive values of APV,
thus implying the Kuroshio’s onshore transport of f /H.
The NEST3 model, however, gives a negative value of
APV, thus implying the Kuroshio’s offshore transportof f /H. This result is consistent with Fig. 10. From Table
4, the JEBAR term gives a dominant contribution to
APV and explains well the path change of the Kuroshio
as the model resolution increases from low (NEST1,
NEST2) to high (NEST3).
The analysis in this subsection demonstrates that alarge offshore transport of f /H accompanied with the
Kuroshio veering is related to the JEBAR. The change
of veering position in the three models may also be

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FIG. 10. Model transport (integrated from the surface down to 1000 m) shown with both vector
and shading for a part of NEST3 domain ( f /H contour values are also shown in units of 10 28 m 21
s 21 ). Boxes are used for calculations of Figs. 15 and 16 and Table 4.

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FIG. 11. Maps of APV term for the same area as in Fig. 10; values are calculated from mean model
fields averaged over the years 1994–98.

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GUO ET AL.

FIG. 12. As in Fig. 11 but for JEBAR; note similarity between Figs. 12 and 11.

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FIG. 13. Maps of the three terms related to nonlinear advection, wind stress, and bottom stress in (2)calculated from NEST3 results.

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TABLE 4. Area-integrated values (m2 s22) of all the terms in (2) except for the time variation term over the block shown in Fig. 10. The
total area is 4.3358 3 1010 m 2.
Model
NEST1
NEST2
NEST3

1H2

J(x, H 21 )

0.440
0.636
20.5530.123
0.655
20.820

M·=

f

curlz

1r H2
ta
0

0.086
0.167
0.167

understood from another viewpoint of the current above
the shelf slope. Figure 14 presents the current distribution in the bottom layer (sigma 5 20.975) over the
shelf slope of the ECS. Obviously, with increasing model resolution, the velocity in the bottom layer decreases(see also Fig. 8). As shown in the previous section, theeffect of model resolution is to increase the baroclinicity
and to decrease the barotropic transport of the Kuroshio.
The low-resolution model is thus more barotropic thanthe high-resolution model and more susceptible to topographic control with a strong current at the bottom.
This explains why the Kuroshio in the NEST1 andNEST2 models tends to follow the topography and extend too far northward, whereas the Kuroshio in the
NEST3 model turns to the east as observed.
It is of interest to examine how each term in (2) varies
with time and contributes to the shift of the veering
position during the spinup of NEST3. Recall the schedule for model to spin up as shown in Fig. 4 and thatthe initial values of the NEST3 model are interpolated
from the NEST2 model results. Then, as spinup progresses, the Kuroshio’s retroflection latitude graduallyshifts southward. After 120 days the Kuroshio path approached the mean position as shown in the bottom
panel of Fig. 6. Figure 15 shows the temporal changeof each term in (2) integrated over the same area as inFig. 10 during the first year of spinup of NEST3. BothAPV and JEBAR terms changed their signs by day 120.
As shown in Table 4, we note that these two terms
change signs as the model resolution is increased from
NEST2 to NEST3. Figure 15 shows that this change
occurred right after NEST3 has started spinning up. After having reached the negative maximum, the negativevalues stay almost the same, and there is no large majorchange in the basic vorticity balance afterward during
the spinup stage.
The change of JEBAR must be associated with thevariation of density in the area; the change of APV must
be associated with the variation of currents. Figure 15
thus implies that the density and current fields vary
simultaneously. This is consistent with the result in section 3, namely, that the Kuroshio in the ECS is approximately in geostrophic balance. Figure 15 cannot
provide a causal relationship of the Kuroshio veering,but it provides a useful diagnosis that the JEBAR plays
a predominant role over the remainder of rhs in (2).
All other terms are less essential to the Kuroshio veering since these terms show no drastic temporal change

0

1H2

0.116
0.103
0.179

0.005
20.00320.0032curlz

1r H2
tb

curlz

D

2curlz

1H2
A

0.092
20.30320.056in Fig. 15. But a few points should be noted. The bottom
stress curl has a positive value throughout the year andthus leads to an onshore transport at the shelf break,which contributes to producing positive vorticity in theinterior geostrophic region (see Hukuda et al. 2001).
The contribution from the wind stress curl has a modest
seasonal variation. It also generates an onshore transport
at the shelf break, as shown in Fig. 13. In summer, thisdirect wind contribution is small, but northerly winds
in winter increase its magnitude, thus counteracting the
JEBAR effect to some extent.
b. Seasonal migration of the Kuroshio veering
position
Figure 15 suggests the existence of seasonal variations in the density and current field. We next examine
how the seasonal variations influence the veering position of the Kuroshio. Using the GEK current data during the years 1953–77, Sun and Su (1994) reported that
the Kuroshio at 1298E clearly shows the seasonal meridional migration. According to their report, the Kuroshio veering latitude shifts southward (northward) insummer (winter). The range of migration is about 50
km. This amount appears small but its influence on theregional life and climate is significant. Adopting thesame longitude as in their paper, we plot in the top panelof Fig. 16 the seasonal variations of the veering latitude
calculated from the NEST3 model. The model result isin good agreement with the observations in both timing
and amplitude.
In Fig. 17 we show the vertical section maps along
1298E in the summer and winter seasons. In summer(Fig. 17a), the Kuroshio axis lies south of 308N and isassociated with a strong density stratification. This density stratification is caused by the surface-intensified
temperature gradient due to summer heating and also
by the low salinity water in the surface layer associatedwith the large river discharge from Changjiang in summer (Chen et al. 1994). In winter (Fig. 17b), the Kuroshio axis shifts northward by about 0.58 and this shiftof the Kuroshio axis coincides with the events of theweakened density gradient, the well-mixed temperature,and the disappearance of the low salinity water in thesurface layer. In addition to these local factors, the basinscale seasonal variation in the heat and salt transports
as well as the current itself may also influence thechange of stratification there.

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FIG. 14. Mean currents in the bottom sigma layer reproduced by the three models for thesame region as in Fig. 10. Note that only the velocity in the region where the depth is between
100 and 1000 m is plotted.

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165

FIG. 15. Temporal variations of six terms in (2) during the early spinup phase of NEST3; shown are the areaintegrated values over the box in Fig. 10.

Shown in the bottom panel of Fig. 16 is the seasonalvariations of terms in (2) calculated for the same area
as in Fig. 15. We see that the summer southward (winternorthward) migration of the veering latitude at 1298E
is associated with the increase (decrease) of JEBAR. In
summer, the stratification is strengthened and the horizontal gradient of density field increases. This leads toincreasing the horizontal gradient of potential energy
across shelf break and, as a result, the JEBAR effectbecomes larger. In winter, the weakened stratification
leads to a weaker potential energy gradient across shelf
break and thus a weakened JEBAR effect. In this coldseason, the role of the wind stress curl as well as thebottom stress curl becomes important and replaces theweakened role of JEBAR.
Before closing this section, we note a close analogy
between the seasonal and intermodel migration of theKuroshio veering position. This analogy is due to thegeneral property of the Kuroshio veering in this section:
the more barotropic the Kuroshio becomes, the more
northward it migrates.
5. Conclusions
Using a one-way nested system, we developed a model in which three ocean models with different resolution
are linked to simulate the Kuroshio in the North Pacificsubtropical gyre system. The volume transport throughthe interface between the coarse and fine model is conserved in an area-integrated sense. The horizontal gridsize of each model varies from 1⁄ 28 to 1⁄188 with the gridratio of 1/3, but the vertical sigma levels are kept thesame for all three models. The three models are allforced by the same wind stress and heat flux data obtained from the nearly real-time satellite observations
and bounded by the bottom topography digitized fromrecently published data: one has a 1⁄ 128-resolution in the
Pacific Ocean and the other has a 500-m resolution in
the Japanese coastal ocean. Using this triply nested
ocean model, we carried out the hindcast experiment
for the years 1992–98 starting just after the spinup.
In the first part of the paper, the effect of the model
horizontal resolution on the simulated Kuroshio was studied. We have shown that an increase in horizontal resolution greatly affects the path, the current intensity, andthe vertical shear associated with the Kuroshio and thevariability of sea level, all of which approach the observed
features as the model resolution increased. Two factors arefound to contribute to this improvement: One is the increased resolution of the model topography, and the otheris the improvement of the baroclinic structure of the model
Kuroshio. The latter compares well with the observed features with increasing the model resolution.
In general, the coarse-grid model underestimates thebaroclinic structure of the Kuroshio. This is because thecoarse-grid model cannot reproduce the large horizontal
gradient of density field across the Kuroshio. Since theKuroshio in the ECS is approximately in geostrophic
balance, a weaker horizontal density gradient corresponds to a more barotropic nature of the Kuroshio. The

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FIG. 16. (top) Seasonal variations of the Kuroshio veering latitude at 1298E; values are monthly averaged ones for the years 1994–98.
The Kuroshio axis is defined at the latitude where maximum surface speeds occur (shifts from the mean latitude of the Kuroshio axis at
308N are measured in kilometers). (bottom) Seasonal variations of six terms in (2); shown are the integrated values over the box in Fig. 10;
monthly averaged results from NEST3 hindcast run for the years 1994–98 are used to calculate these terms.

high-resolution model improves this weak baroclinicityof the current by realizing sharp and realistic density
fronts across the shelf break. It is worth noting that only
the horizontal grid size is changed in our nested model
while the vertical resolution is kept the same. Increasing

the vertical resolution could directly influence the baroclinic structure. However, with use of a sigma-coordinate model, the refinement of vertical resolution has
no effect on the improvement in the bottom topographythat plays a crucial role in JEBAR.

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FIG. 17. Vertical section maps at 1298E of the eastward velocity (Vel: cm s 21 ), density ( r : 0.1 sigma-t), water temperature(T: 8C), and salinity (S: 0.1 psu) in (a) Aug 1998 and in (b) Feb 1998; values are monthly averaged over each monthand taken from NEST3 results.

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The refinement of both topography and baroclinicity
in the high-resolution model has naturally led to better
representation of the interaction between baroclinicity
and topography. We have shown that to resolve thisinteraction, that is, JEBAR, it is crucial to reproduce
the Kuroshio path in the ECS because of the existenceof a sharply defined shelf break in the ECS continental
shelf/slope region. Tokara Strait is the primary factor
that determines where the Kuroshio leaves the ECS. The
JEBAR, however, is proved to influence largely the pathof the Kuroshio in the ECS. For example, our threemodels, in which the position of Tokara Strait is thesame except for the resolution, reproduced three different paths of the Kuroshio in the ECS.
The NEST3 model reproduced the observed seasonal
meridional migration of the Kuroshio path at 1298E.
This migration is consistent with the seasonal variationof the JEBAR through seasonal changes of stratification.
Interestingly, there is a close analogy between the intermodel difference and the seasonal migration of theKuroshio veering position. This analogy is due to themechanism by which the Kuroshio becomes more barotropic and thereby susceptible to topographic control.
A coarse (fine) horizontal resolution model tends toyield more barotropic (baroclinic) structure in the model
Kuroshio and this structure shifts the Kuroshio veering
latitude northward (southward) as in the winter (summer) season when the Kuroshio is more barotropic (baroclinic).
Although the importance of the model horizontal resolution is emphasized in the present article, some problems still remain to be solved. For example, even withthe 1⁄188-resolution model, we failed to reproduce theshort-lived Kuroshio meandering path south of Japanobserved, for example, in 1993. One reason for this may
be attributed to the failure in reproducing mesoscaleeddies south of Honshu, which seem to play an important role in the Kuroshio meandering south of Japan(Ebuchi and Hanawa 2000; Ichikawa 2001; Endoh andHibiya 2001; Ihara et al. 2001). Resolving the Kuroshio
large meander south of Japan in addition to the shortlived meander will be discussed in a subsequent paper(Y. Miyazawa, X. Guo, and T. Yamagata 2002, unpublished manuscript).
Acknowledgments. This work is a part of J-COPE(Japanese Coastal Ocean Predictability Experiment) of
FRSGC, which is supported by National Space Development Agency and Japan Marine Science and Technology Center. We also acknowledge the kind support
from IOC/UNESCO NEAR-GOOS project (Chairperson Prof. K. Taira). Discussions with Drs. T. Kagimoto,
S. Minato, and H. Sakuma were very helpful in themodel development. We also thank Dr. E. Oka for kindly
providing the figure of observation data at PN line. Several comments of anonymous reviewers helped to improve the original manuscript.

VOLUME 33

APPENDIX
Adjustment of Volume Transport through the Interface between the Fine and Coarse Grid ModelIn this appendix we consider how the one-way nested
model can conserve the volume over the nested area.
Let us consider the continuity equation,]h
5 2= · [(H 1 h)u],
]t

(A1)

where h, H, and u are the elevation, depth, and verticalaveraged velocity vector, respectively. Integrating (A1)over the nested area yields]]t

1EE h dx dy2 5 T 1 T 1 T 1 T , (A2)
N

where

5 E
5E
5E
5 E

S

W

6

E

TN 52

E

[(H 1 h)y ]N dx ,

W

6
6

E

[(H 1 h)y ]S dx ,

TS 5

W

N

[(H 1 h)u]W dx ,

TW 5

S

6

N

TE 52

and

[(H 1 h)u]E dx

S

represent the transport (taken positive inward) acrossthe northern, southern, western, and eastern nested
boundaries, respectively. Now, in order to conserve thevolume between the fine and coarse grid models, it isnecessary to satisfy the following relation:]]t

1EE h dx dy2 5 ]t 1EE h dx dy2 , (A3)]fcwhere h f and h c are the elevation of the fine and coarse
grid models, respectively, and the surface integral istaken over the nested area. Now, a deficit in the transportof the fine grid model, dT, is given bydT 5 (TN,c 1 TS,c 1 TW,c 1 TE,c )2 (TN, f 1 TS, f 1 TW, f 1 TE, f ),(A4)

where the subscripts f and c refer to the fine and coarse
grid model, respectively. The total transect area of thefine grid model along the nested boundary is given by

O (H 1 h )dl,(A5)

du 5 dT/S f .

(A6)

Sf 5

f

f

where dl is the grid interval of the fine mesh. Define
the average of the transport deficit by

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GUO ET AL.

The corrected normal component of the fine grid model
external velocity is thusy N,
* f 5 y N, f 2 duy *S, f 5 y S, f 1 duu*W, f 5 uW, f 1 duu*E, f 5 uE, f 2 du.

(A7)

The plus (or minus) sign in (A7) means that the averaged
deficit in the transport (i.e., | du | ) should be subtracted
from the normal velocity on the northern and easternsides, but added to the normal velocity on the southern
and western sides. It is easily shown that (A7) satisfies
T*f 5 T f 1 (T c 2 T f ) 5 T c .

(A8)Thus the velocity defined by (A7) can satisfy the volumeconservation equation, (A3).
As shown in Fig. 4, each model gives very similar
distributions and amplitudes of sea level. This suggeststhat the volume transport through each model interface
is conserved well and the simple adjustment of the normal flux as expressed by (A7) works quite well.
Furthermore, although the above correction is enoughto give the volume conservation for our nested model,
this does not necessarily means that the sea level islocally continuous across the nested boundary. The final
value of the normal external velocity at the fine-meshboundary is thus given by the value as corrected in (A7)plus a flux toward the outside (or inside) of the boundary, whose value is proportional to the sea level difference between two grids on opposite sides of theboundary with a proportionality constant equal to0.1Ïg/H, where g is the gravitational acceleration. This
local adjustment of the normal component of the external mode velocity is necessary for a smooth continuous sea level across the nested boundary, as used insubroutine BCOND of the POM.
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