JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, C12008, doi:10.1029/2003JC002203, 2004

Residual currents in a semi-enclosed bay of the Seto Inland Sea, Japan
Xinyu Guo
Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan

Akira Futamura
Graduate School of Science and Engineering, Ehime University, Matsuyama, Japan

Hidetaka Takeoka
Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan
Received 13 November 2003; revised 1 September 2004; accepted 27 September 2004; published 7 December 2004.

[1] On the basis of the Princeton Ocean Model, a robust diagnostic model is developed to

calculate the residual currents in the Hiuchi-Nada, a semi-enclosed bay of the Seto Inland
Sea. The input water temperature and salinity data are from six hydrographic surveys
in 2002, and the model results in the summer show a clockwise eddy in the western part ofthe bay and an anticlockwise eddy in the eastern part. The magnitude of two eddies is10 cm/s. The modeled flow pattern is consistent with early observations derived frommoored arrays. The two eddies are persistent throughout the summer because winds areusually weak and cannot influence their existence. The tide-induced residual currents
are appreciable only in the close vicinity of the Kurushima Strait and Bisan Strait, the twostraits connecting the bay to the other bays, and have little affect on the two eddies that are
inside the bay. Thus the two density-driven eddies in the Hiuchi-Nada are the basic patternof circulation in the summer. Using the calculated residual currents, we examined the
intrusion route of waters from the Kurushima Strait and Bisan Strait with passive tracer
experiments. The results show that the water in the Kurushima Strait intrudes into the bay
mainly through the middle and bottom layers while the water in the Bisan Strait intrudes
mainly through the surface layer. Furthermore, the tracer cannot reach the center of the
anticlockwise eddy in the eastern part of the bay. This indicates that the eddy prevents
water exchange between its center and outer edges and provides favorable conditions for
INDEX TERMS:
the formation of oxygen-deficient waters in the central part of the eddy.
4243 Oceanography: General: Marginal and semienclosed seas; 4255 Oceanography: General: Numericalmodeling; 4512 Oceanography: Physical: Currents; KEYWORDS: residual current, diagnostic model, coldbottom water, eddy, Seto Inland Sea
Citation: Guo, X., A. Futamura, and H. Takeoka (2004), Residual currents in a semi-enclosed bay of the Seto Inland Sea, Japan,
J. Geophys. Res., 109, C12008, doi:10.1029/2003JC002203.

1. Introduction[2] Residual current is one of the fundamental issues incostal waters. Because of the presence of tidal current,
observation of residual current in coastal waters is not easy.
In this study, we present the residual current in the HiuchiNada, a semi-enclosed bay of the Seto Inland Sea, Japan(Figure 1), calculated by a robust diagnostic model fromtemperature and salinity data. This bay has a size of about
50 km  30 km and an average depth of about 20 m. Its
western side is a narrow but deep strait (>50 m), Kurushima
Strait, and its eastern side is a wide but shallow strait(<20 m), Bisan Strait.
[3] The predominant tidal constituent in the Seto Inland
Sea is the lunar semidiurnal M2 [Yanagi and Higuchi,
1981]. The tide propagates from the Pacific into the Seto
Copyright 2004 by the American Geophysical Union.
0148-0227/04/2003JC002203$09.00

Inland Sea through two channels, the Bungo Channel on thewest and Kii Channel on the east, respectively. After
entering through these channels, the tide propagates in
opposite directions and converges at the Bisan Strait,
inducing a standing wave in the Hiuchi-Nada [Yanagi
and Higuchi, 1981]. The amplitude of the M2 tide in the
Hiuchi-Nada is over 1 m and produces strong tidal
currents in the Kurushima Strait and Bisan Strait where
the cross-sectional areas are small. The amplitude of M2
tidal currents is 2.5 m/s in the Kurushima Strait and0.95 m/s in the Bisan Strait [Yanagi and Higuchi, 1981]. The
tidal current weakens rapidly as it enters the Hiuchi-Nada
where the cross-sectional area expands. The weakest tidal
currents appear in the eastern region of Hiuchi-Nada where
the amplitude of the M2 tidal current is around 0.1 m/s[Yanagi and Higuchi, 1981].
[4] An important environmental problem in the HiuchiNada is the formation of a bottom oxygen-deficient watermass in the eastern region during the summer. This arises

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C12008Figure 1. (a) Map of the Seto Inland Sea, Japan and (b) bathymetry of the Hiuchi-Nada, Kurushima
Strait, and Bisan Strait. The contours in Figure 1b indicate water depth (m) and the numbers 1 – 26 andcharacters of A– Q denote CTD stations. The numbered triangles denote the stations where wind records
are available from AMeDAS (Automated Meteorological Data Acquisition System), maintained by
Japan Meteorological Agency. The names of station are IMABARI (1), TAMBARA (2), NIIHAMA(3), MISHIMA (4), TADOTSU (5), KASAOKA (6), FUKUYAMA (7), INNOSHIMA (8), andOMISHIMA (9).
from strong stratification in the eastern portion of HiuchiNada, derived mostly from surface heating [Takeoka,
1985a]. Summer stratification prevents vertical supply of
dissolved oxygen to the bottom layer. As degradation oforganic materials consumes dissolved oxygen, an oxygendeficient water mass forms in the bottom layer of the easternregion of the bay [Ochi and Takeoka, 1986]. Obviously, this
explanation only considers the oxygen exchange in thevertical.
[5] The horizontal processes in the Hiuchi-Nada have notbeen well known. This is because the observations in the
Hiuchi-Nada have mainly focused on the density structure
and the biochemical parameters related to the oxygen
consumption [Ochi and Takeoka, 1986; Takeoka et al.,1991]. Knowledge of the residual current field is very
limited. From 26 July to 8 August 1973 the 6th Regional

Japan Coast Guard Headquarters carried out a survey of tidal
current with 25-hour mooring current meters at 42 stations in
the Hiuchi-Nada. As a byproduct, the residual current at a
depth of 5 m was obtained (Figure 2). This is the only
document on the residual current of this area. Because it
offers no information on the current’s vertical structure or its
temporal variability, the circulation has not been linked to
the formation of bottom oxygen-deficient water mass.
[6] As shown in Figure 1, the Hiuchi-Nada is locatedbetween two straits. The water exchange between the bay
and the straits in the summer is suggested to be important to
the density structure and nutrient supply in the bay [Takeoka
et al., 1991; Takeoka, 2002]. However, this process has notbeen well investigated. One reason is the existence of tidal
fronts in the summer between the straits and the bay. In
Figure 3, the distribution of log10 (H/u3) is shown, where H

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C12008and the inflow pathway of strait water into the bay, we
carried out six hydrographic surveys in 2002 in the HiuchiNada, Kurushima Strait, and Bisan Strait. A brief description of the observations is given in the next section.
These observations are used in a robust diagnostic model(described in section 3) to obtain the residual current fromeach of the observed density fields (section 4). The verticalstructure of two eddies obtained by the diagnostic model is
examined in section 5. Through the release of passive tracer
in the Kurushima Strait and Bisan Strait in the numericalmodel, we identified the inflow routes of strait water(section 6). Influences of tidal mixing on the calculated
residual current, the response of the bay to winds in thesummer, and tide-induced residual currents are discussed in
section 7, followed by a short summary.

2. Observation and Results
Figure 2. Distribution of residual currents observed with
25-hour mooring current meters from 26 July to 8 August
1973 by the Sixth Regional Japan Coast Guard Headquarters [after Takeoka, 1985b]. Short arrows are observed
data and long arrows are inferred flow patterns.
is the water depth and u is the amplitude of the M2 tidal
current from the observed data [Yanagi and Higuchi,
1981]. Simpson and Hunter [1974] have shown that the
tidal fronts should align along the contour of a criticalvalue of this parameter. The critical value in the Seto
Inland Sea is between 2.5 and 3.0 [Yanagi and Okada,1993], and one of its corresponding tidal fronts has been
observed between the Kurushima Strait and Hiuchi-Nada[Yanagi and Yoshikawa, 1987; Takeoka, 1990]. Usually thesubtidal flow along fronts is 1 order of magnitude stronger
than that across fronts [Garrett and Loder, 1981]. Therefore it is difficult to observe the inflow of strait water into
the bay, which is across fronts, particularly with thepresence of tidal currents.
[7] With the two above issues in mind, i.e., the threedimensional structure of residual current in the Hiuchi-Nada[8] From the end of May to the beginning of December
2002, we carried out six hydrographic surveys at 43 stationsin the Hiuchi-Nada, Kurushima Strait, and Bisan Strait(Figure 1). The dates and stations are listed in Table 1.
Most surveys were completed in 2 or 3 days.
[9] The horizontal distributions of water temperature,salinity and density in the surface layer are depicted in
Figure 4. At the end of May (Figure 4a), the lowest
temperature was observed in the Kurushima Strait, thehighest temperature in the eastern part of Hiuchi-Nada,
and an intermediate temperature in the Bisan Strait andnorthern part of Hiuchi-Nada. This distribution pattern was
unchanged in June and July (Figures 4b and 4c). In August(Figure 4d), the Bisan Strait and northern part of HiuchiNada had similar high temperatures, but the eastern part ofHiuchi-Nada showed slightly decreased temperatures. In
June, July, and August, the strongest horizontal gradients
could be identified between the Kurushima Strait andHiuchi-Nada. At the end of September (Figure 4e), the entire
area had nearly the same temperature. At the end of November (Figure 4f ), the coldest water was observed in the Bisan
Strait and the warmest water in the Kurushima Strait.

Figure 3. Distribution of log10 (H/u3) in the Seto Inland Sea [after Yanagi and Okada, 1993]. Regionswith values smaller than 2.5 are stippled.
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Stations

Dates given as dd/mm.

a

Date

PEA ¼

27/05 – 28/05
18/06 – 20/06
18/07 – 23/07
19/08 – 21/08
26/09 – 01/10
28/11 – 03/12

Table 1. Dates and Stations of Observations in 2002a

C12008[10] The distribution of water temperature and its temporalvariation (Figures 4a – 4f ) can be understood qualitatively by
local heating or cooling. As suggested by Figure 3, theKurushima Strait and Bisan Strait are well mixed throughout
the year. In these straits, the surface heating or cooling affects
the entire water column and the water temperature is inversely
proportional to the water depth. With a nearly uniform heat
flux input in the two straits [Tawara, 1986], the shallow
Bisan Strait is more easily warmed or cooled than the deep
Kurushima Strait. In the Seto Inland Sea, the warming andcooling start in March and September, respectively [Ishizaki
and Saito, 1978]. Therefore we observed a higher temperature in the Bisan Strait than in the Kurushima Strait from May
to August, the same temperature in the two straits at the endof September, and a lower temperature in the Bisan Strait
at the end of November. On the other hand, water column
stratification makes heat accumulate in the surface layer andreflects the highest surface temperature in the eastern regionof Hiuchi-Nada in May, June, and July. The low surface
temperature in the eastern region of Hiuchi-Nada in August
may be caused by a relatively strong wind during theobservation period (Figure 5), accompanied by the passage
of a typhoon south of Shikoku 1 day before our observation.
[11] There are two low-salinity areas in the surface layerfrom May to September (Figures 4g –4l). One is at thenorthern part of Bisan Strait. The other is at the southwestern part of Hiuchi-Nada. They are likely direct results ofrunoff from Takahashi River, a major river located at thenorthern coast of Bisan Strait (Figure 1), and some small
rivers along the southwestern coast of Hiuchi-Nada.
[12] With the lowest temperature and highest salinity, thewater in the Kurushima Strait was the heaviest from May to
September (Figures 4m – 4r); with the lowest salinity andincreasing temperature, the water in the Bisan Strait gradually became the lightest. Being the warmest, the surface
water in the eastern part of Hiuchi-Nada was always among
the lightest. As shown later, the bottom water in the easternpart of Hiuchi-Nada that had the lowest water temperatureand highest salinity was also the heaviest water mass in thisarea in June, July, and August.
[13] In order to examine stratification in the entire watercolumn, the potential energy anomaly is calculated (Figure 6).
This variable has been used as an indicator of verticalstratification in many studies [Simpson et al., 1977; Hill etal., 1997; Bisagni, 1999]. It is defined as

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, A, B, C, D, E, F, G, H, J, K, L, M, N, O, P, Q
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, A, B, C, D, E, F, G, H, I, J, L, M, Q

C120081hZ0ðr  rÞgzdz;

ð1Þ

h

where h is the water depth, r is the water density, g is
gravity, z is vertical coordinate
with origin at sea surface andR0
positive upward, and r ¼ 1h h rdz. PEA in (1) has units ofJoule/m3 and is the potential energy anomaly per unit
volume. The larger the PEA is the stronger the stratification.
[14] In May, the largest value of PEA (>80 Joule/m3)
appeared in the southeastern part of Hiuchi-Nada and thesmallest value in the Kurushima Strait and Bisan Strait.
This pattern was maintained in June and July with small
increase of the maximum value of PEA, suggesting the fulldevelopment of stratification by May continuing on through4 of 23

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C12008Figure 4. (a – f ) Water temperature, (g – l) salinity, and (m – r) density at surface layer observed in 2002.
Observation dates are plotted in each panel. H denotes high value, and L denotes low value. An objective
interpolation scheme has been used to calculate the value at each grid point. The weight of each data usedin the interpolation is calculated by exp(r/r0) where r is the distance (in degrees) between CTD stationand grid point and r0 is a given value (0.10.3) which is variable to ensure at least three CTD data to
be involved in the interpolation.

June and July. However, the area with the largest PEA(>80 Joule/m3) shifted slightly northward between May andJuly. In August, the stratification weakened because of thestrong wind event during the observation (Figure 5). In
September and November the entire area was vertically
mixed due to surface cooling and wind.

3. Robust Diagnostic Model[15] Residual currents in the Seto Inland Sea have threemain components: density-driven, wind-driven, and tideinduced currents. The barotropic throughflow is very weakin the Seto Inland Sea [Fujiwara and Higo, 1986] and isomitted in this study.
[16] Because of the strong effects of tidal mixing near thetwo straits, a diagnostic model [Sarkisyan and Ivanov, 1971;
Holland and Hirschman, 1972] rather than geostrophic
method is used to calculate residual currents in this study.
Holland and Hirschman [1972] show that the calculated
currents tend to be sensitive to the input density field that isfixed in the diagnostic model. To overcome this problem,

Sarmiento and Bryan [1982] propose a robust diagnostic
model that solves the conservation equations for temperature and salinity in a prognostic way. The observed temperature and salinity data are included in the conservation
equations with an additional damping term. Compared to atypical diagnostic model [Sarkisyan and Ivanov, 1971;
Holland and Hirschman, 1972], the robust diagnostic model
is more resistant to minor inconsistencies in the input
density data and produces a smooth current field and aconsistent density field [Sarmiento and Bryan, 1982].
[17] To avoid inconsistencies in the input density data isdifficult in coastal waters. Tidal currents always induceinconsistencies in the density field obtained by a snapshot
observation. Objective interpolations, which produce theinput density field from limited observed data, also introduce inconsistencies. Therefore a robust diagnostic model
rather than a diagnostic model is the choice for calculating
residual currents in coastal waters.
[18] One of the community ocean models for coastal
waters, the Princeton Ocean Model (POM [Blumberg andMellor, 1987; Mellor, 1998]), is adopted to be the base of

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C12008Figure 4. (continued)
the robust diagnostic model. The original POM is modified
through the introduction of a damping term in the equations
for temperature and salinity as follows:




@T
@T
@T
@T
@
@T
@
@T
þ
þu
þv
þw
¼
AH
AH
@t
@x
@x
@z @x
@x
@y
@y


@
@T
þ gðT *  T Þ;
þ
AV
@z
@z

ð2Þ

where T is temperature or salinity, u, v, w are the threecomponents of velocity, AH and AV are horizontal andvertical diffusivities, respectively, and T* is observed
temperature or salinity; g is a parameter controlling therole of observed data T*.
[19] The model domain and topography are shown in
Figure 1b. The horizontal resolution is roughly 500 m(1/160 in the zonal direction and 1/240 in the meridional
direction). The relatively high resolution in the horizontal isnecessary to represent the narrow channels around theKurushima Strait (Figure 1). There are 21 sigma-levels inthe vertical (Table 2) with finer grid interval near surface
and bottom. The bottom stresses are calculated using a

Figure 5. Time series of daily mean wind speed (m/s) records at stations 4 and 6 from May to the end of
2002. Data at the other stations (see Figure 1 for positions of all stations) show a similar temporalvariation. The time between two broken lines are the periods of observations.
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C12008Figure 6. Distribution of potential energy anomaly per unit volume. See equation (1) for the definition.
quadratic friction law, and the bottom drag coefficient iscalculated by the embedded formula in the POM [Mellor,1998]. The time step is 2 s for the external mode and 60 s
for the internal mode.
[20] To ensure that the current related to the pressure
gradient error is small, the topography data are smoothedwith the embedded subroutine SLPMIN in the POM tosatisfy the criteria given by Mellor et al. [1994],
j Hiþ1  Hi j
ðHiþ1 þ Hi Þ

a;

ð3Þ

where Hi+1 and Hi are the depths at two adjacent grids, a isa slope factor (=0.2).

[21] Physically, the pressure gradient error should besmall in this study. This is because the pressure gradienterror tends to be large only when water depth variations
combine with strong stratification [Mellor et al., 1994]. In
our study area, the water depth varies greatly near or in
the straits (Figure 1) where the water is always homogeneous (Figure 6). On the other hand, the regions withstrong stratification (Figure 6) have small gradients ofdepth (Figure 1). Estimation of velocity induced by thepressure gradient error in a manner similar to Beckmann
and Haidvogel [1993] and Mellor et al. [1998] shows thatthe maximum velocity with the vertical profiles of density
obtained from six surveys occurs around the Kurushima
Strait and is less than 2 cm/s. Beyond the Kurushima

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Table 2. Values of Sigma-Coordinate
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
0.009
0.018
0.036
0.071
0.143
0.214
0.286
0.357
0.429
0.5000.571
0.643
0.714
0.786
0.857
0.929
0.964
0.982
0.991
1.000Strait, the magnitude of velocity is less than 1 cm/s.
Therefore the effects of pressure gradient error can be
negligible in this study.
[22] We do not directly include tidal currents in diagnostic calculations but consider their mixing effects by relating
eddy viscosities and diffusivities to tidal currents. Usually,tidal currents are stronger than residual currents by 1 orderof magnitude. Direct inclusion of tidal currents in thecalculations of residual currents could induce residual
currents to be of the same order of magnitude as thecalculation error of tidal currents. Furthermore, separationof density-driven, wind-driven, and tide-induced components of residual currents becomes impossible.
[23] The Mellor-Yamada (MY) turbulence closure model[Mellor and Yamada, 1982] embedded in the POM is used
to estimate vertical eddy viscosity and diffusivity dependent
on tidal currents. Simpson et al. [1996] show that the MY
closure model can simulate well their observed turbulent
dissipation in the Irish Sea where the tidal currents have anamplitude from 0.45 m/s to 1.0 m/s. Burchard et al. [1998]
compare the performance of MY and k  e turbulencemodels and show that both models can predict well the dataobtained by Simpson et al. [1996]. Wijesekera et al. [2003]
compare three turbulent closure schemes (MY closure,k  e closure, and K-Profile Parameterization) and show that
all three turbulent models produce similar features in thecirculation and qualitatively similar eddy diffusivities andeddy viscosities.
[24] Several prognostic calculations were carried out inadvance to obtain the vertical eddy viscosity and diffusivity
related to tidal currents. The M2 tidal current was imposed
along the western and eastern boundaries of the model
domain where the harmonic constants were obtained froma tidal model of the entire Seto Inland Sea [Harai etal., 2001]. The observed temperature and salinity fields(Figure 4) were used as the initial values. The calculations
also produce horizontal eddy viscosity on the basis of the
Smagorinsky formula [Mellor, 1998] with a proportionality
parameter of 0.1, and horizontal eddy diffusivity with agiven inverse Prandtl number (=0.5).

C12008[25] As shown by Simpson et al. [1996], Stacey et al.
[1999], and Lu et al. [2000], the vertical eddy viscosity
varies temporally with tidal phase. The horizontal eddy
viscosity has similar temporal variations as well. The
combined effects of temporally varying vertical or horizontal eddy viscosities and vertical or horizontal shears of
tidal currents could induce residual currents, but they areparts of the tide-induced residual current. In our diagnostic
calculations, tidally averaged vertical and horizontal eddy
viscosities and diffusivities were used.
[26] Figure 7 presents horizontal distributions of AH and
AV at three depths. Eddy viscosities have similar distributions to these two parameters. In the Kurushima Strait andBisan Strait, large vertical (0.010.1 m2/s) and horizontal(10100 m2/s) eddy diffusivities are obtained. In theeastern part of bay, small vertical (105 m2/s) andhorizontal (0.1 m2/s) eddy diffusivities are obtained.
Relatively large vertical eddy diffusivity is obtained near
the bottom (Figure 7c).
[27] We have no direct observations to verify the calculated vertical and horizontal eddy viscosities (Figure 7),particularly the large values in the Kurushima Strait.
However, in a partially stratified channel in northern San
Francisco Bay, where the amplitude of tidal current is 0.7–
0.9 m/s, Stacey et al. [1999] show an observed vertical eddy
viscosity ranging from 0.005 m2/s to over 0.02 m2/s, with the
maximum values occurring near the bottom. Lu et al. [2000]
also present an observed vertical eddy viscosity ranging from0.001 m2/s to over 0.3 m2/s in a tidal channel where theamplitude of the tidal current was about 1.0 m/s. Thus,
considering the stronger M2 tidal current (2.5 m/s) in the
Kurushima Strait, the estimates of vertical eddy viscosity(Figure 7) seem reasonable. As for the horizontal eddy
diffusivity, Hayami and Unoki [1970] suggest a value of1000 m2/s for the reproduction of salinity distribution in
the Seto Inland Sea in a one-dimensional model. Whendensity-driven currents are considered, this value can be
reduced by 30 to 50% [Murakami et al., 1985], which is on
the same order as those obtained in the two straits (Figure 7).
[28] An important issue of the robust diagnostic model isthe determination of g, which is a free parameter. Physically,
it controls the role of observed data in (2). Sarmiento andBryan [1982] show that the ratio of the damping term g(T* T ) to the horizontal advection term in (2) is g L*/V*, where
V* is a scale velocity and L* is a scale length. A small g
weakens the effects of damping term, and the advection term
dominates the conservation equation. In this case, the model
approaches a prognostic model. On the other hand, a large g
makes the model approach a pure diagnostic model (T = T*)
in which the advection effect is weak. In the calculations of
the Atlantic, Sarmiento and Bryan [1982] use a depthdependent g that ranges from 1/50 day1 to 1/250 day1.
In the calculations of the Pacific, Fujio and Imasato [1991]
use a latitude-dependent g that ranges from 1/50 day1 tozero. From g L*/V*, we know that in the application withsmall horizontal scale like the Hiuchi-Nada, a large g isneeded to keep the same ratio of damping term to theadvection term as that in the application with large horizontal
scale such as the Atlantic or the Pacific, if the scale velocities
are of the same order.
[29] We carried out a series of calculations to examine theresponse of model results to g. With a decrease of g, the

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C12008Figure 7. Horizontal distribution of tidally averaged (a– c) vertical and (d – f ) horizontal eddy
diffusivities at 5, 10, and 20 m from the calculation for July with tide.

calculated temperature and salinity deviates gradually fromthe initial values (Figure 8). From the viewpoint of diagnosing the velocity from hydrographic data, a larger g ispreferable. The difference between the calculated currents
and observations (Figure 2) reaches a minimum as g equals to
0.5 day1. Because there is little difference in the calculated
currents as g varies from 1.0 to 0.2 day1, we set g to 1 day1.
We notice that the same value of g has been used in thecalculations of the East China Sea [Yanagi and Takahashi,
1993] and the Tokyo Bay, Japan [Guo and Yanagi, 1996].
[30] The initial temperature and salinity in the diagnostic
model are the same as the observed water temperature andsalinity fields (Figure 4). The initial velocity and sea level iszero. The western and eastern boundaries are treated as wallin the diagnostic calculations. As the calculations started,
the pressure gradient from the initial temperature andsalinity produced currents that in turn are used to adjust
the distribution of temperature and salinity. At the sametime, the damping term in (2) constrains the calculated
temperature and salinity to the observations. After 10 days,
the model approaches a steady state where the mean
velocity over the entire model domain has been stable andthe calculated currents and density field are dynamicallyconsistent with each other. The wind stresses were notinitially included, and their impact will be discussed in

section 7.2. Therefore the currents from the above calculations are density-driven flows.

4. Current Patterns[31] In May, a large clockwise eddy in the southern partof Hiuchi-Nada dominates the surface layer (Figure 9a),while a southward current in the central part dominates the
middle layer (Figure 9b). An anticlockwise eddy forms in
the northeastern part, which is stronger in the middle layer
than in the surface layer (Figures 9a and 9b). The current in
the bottom layer (Figure 9c) is weak. In June, a clockwise
eddy dominates the surface layer in the western part ofHiuchi-Nada (Figure 9d). In the eastern part, an anticlockwise eddy develops, and it is stronger in the surface layer thanin the middle layer (Figure 9e). The southward current in thecentral part of the middle layer remains and extends to thesurface layer. In the bottom layer (Figure 9f ), a northwardcurrent is found along the eastern coast of Hiuchi-Nada. In
July (Figures 10a– 10c) and August (Figures 10d and 10e),the current pattern is similar to that in June, but the current
itself intensifies in July and weakens in August. In
September and November (Figure 11), the current patterns
are completely different from those in June, July, andAugust and show rather incoherent distributions.

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C12008Figure 8. Model response to the change of g. Errors for temperature (T) and salinity (S) are defined asor salinity,
the average of jTinitial  T j at all grid points, where Tinitial is the initial value of temperatureqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ
and T is the calculated one; error for velocity (V) is defined as the average of ðuobs  uÞ2 þðvobs  vÞ2 at
42 stations shown in Figure 2, where uobs} and vobs are the eastward and northward components ofobserved currents (Figure 2), u and v are calculated ones at the corresponding grid point. All three errors
are normalized by the corresponding maximum values, 0.68, 0.09 psu, and 9 cm/s for temperature,salinity, and velocity, respectively. All the results are from the July calculations.

[32] The calculated current pattern in the surface layer inJuly (Figures 10a and 10b) can be compared with theobserved currents (Figure 2) because wind forcing during
the period of current observations was very weak, and thetide-induced residual current is restricted to the vicinity of
the Kurushima Strait and Bisan Strait (shown later). In theeastern part of Hiuchi-Nada, the anticlockwise eddy with aspeed of 10 cm/s (Figures 10a and 10b) is consistent withobservations (Figure 2). Over the western part of the
Hiuchi-Nada, observations show a northward current southeast of the Kurushima Strait and a northeastward current
northeast of the Kurushima Strait. Lack of data between
these two locations makes it difficult to link them as anorthward current. Model results suggest they are part ofa northward current between the Kurushima Strait andHiuchi-Nada. Therefore, in the summer the basic flow patternin the Hiuchi-Nada consists of a clockwise eddy in thewestern part and an anticlockwise eddy in the eastern part.

5. Vertical Structure of Two Eddies[33] Figure 10 shows that the two eddies have different
vertical structure. The clockwise eddy in the western partconcentrates in the surface layer, while the anticlockwise
eddy in the eastern part intrudes into the middle layer.
Further examination of the vertical structure of the two

eddies can be effected with the distributions of temperature,salinity, density, and northward current along a section acrossthe two eddies (Figure 12; see Figure 10f for section’s
position). In the western part of Hiuchi-Nada, a tidal front
with horizontal density gradient of 1 kg m3/10 km can be
identified (Figure 12c). The northward current accompanying this front has a strong vertical shear and its speed at
the surface reaches 10 cm/s (Figure 12d). Dynamically, thisnorthward current is the geostrophic flow associated with thedensity structure of the tidal front [Garrett and Loder, 1981].
Because the northward current accompanying the tidal front
is the major part of the clockwise eddy in the western part ofthe bay, the tidal front formed in the summer is therefore themajor cause for the formation of the clockwise eddy. The tidal
front can be maintained only in the summer. When thecooling starts, the clockwise eddy on the western part
disappears (Figure 11).
[34] In the eastern part of Hiuchi-Nada, the presence ofcold bottom water is evident and results in a temperature
difference of more than 6 between surface and bottom.
Combined with the salinity difference (0.4 psu), thevertical gradient of density is about 1 kg m3/10 m. The
anticlockwise eddy exists above the cold (also dense)
bottom water with small vertical shear. This eddy is also
geostrophically balanced by looking at the sea level distribution in Figure 10. Dynamically, it is possible for a

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C12008Figure 9. Horizontal distribution of residual currents at 0, 10, and 20 m in May and June. Sea level
distributions are also shown in all panels as a reference.

clockwise circulation to develop in the dense (cold) bottom
dome water while the water above it remains at rest.
However, this situation is difficult to maintain in coastal
waters because the bottom layer spins down to rest in a few
days due to bottom friction, and an anticlockwise circulation

finally develops above the dense (cold) bottom dome water[Hill, 1996]. This mechanism has been used to explain theexistence of a cyclonic gyre in the summer in the surface
layer of the western Irish Sea where cold bottom water
exists [Hill et al., 1997]. The same mechanism could also be

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Figure 10. The same as Figure 9 but for July and August. The zonal line in Figure 10f represents the
position of a section, along which the distribution of temperature, salinity, density, and northward
velocity are shown in Figure 12.

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C12008Figure 11. The same as Figure 9 but for September and November.
responsible for the presence of the anticlockwise eddy in theeastern part of Hiuchi-Nada.

6. Intrusion Routes of Strait Water[35] To clarify the pathways of strait water into the HiuchiNada, we continually release passive tracers with a value of

100 in the Kurushima Strait (tracer A, 132.95 – 130.05E,
34.0– 34.4N, see Figure 1b for location) and Bisan Strait(tracer B, 133.6 – 133.75E, 34.25 – 34.5N), respectively.
Both passive tracers are controlled by the same equation as
the temperature, but without the g term. The currents shownin Figures 9 – 11 and the horizontal and vertical eddy
diffusivities (Figure 7) are adopted in the tracer calculations.

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C12008Figure 12. Vertical distribution of (a) temperature, (b) salinity, (c) density, and (d) northward velocity
along a zonal section shown in Figure 10f. Results are from July calculations.

[36] The distributions of tracers, 30 days after theirrelease in the Kurushima Strait and Bisan Strait, are shownin Figures 13 and 14, respectively. From May to August, thetracer A cannot enter the Hiuchi-Nada through the surface
layer because of the northward current along the tidal front
east of the Kurushima Strait. In the middle and bottom
layers, the tracer A reaches as far as the central part ofHiuchi-Nada, particularly in July and August. Figures 10c
and 10f show a flow from the Kurushima Strait to theHiuchi-Nada in the bottom layer, which must be responsible
for the bottom intrusion of Kurushima Strait water. In the
middle layer, we do not observe a clear current toward theHiuchi-Nada in Figures 10b and 10e. Therefore the strong
vertical mixing near the bottom (Figure 7c) could be
responsible for the tracer in the middle layer in July andAugust. In November, breakdown of the tidal front enables
the tracer A to enter the Hiuchi-Nada through the surface
layer, together with the current along the southern coast ofHiuchi-Nada (Figure 11d).
[37] The tracer B shows a different intrusion route(Figure 14). A major intrusion occurs in the surface layer.
In May, the intrusion is weak and most of the tracer stays in
the northern part of Hiuchi-Nada. From June to August, theintrusion becomes gradually strong. After reaching thesouthern coast of Hiuchi-Nada, the tracer B in the surface
layer is caught by the anticlockwise eddy in the eastern partof Hiuchi-Nada, except in July when portions of the tracer
are transported westward and reach the tidal front area eastof the Kurushima Strait. In September and November, theintrusion becomes weak.
[38] In summer, the water of the Kurushima Strait enters
the Hiuchi-Nada through the bottom layer while that of the
Bisan Strait enters through the surface layer. The counterintrusion route of the water from two straits can be understood from the density structure between the straits and theHiuchi-Nada. As shown in Figure 4, with strong tidal
mixing in the two straits, the deepest water column makes
the water in the Kurushima Strait the heaviest in summer,
while the shallowest water column makes the water in the
Bisan Strait the lightest. Therefore the water from theKurushima Strait intrudes mainly from the bottom layer,
while that from the Bisan Strait intrudes from the surface
layer.
[39] In July and August, most of the tracer B trapped by
the anticlockwise eddy in the eastern part of Hiuchi-Nada
stays only in the outer side of the eddy and does not reachthe center of the eddy (Figure 14). This indicates the
anticlockwise eddy isolates the water in its center fromthe water in its outer edges. This isolation could contributeto the formation of oxygen-deficient water mass in thecenter of the eddy in summer because the concentration ofoxygen is usually high outside the cold bottom water. An
example is given in Figure 15, in which the temperature andconcentration of dissolved oxygen (DO) at 10 m and 20 mfrom an observation in July 2003 are shown. At 10 m, a
cold water mass can be identified in the eastern part of the

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Figure 13. Horizontal distribution of tracer concentration at 0, 10, and 20 m, 30 days after being
released in the Kurushima Strait.
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Figure 14. Horizontal distribution of tracer concentration at 0, 10, and 20 m, 30 days after being
released in the Bisan Strait.
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C12008C12008Figure 15. (a, b) Horizontal distribution of temperature and (c, d) concentration of dissolved oxygen at
10 and 20 m, from an observation in July 2003. The black triangles denote the observation stations.

bay but the concentration of DO in the cold water is not
lower than the surrounding waters. At 20 m, a cold watermass can also be identified and the concentration of DO islower than the surrounding areas; that is, the area with low
concentration of DO coincides with the area with low
temperature. Outside the bottom cold water, high concentration of DO was observed.
[40] The observed distribution of DO cannot be explained
only by the isolation of the eddy. In addition to thehorizontal processes, the vertical supply of oxygen andthe biological processes related to the supply and consumption of oxygen also affect concentrations of DO. However,isolation of the eddy (Figure 14), at least, hinders thehorizontal supply of oxygen to the center of the eddy.

7. Discussions
7.1. Effects of Tidal Mixing on Density-Driven Current[41] To demonstrate the effects of tidal mixing on densitydriven currents, as well as to examine the sensitivity ofdensity-driven currents to the vertical eddy viscosity, we
carried out some calculations in which the vertical andhorizontal eddy viscosities were also calculated by the
MY turbulent closure model and Smagorinsky formula,respectively, but without tide. An example of vertical andhorizontal eddy viscosities given by these new calculations
is shown in Figure 16. Compared to Figure 7, the newvertical and horizontal eddy viscosities are much smaller
than those related to tidal currents, in particular in the
Kurushima Strait and Bisan Strait.
[42] From Figure 17, we see that smaller viscosity isfavorable for the development of density-driven currents instraits. Comparing Figure 17 to Figures 9 – 11, the basic
flow patterns in each month are the same but the intensity ofthe two eddies becomes stronger in the cases without effectsof tidal mixing (Figure 17). The largest difference is in the
Kurushima Strait, where strong currents develop in thecases without effects of tidal mixing. This demonstrates
the importance of tidal effects in calculations of the residual
current in the Seto Inland Sea, where the strong tidal current
in the straits produces large viscosity that weakens theresidual current in the straits.
7.2. Effect of Wind[43] In addition to density-driven currents, wind-driven
currents are also important for the residual current in coastal
waters. As shown in Figure 5, summer winds over the
Hiuchi-Nada are usually weak. Although there are somespatial variations from station to station, the mean windspeed in the summer can be taken as 2 m/s. After September, winds become strong with several energetic pulses.
[44] To examine the effects of wind on the two eddies inthe Hiuchi-Nada during the summer, winds from the east,
west, north, and south with speeds of 2 m/s were added in
the July calculation. The wind stress, t, prescribed in themodel is calculated with t = raCdU2a, where ra(= 1.2 kg/m3)
is air density, Cd (= 1.3  103) is drag coefficient, and Ua
is wind speed. The currents obtained in the surface layer
respond directly to the imposed wind and are different fromthe results without wind forcing (Figure 10a). However, inthe layer just underneath, for example at 5 m (Figure 18),
little difference can be found in the calculated currents by
the cases with and without wind forcing. The clockwise
eddy in the western side and the anticlockwise eddy in theeastern side are hardly affected by the summer wind. Thissuggests that the basic circulation pattern of the two eddies
persists throughout the summer. In fact, the calculated
current pattern in August (Figure 10) implies that the two

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C12008Figure 16. Horizontal distribution of (a – c) vertical and (d– f ) horizontal eddy viscosities at 5, 10, and20 m from the July calculation without tide.

eddies can exist even after a strong wind event that mixed
the surface layer.
7.3. Tide-Induced Residual Current[45] Tide-induced residual currents resulting from nonlinear effects of tidal currents are the third component of theresidual flow in our study area. To obtain the tide-induced
residual currents, the model with spatially constant temperature and salinity was driven by the M2 tidal current in amanner the same as that in the prognostic model describedin section 2. Harmonic analysis of model results gives the
distribution of tide-induced residual currents (Figure 19).
Only in the vicinity of the two straits, tide-induced residual
currents are strong. Near the Kurushima Strait, tide-induced
residual currents form an anticlockwise eddy that slightly
weakens with depth. In the Hiuchi-Nada, tide-induced
residual currents are weaker than 2 cm/s. Thus they do
not affect the fate of the two eddies in the Hiuchi-Nada in
the summer.
[46] With inclusion of tide-induced residual currents, we
carried out passive tracer experiments again. The tracer
released in the Kurushima strait (Figure 20) is greatly
influenced by tide-induced residual currents but the tracer
released in the Bisan Strait is little affected (not shown here).
As tide-induced residual currents are added to density-driven

currents in the tracer experiments, much more tracer istransported from the Kurushima Strait to the Hiuchi-Nada(Figure 20). After 30 days, it reaches the central area of
Hiuchi-Nada or the eastern area of Hiuchi-Nada. However,
the intrusion of water from the Kurushima Strait is still
stronger in the middle and bottom layers than in the surface
layer. This is because the tide-induced residual current near
the Kurushima Strait has little variation in the vertical(Figure 19). Therefore, tide-induced residual currents do
not affect the intrusion pathway of waters from the twostraits into the Hiuchi-Nada.

8. Summary[47] This study clarifies two issues, the three-dimensional
structure of residual currents in the Hiuchi-Nada and the
intrusion pathway of waters from the Kurushima Strait andBisan Strait into the Hiuchi-Nada. The main results are
summarized in Figure 21.
[48] With a robust diagnostic model, we obtain thedensity-driven current in the Hiuchi-Nada from hydrographic data and find the existence of two eddies in thesummer, which is consistent with early observations derived
from moored arrays. One is a clockwise eddy in the westernpart, associated with the tidal front between the Kurushima

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C12008Figure 17. Horizontal distribution of residual current at the surface layer from the calculations without
tide. Sea level distributions are also shown as a reference.

Strait and the Hiuchi-Nada. The other is an anticlockwise
eddy in the eastern part, related to cold and dense bottom
waters. The magnitude of the two eddies is 10 cm/s.
[49] The average wind speed in the Hiuchi-Nada during
the summer is around 2 m/s. The wind-driven current isvery weak and is limited to the surface layer. It is difficult to
identify the difference in the current distribution at 5 m
depth from the calculations with and without wind
(Figure 18). Therefore the existence of the two eddies inthe bay in the summer is not affected by the wind. On the

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Figure 18. Residual current at 5 m in July, from the calculation (a) without wind, and with (b) east
wind, (c) west wind, (d) north wind, and (e) south wind. Sea level distributions are also shown as areference.

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C12008Figure 19. Horizontal distribution of tide-induced residual current at 0 and 20 m. The magnitude of thecurrent is presented by dark tone.

other hand, tide-induced residual currents are restricted tothe close vicinity of the Kurushima Strait and Bisan Strait.
This component also does not affect the existence of thetwo eddies because the two eddies are located inside thebay.
[50] As a method to obtain the density-driven current, we
adopted the robust diagnostic model. Another method could
be geostrophic computation, which is simpler than the
diagnostic calculation. There are two reasons why we did
not use the geostrophic computation. Dynamically, in
addition to the geostrophic balance, the internal friction
also plays an important role in the density-driven current ina tide-dominant coastal area. The internal friction could
alter the vertical structure of the geostrophic current.
Technically, the geostrophic computation can obtain only
the current component normal to the section of two hydrographic stations and is difficult to represent the horizontal
distribution of the current in a bay. If the two hydrographic
stations are across the flow direction, the geostrophic
computation can produce the current. However, if the twohydrographic stations are along the flow direction, thegeostrophic computation cannot produce the current. In
our application, the hydrographic stations are not designed
to be across the two eddies. Consequently, the purely
geostrophic computation cannot produce the two eddies(not shown here).
[51] Usually, we cannot correctly predict the current
pattern in a bay before the hydrographic survey and also
cannot assure that the hydrographic stations are across the
major currents in a bay. Therefore, although the geostrophic
balance is an important dynamic in the coastal areas, thegeostrophic computation is not a good method to produce
the horizontal distribution of residual current in a bay.
[52] The robust diagnostic model is a useful tool to obtain
the density-driven current from the results of hydrographic
survey. Careful preparations of input density data areimportant to the diagnostic model. This can be achievedby rapid completion of hydrographic surveys over a wide

coverage, which helps to reduce the inconsistency of input
density data. Another important factor while applying
robust diagnostic models to coastal waters is the treatmentof tidal mixing in the model. In this application, we related
the eddy viscosity/diffusivity to the tidal current. In the twostraits where the tidal currents are stronger than 1 m/s, large
vertical (0.010.1 m2/s) and horizontal (10100 m2/s)
eddy diffusivities are obtained (Figure 7). In the easternpart of bay where the tidal current is weaker than 0.1 m/s,
small vertical (105 m2/s) and horizontal (0.1 m2/s)
eddy diffusivities are obtained. In the vertical, relatively
large vertical eddy diffusivity is obtained near the bottom(Figure 7c). As shown in section 7, the distribution of eddy
viscosity/diffusivity influences strongly on the intensity ofcalculated currents.
[53] From passive tracer experiments, we obtain different
intrusion routes for waters from the Kurushima Strait andfrom the Bisan Strait into the Hiuchi-Nada. The water fromthe Kurushima Strait intrudes through the middle andbottom layers, while the water from the Bisan Strait intrudes
through the surface layer. In Figure 21, we also show thatwater in the Hiuchi-Nada may enter the Kurushima Strait
through the surface layer and move into the Bisan Strait
through the bottom layer, which can be considered ascompensatory effects to the intrusion of water from thetwo straits. This result can be inferred easily from current
fields (Figure 10) and has been confirmed by additional
calculations in which passive tracers have been released in
the Hiuchi-Nada.
[54] The anticlockwise eddy in the eastern part of HiuchiNada traps most of the tracer from the Bisan Strait andmaintains it along the outer edge of the eddy, preventing thetracer from reaching the center of the eddy (Figure 14). This
indicates that the anticlockwise eddy has no water exchange
between its center and its outer edges, and therefore allows
the development of oxygen-deficient waters in the central
part of the eddy. However, the extent to which this horizontal isolation contributes to the formation of oxygen-

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Figure 20. Horizontal distribution of tracer concentration at 0, 10, and 20 m, 30 days after being
released in the Kurushima Strait, from the calculations including tide-induced residual current.
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Figure 21. Schematic of circulation pattern in the HiuchiNada in the summer and intrusion routes of passive tracer
between the Hiuchi-Nada and Kurushima Strait andbetween the Hiuchi-Nada and Bisan Strait. Arrows denotedby an ‘‘S’’ indicate the intrusion in the surface layer. Arrows
denoted by a ‘‘B’’ indicate the intrusion in the bottom layer
referred to the local depth of two straits.

deficient water mass is still unknown and should be studied
in the future with an ecosystem model.
[55] Acknowledgments. This research was supported by Grant-inAid for Scientific Research (A) from Japan Society for Promotion of
Science (grant 12308027). Discussions with A. Kaneda and Y. Hayami
were very helpful in planning observations. We appreciate Arnoldo ValleLevinson and Andres Tejada-Martinez for their valuable suggestions on the
manuscript and the reviewers whose comments helped to improve themanuscript. This paper was written while X. Guo was visiting the Centerfor Coastal Physical Oceanography at Old Dominion University. He thanks
support from Ministry of Education, Culture, Sports, Science and Technology, Japan.

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

A. Futamura, Graduate School of Science and Engineering, Ehime
University, Matsuyama 790-8577, Japan.
X. Guo and H. Takeoka, Center for Marine Environmental Studies,
Ehime University, 2-5 Bunkyo-Cho, Matsuyama 790-8577, Japan.
(guoxinyu@dpc.ehime-u.ac.jp)

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