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On the seasonal variation in in- and outflow volume transport of the Japan Sea
Prog. Oceanog. Vol. 21, pp. 269-279. 1988. Printed in Great Britain. All rights reserved.
0079-6611/88 $0.00 + .50 Copyright © 1989 Pergamon Press plc
On the Seasonal Variation in In- and Outflow Volume Transport of the Japan Sea YOSHIHIKO SEKINE*
Institute of Geoscience, National Defense Academy, Yokosuka 239, Japan (Received 28 March 1988; in revised form 8 August 1988; accepted 10 August 1988) Abstract--Dynamics of the seasonal variation in the volume transport of the Tsushima Current is considered from the view point that the in- and outflow of the Japan Sea is essentially due to the sea level difference between the inflow re#on and outflow region. The sea level difference is estimated by a numerical model driven by the observed wind stress over the North Pacific. It is shown that the sea level difference is largest in winter and relatively small in summer to autumn. On the other hand, because the density stratification is very weak in winter, water has a tendency to flow along the geostrophic contour. This decreases the in- and outflow transport. The transport of the in- and outflow of the Japan Sea varies with the intensity of density stratification rather than to the sea level difference, though its mean essentially depends on the sea level difference. The observed maximum (minimum) inflow transport in summer (winter) is due to the strong (weak) density stratification in the straits. The low density river water discharged in the East China Sea plays an important role in the larger inflow of the Tsushima Current in summer to autumn.
!. INTRODUCTION THE JAPAN SEA is a marginal sea surrounded by the Japanese Islands and the Asian continent. The major feature of the current system in the Japan Sea is an inflow of the Tsushima Current through the Tsushima Strait and two outflows through the Tsugaru Strait and the Soya Strait. It has been suggested by MINATO and KIMORA (1980) that the in- and outflow of the Japan Sea are caused by the pressure difference between the Tsushima Strait and the Tsugaru and Soya Straits. Later their theory was supported by TOBA, TOMIZAWA, KURASAWAand HANAWA (1982), in which the observed dynamic height was shown to be highest at the inlet of the Tsushima Strait and lowest in the outlet of the Tsugaru Strait. MINAMI (1985) suggested that the downstream pressure gradient exists in the Tsugaru and Soya Current, but the sea level is almost constant through the Tsushima Strait. The Tsugaru and Soya Currents have been demonstrated to be semi-geostrophic by observations (e.g. AOTA and MArSUYhMA, 1987), in which the geostrophic balance is possible in the cross stream direction but impossible in the downstream direction. Therefore, the total in- and outflow of the Japan Sea is basically due to the sea level difference as proposed by MINATO and KIMURA (1980), hereafter referred to as M&K. Figure l(a) shows the schematic view of the model used in M&K. An equivalent barotropic model is assumed and the depth (D) of the ocean is actually represented by the *Present address: Institute of Oceanography, Faculty of Bioresources, Mie University, 1515 Kamihama, Tsu, Mie, 514 Japan. 269
270
Y. SEKINE Y
a i
°--~
I"
°
" . . . . . . . . . .
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C
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FIG. 1. (a) The model ocean by MINATO and KIMURA (1980). (b) Typical stream lines obtained by MINATO and KIMtJRA (1980). (C) Ratio of the volume transport into the marginal sea (~b to the maximum value of the volume transport in the open ocean (~#(max)) as a function of ~' = 2 Y D o f l / A v . All parameters in (c) except for r are the same as those in (b).
thickness of the upper layer where the current velocity is relatively large. The sea level difference between the two straits is estimated by a simple wind-driven circulation model similar to STOM~L (1948). They showed that the inflow into a marginal sea depends on not only the pressure difference but also the intensity of bottom friction representative of the topographic effect. If the ratio r of the upper layer thickness of the marginal sea to that of the open ocean (Fig. l(a)) approaches 1 (zero), the larger (smaller) inflow appears (Fig. l(b,c)). Namely, because a barotropic geophysical fluid has a strong tendency to flow along the geostrophic contour f/D, where f is the Coriolis parameter and D is the upper
Seasonal variation in in- and outflowvolume transport
271
layer thickness (e.g. PEDLOSKY, 1979; GILL, 1982), the motion across the geostrophic contour is greatly suppressed. Therefore, as the gap in the upper layer thickness between the open ocean and the marginal sea becomes small (large), and in- and outflow volume transport across the strait is increased (decreased). By applying the representative values of the Japan Sea and the two straits, M&K showed that 2% of the volume transport of the Kuroshio penetrates into the Japan Sea. Figure 2 shows the seasonal change in the observed current velocity through the Tsushima Strait (INOUE, MIITA and TAWARA, 1985). The velocity is relatively large in summer and weak in winter. On the other hand, the vertical velocity shear is remarkable in summer to autumn and small in winter. Although the calculation of the in- and outflow was made only for one representative case by M&K, there is a clear seasonal variation in the volume transport of the in- and outflow of the Japan Sea. In the present study, the seasonal variation in the in- and outflow volume transport of the Japan Sea is studied by use of the model of M&K. Although M&K modeled the annual mean state, the application of their theory is possible if the adjustment of the system to the change in the sea level difference is fast. However, because the sea level change is considered to be the barotropic response and it is well-known that the barotropic response is very fast (e.g. GILL, 1982), the representative response time is less than the seasonal time scale. So it is reasonable to apply M&K's theory to the seasonal variation. In the present study, the sea level difference between the Tsushima and Tsugaru Straits is estimated by a numerical model covering the north Pacific, because there are neither observational data of the seasonal variation of the sea level nor data of the barotropic component of the velocity. The effect of the density stratification on the transport variation will be discussed by use of the equivalent barotropic theory. The model will be described in Section 2. The results will be presented in Section 3 with reference to the sea level difference and the parameterization of the density stratification. Summary and discussion will be made in Section 4. 2. FORMULATION The non-dimensional in- and outflow volume transport ~b proposed by M&K is
DofoH/(Av/7) SLD t~ = D0fl( 1 + ro~)Y/2A v + (r~t + r~2)Lt/W ~+ ( r ~ + r~2)L2/W2 FLAT FTSM FTGR
(1)
The notation is as follows:
Av: coefficient of the bottom friction 13: linear change rate of the Coriolis parameter Do: upper layer thickness of the Pacific ocean f0: Coriolis parameter H: sea level difference /7: mean sea level difference L~: length of the strait r i : ratio of the thickness of upper layer in the strait, where relatively large velocity is found, to that of the Pacific ocean
WINTER
~
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.I/~
/
~
s
SUMMER AUTUMN
~
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" M ~'-w~sl
. ~,( ,
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. SUMMER AUTUMN
in the inserted map.
et al., 1985), All the available data by the direct current m e a s u r e m e n t s in 192~1974 are plotted. The locations o f the two stations are shown by solid circles
FIG. 2. Seasonal change in the observed mean current velocity at two points in the Tsushima Strait, west strait (left) and east strait (right) (after |NO~
s0m
20 rn
/ / /
,.<
Seasonal variation in in- and outflow volume transport
273
r0: ratio of the similar thickness of upper layer in the marginal sea to that of the Pacific ocean W: width of the strait Y: latitudinal distance of the two straits (Y = Y2-Yl, cf. Fig. l(a)). Subscripts 1,2: quantities in the inflow strait (the Tsushima Strait) and the outflow strait (Tsugaru Strait), respectively. Letters SLD, FLAT, FTSM and FTGR: terms used in the discussion. The sea level difference H is non-dimensionalized by the mean sea level difference H, while H is non-dimensionalized by the relation of the Sverdrup balance in M&K. The interpretation of eqn (1) is similar to Ohm's law: the volume transport (electric current) is proportional to the pressure gradient represented by the sea level difference (voltage) shown in the numerator (SLD) and inversely proportional to the friction (electric resistance) in the denominator; the first (FLAT), second (FTSM) and third (FTGR) terms represent the friction in the Japan Sea, the Tsushima Strait and Tsugaru Strait, respectively (for details of eqn (1), see M&K). Although some parameters in (1) cannot be defined clearly, we put Y = 1215km, L~ = 500 km, L2= 100km, W~ = 100 km, I4/2= 35km, f = 1 0 - 4 S - l , fl = 10-13cm -I s -I and Av = 0.1 cm s-', as in M&K. B is assumed to be 50cm. Then, (1) becomes 2 x 10-5 Doll SLD ~b = 6.08 x 10-5 D0(1 + ro ~) + 5(r i-~ + r i-2) + 2.86(r~-' + r~-2) FLAT FTSM FTGR
(2)
The difference of the sea level H and thickness of the upper layer of the north Pacific Do are estimated by a numerical model. If the seasonal changes of the parameters r0, r~ and r2 are estimated by observational data in the four seasons, the seasonal change in the in- and outflow volume transport ~b is determined from eqn (2). 3. IN- AND OUTFLOW VOLUME TRANSPORT INTO THE JAPAN SEA The domain of the numerical model used to estimate the sea level difference H and the upper layer thickness Do in (2) is shown in Fig. 3. A two-layer model driven by the observed wind stress is considered (Fig. 4). The sea level difference H in (2) is estimated at the two points a,b shown in Fig. 3. The basic equations under the Boussinesq,/~ and hydrostatic balance approximations are the same as in the previous paper of Sekine (SEKINE, 1986). We put fl = 2.0 x 10 -13 c m - I s - I , g* = gAp/p (reduced gravity) 2.0 cm s -2 and the coefficent of horizontal eddy viscosity Ah = 107 c m 2 s - I . The monthly mean wind stress over 1961-1983 compiled by KUXStrWADAand TERAMOTO(1987)is used (for details, see SEKn~Eand KUTSUWADA, 1989). Because the geostrophic balance holds good, the sea level anomaly is estimated by = f_0_~ + g- -*, 7
gDo
(3)
g
where ~' is the total volume transport function showing the barotropic transport in the upper and lower layer and ~/the interface deviation from the mean level of H (= 600 m) (Fig. 4).
274
Y. SEKINE
:::: .:
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I
180°
I
125 Iw
10°N
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FzG. 3. Domain of the numerical model (hatched region) to estimate the sea level difference between the two points a and b.
Figure 5 shows the calculated results. The volume transport of the subtropical circulation is maximum in winter and minimum in summer to autumn. There exists a clear latitudinal variation in the location of the subtropical circulation; the subtropical circulation is centered to the south of 30°N in winter, but at about 37°N in autumn. In contrast to this, no seasonal change in the thickness of the upper layer is clearly visible in the western boundary region (Fig. 5(b)), which indicates the predominance of the barotropic mode response of the ocean to the seasonal change in the wind stress. The results are essentially similar to other models developed so far (e.g. ANDERSONand CORR¥, 1985). Figure 6 shows the seasonal changes in the temperature and salinity at the two points in the Tsushima Strait. In winter, the mixed layer develops to about 150 m deep and the density stratification becomes very weak. On the other hand, warm and less saline water is found in summer to autumn and the density stratification is intensified. If the geostrophic balance holds good, these observational features agree with the vertical velocity fields shown in Fig. 2, in which small (large) vertical velocity shear in winter (summer to autumn) corresponds to weak (intensified) density stratification. These observations suggest that the baroclinic structure in summer is required to be included in the dynamics of the inflow. It is also indicated in Fig. 6 that the large inflow in summer is associated with the warm and less saline water, which is originated from the fresh river water discharged in the East China Sea.
H
h.I ~
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h2
U~.,.~.LAYER
P*~P LOWER LAYER
FIG. 4. Schematic representation of the two-layer model, P and p + Ap, and h~ and h 2 denote the density and thickness of upper and lower layer, respectively.
Seasonal variation in in- and outflow volume transport
275
a f10N T H
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FIG. 5. Seasonal change in the volume transport function (a) and upper layer thickness (b). The contour interval in (a) is 10 Sv. Regions with negative volume transport function (cyclonic circulation) are stippled. The contour intervals in (b) are 25 m.
Figure 7 shows the estimated value of ro, rt and r2 (hereafter referred to as the thickness parameters). According to the geophysical fluid dynamics, when the mixed layer reaches the bottom, the thickness parameters turn out to be underestimated if defined as the ratio
276
Y. SEKINE
a J F PIAPI J J A S O N D
b
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FIG. 6. Seasonal variations in (a) temperature and (b) salinity in the Tsushima Strait East strait (34004 , N, 129032 ' E) (upper panel) and the West strait (34050 ' N, 129°19 ' E) panel) near the two points shown in Fig. 2 (after INoi.~ et al., 1985).
at the (lower
of the depth of the strait to the upper layer thickness of the ocean. If the mixed layer does not reach the bottom, the thickness parameters are estimated so as to be proportional to the vertical average of the vertical stability. Because the stability is strongest in summer to autumn, the thickness parameters reach a maximum in September. As the Tsushima Strait is rather shallow (100-300 m) in comparison with other regions, r~ has the largest seasonal variation. Figure 8 shows the seasonal variation in the intensity of the inflow volume transport. The details of the estimation by eqn (2) are tabulated in Table 1. If the thickness parameters are assumed to be constant similarly to M&K (Case I), the inflow volume transport is a function of H and D. Since the seasonal change in D is very small, the term i
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i
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Seasonal variation in in- and outflow volume transport
277
••" ~
Case I I
I
I
I
-' J ' F 'M A H J
~/
I
I
i
J A S 'O'N'D'
FIG. 8. Estimated seasonal variation in the normalized volume transport qb, Case I (open marks) and Case II (closed marks).
FLAT is almost constant in time (see Table 1). Therefore, the variation in ~b exclusively depends on H in the SLD term in eqn (2), which is large in winter and minimum in autumn. This tendency represents the seasonal variation in q~. In particular, the SLD term becomes negative in October to November, resulting from the northward shift of the subtropical circulation (Fig. 5), which gives rise to the higher sea level at the point b. On the whole, the result in Case I is quite different from the observed evidence shown in Fig. 2, in which the maximum exists in summer and the minimum in winter. If the seasonal change in the thickness parameters are included (Case II), the peak of in winter is not as dominant as in Case I, although the SLD term is the same as in TABLE 1. ESTIMATEDVALUESIN (2) FOR TrtE TWO CASES
Month
r0
rI
r2
SLD
FLAT
FTSM
FTGR
I
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
1/4 1/4 1/4 1/4 1/4 1/4 1/4 I/4 1/4 1/4 1/4 I/4
1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
1/8 1/8 1/8 1/8 1/8 1/8 I/8 1/8 1/8 1/8 1/8 1/8
235.9 264.6 233.1 110.6 14.0 24.8 31.1 20.7 11.0 -25.9 -26.9 52.2
18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1
360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0
205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7
40.4 45.3 39.9 18.9 2.4 4.3 5.3 3.5 1.9 -4.4 -4.6 8.9
II
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
0.23 0.21 0.19 0.21 0.24 0.28 0.31 0.34 0.38 0.34 0.28 0.25
0.10 0.06 0.05 0.30 0.50 0.70 0.80 0.93 0.95 0.80 0.30 0.20
0.15 0.12 0.10 0.15 0.18 0.20 0.23 0.28 0.30 0.24 0.18 0.13
235.9 264.6 233.1 110.6 14.0 24.8 31.1 20.7 11.0 -25.9 -26.9 52.2
19.6 21.1 23.0 21.1 18.7 16.7 15.3 14.2 13.0 14.2 16.7 18.3
550.0 1472.2 2100.0 72.2 30.0 17.4 14.1 11.2 10.8 14.1 72.2 150.0
209.5 420.6 600.0 82.5 47.6 34.7 28.0 21.2 19.6 26.8 68.8 131.9
30.3 13.8 8.6 62.9 14.6 36.1 54.3 44.4 25.3 -47.0 -17.0 17.4
$ ( x 10 -2)
278
Y. SEKINE
Case I. Because of the change in the thickness parameters, the FLAT, FTSM and FTGR terms vary seasonally (Table 1). It should be noted that the FTSM and FTGR terms are very sensitive to the thickness parameter rl and r 0, respectively, due to the inverse square part. Relatively large values of the FTSM term are found in winter. This is due to the small values of the thickness parameter rl which reflects the barotropic flow structure of the Tsushima Strait in winter. It is clear that the large FTSM term results in the small volume transport in winter. In contrast to this, the thickness parameters are relatively large in summer, and yield a peak of volume transport in summer. This result agrees with the observational features in Fig. 2. Two peaks are found in December to January and also in April. A prominent peak in April is due to the relatively large SLD term and the large thickness parameters (Table l). In April, the SLD term is relatively large corresponding to the last period of the winter peak in Case I and the thickness parameters are relatively large due to the development of the seasonal thermocline. Similarly, a peak in December to January is caused by the large SLD term and the relatively large thickness parameters, which are due to the incomplete development of the mixed layer in early winter. Thus increases in the early and late period of winter.
4. SUMMARY AND DISCUSSION Dynamics in the seasonal variation of the volume transport flowing into the Japan Sea has been discussed by MINATO and KIMURA (1980). In their model, the inflow volume transport is proportional to the sea level difference between the inflow strait and outflow strait. The inflow volume transport also depends on three thickness parameters, r0, rl and rE, which actually specify to what degree the flow crosses the geostrophic contour in the equivalent barotropic model. In the present study, a two layer numerical model driven by the observed wind stress is used to estimate the sea level difference between the Tsushima and Tsugaru Straits. The seasonal change in the density stratification in the straits is parameterized by the thickness parameter. The main results are summarized as follows: (1) It is shown from the numerical model driven by the observed wind stress that the sea level difference has a maximum in winter and minimum in autumn. The winter maximum is caused by the strong wind stress in winter, while the autumn minimum is caused by the northward shift of the subtropical circulation. (2) From the observed hydrographic data, the thickness parameter is shown to be largest in summer and smallest in winter. The inflow volume transport is sensitive to the thickness parameter in the strait rather than to the sea level difference. (3) The above results denoted in (1) and (2), show that the observed maximum inflow volume transport in summer is closely related to the large thickness parameter. Therefore, the development of the density stratification in the shallow strait is essential to the large inflow transport in summer. In contrast, the observed small transport in winter is caused by the barotropic structure in the strait, which means that the large sea level difference in winter is of secondary importance. (4) Because of the important role of the thickness parameter in the inflow intensity, the local oceanic phenomena should be more essential than the global oceanic variation. The observational data suggest that the warm and less saline water formed in the East China Sea takes an important role in the large inflow in summer.
Seasonal variation in in- and outflow volume transport
279
One of the shortcomings of the present study is the neglect of the thermohaline effect in the estimation of the sea level difference. Furthermore, the detailed local phenomena have not been included in the numerical model. If they could be included, the intensity of the in- and outflow could be calculated routinely from the model. Such a model will be developed in a near future study. Acknowledgements--The author wishes to thank Professor K. Takano of Tsukuba University for his critical reading of the manuscript and valuable comments. Thanks are extended to Dr T. Miita for his comment on the oceanic condition of the Tsushima Current. The numerical calculation was carried out on HITAC M200(H) of the computer center of the National Defense Academy. The author also thanks Mr M. Ootachi for his help in performing the numerical calculations.
REFERENCES ANDERSON, D. L. and R. Coggv (1985) Seasonal transport variations in the Florida Straits: A model study. Journal of Physical Oceanography, 15, 773-787. AOTA, M. and M. MATSUYAMA(1987) Tidal current fluctuations in the Soya Current. Journal of Oceanographical Society of Japan, 43, 276-282. GILL, E. G. (1982) Atmosphere-Ocean Dynamics. Academic Press, New York, 662 pp. INOUE, N., T. MIITA and S. TAWARA (1985) Tsushima Strait II: physics. In: Coastal Oceanography of Japanese Islands, H. KuNIsm et al., editors, Tokai University Press, 914-933 (in Japanese). KUTSUWADA, K. and T. TEgAMOTO (1987) Monthly maps of surface wind stress over the north Pacific during 1961-1984. Bulletin of the Ocean Research Institute, University of Tokyo, 24, 1-100. MINAMI, H. (1985) Sea conditions in the southern part of the Japan Sea. Umi to sora, 60, 77-88 (in Japanese). MINATO, S. and R. KIMURA(1980) Volume transport of the western boundary current penetrating into a marginal sea. Journal of Oceanographical Society of Japan, 36, 185-195. PEDLOSKY,J. (1979) Geophysical Fluid Dynamics. Springer-Verlag, New York, 617 pp. SEKINE, Y. (1986) Wind-driven circulation in the Japan Sea and its influence on the branching of the Tsushima Current. Progress in Oceanography, 17, 297-312. SEKIr,rE, Y. and K. KtrrsuwADA (1989) A numerical model for the wind-driven circulation in the north Pacific Subtropics (to be submitted to Journal of Physical Oceanography). STOMrCIEL, H. (1948) The westward intensification of wind-driven currents. Transactions of the American Geophysical Union, 29, 202-206. TOBA, Y., K. TOMIZAWA,Y. KURASAWAand K. HANAWA (1982) Seasonal and year-to-year variability of the Tsushima-Tsugaru Warm Current System with its possible cause. Lamer, 20, 40-51.
0079-6611/88 $0.00 + .50 Copyright © 1989 Pergamon Press plc
On the Seasonal Variation in In- and Outflow Volume Transport of the Japan Sea YOSHIHIKO SEKINE*
Institute of Geoscience, National Defense Academy, Yokosuka 239, Japan (Received 28 March 1988; in revised form 8 August 1988; accepted 10 August 1988) Abstract--Dynamics of the seasonal variation in the volume transport of the Tsushima Current is considered from the view point that the in- and outflow of the Japan Sea is essentially due to the sea level difference between the inflow re#on and outflow region. The sea level difference is estimated by a numerical model driven by the observed wind stress over the North Pacific. It is shown that the sea level difference is largest in winter and relatively small in summer to autumn. On the other hand, because the density stratification is very weak in winter, water has a tendency to flow along the geostrophic contour. This decreases the in- and outflow transport. The transport of the in- and outflow of the Japan Sea varies with the intensity of density stratification rather than to the sea level difference, though its mean essentially depends on the sea level difference. The observed maximum (minimum) inflow transport in summer (winter) is due to the strong (weak) density stratification in the straits. The low density river water discharged in the East China Sea plays an important role in the larger inflow of the Tsushima Current in summer to autumn.
!. INTRODUCTION THE JAPAN SEA is a marginal sea surrounded by the Japanese Islands and the Asian continent. The major feature of the current system in the Japan Sea is an inflow of the Tsushima Current through the Tsushima Strait and two outflows through the Tsugaru Strait and the Soya Strait. It has been suggested by MINATO and KIMORA (1980) that the in- and outflow of the Japan Sea are caused by the pressure difference between the Tsushima Strait and the Tsugaru and Soya Straits. Later their theory was supported by TOBA, TOMIZAWA, KURASAWAand HANAWA (1982), in which the observed dynamic height was shown to be highest at the inlet of the Tsushima Strait and lowest in the outlet of the Tsugaru Strait. MINAMI (1985) suggested that the downstream pressure gradient exists in the Tsugaru and Soya Current, but the sea level is almost constant through the Tsushima Strait. The Tsugaru and Soya Currents have been demonstrated to be semi-geostrophic by observations (e.g. AOTA and MArSUYhMA, 1987), in which the geostrophic balance is possible in the cross stream direction but impossible in the downstream direction. Therefore, the total in- and outflow of the Japan Sea is basically due to the sea level difference as proposed by MINATO and KIMURA (1980), hereafter referred to as M&K. Figure l(a) shows the schematic view of the model used in M&K. An equivalent barotropic model is assumed and the depth (D) of the ocean is actually represented by the *Present address: Institute of Oceanography, Faculty of Bioresources, Mie University, 1515 Kamihama, Tsu, Mie, 514 Japan. 269
270
Y. SEKINE Y
a i
°--~
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°
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region A
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~(r=0.Z>
,00
FIG. 1. (a) The model ocean by MINATO and KIMURA (1980). (b) Typical stream lines obtained by MINATO and KIMtJRA (1980). (C) Ratio of the volume transport into the marginal sea (~b to the maximum value of the volume transport in the open ocean (~#(max)) as a function of ~' = 2 Y D o f l / A v . All parameters in (c) except for r are the same as those in (b).
thickness of the upper layer where the current velocity is relatively large. The sea level difference between the two straits is estimated by a simple wind-driven circulation model similar to STOM~L (1948). They showed that the inflow into a marginal sea depends on not only the pressure difference but also the intensity of bottom friction representative of the topographic effect. If the ratio r of the upper layer thickness of the marginal sea to that of the open ocean (Fig. l(a)) approaches 1 (zero), the larger (smaller) inflow appears (Fig. l(b,c)). Namely, because a barotropic geophysical fluid has a strong tendency to flow along the geostrophic contour f/D, where f is the Coriolis parameter and D is the upper
Seasonal variation in in- and outflowvolume transport
271
layer thickness (e.g. PEDLOSKY, 1979; GILL, 1982), the motion across the geostrophic contour is greatly suppressed. Therefore, as the gap in the upper layer thickness between the open ocean and the marginal sea becomes small (large), and in- and outflow volume transport across the strait is increased (decreased). By applying the representative values of the Japan Sea and the two straits, M&K showed that 2% of the volume transport of the Kuroshio penetrates into the Japan Sea. Figure 2 shows the seasonal change in the observed current velocity through the Tsushima Strait (INOUE, MIITA and TAWARA, 1985). The velocity is relatively large in summer and weak in winter. On the other hand, the vertical velocity shear is remarkable in summer to autumn and small in winter. Although the calculation of the in- and outflow was made only for one representative case by M&K, there is a clear seasonal variation in the volume transport of the in- and outflow of the Japan Sea. In the present study, the seasonal variation in the in- and outflow volume transport of the Japan Sea is studied by use of the model of M&K. Although M&K modeled the annual mean state, the application of their theory is possible if the adjustment of the system to the change in the sea level difference is fast. However, because the sea level change is considered to be the barotropic response and it is well-known that the barotropic response is very fast (e.g. GILL, 1982), the representative response time is less than the seasonal time scale. So it is reasonable to apply M&K's theory to the seasonal variation. In the present study, the sea level difference between the Tsushima and Tsugaru Straits is estimated by a numerical model covering the north Pacific, because there are neither observational data of the seasonal variation of the sea level nor data of the barotropic component of the velocity. The effect of the density stratification on the transport variation will be discussed by use of the equivalent barotropic theory. The model will be described in Section 2. The results will be presented in Section 3 with reference to the sea level difference and the parameterization of the density stratification. Summary and discussion will be made in Section 4. 2. FORMULATION The non-dimensional in- and outflow volume transport ~b proposed by M&K is
DofoH/(Av/7) SLD t~ = D0fl( 1 + ro~)Y/2A v + (r~t + r~2)Lt/W ~+ ( r ~ + r~2)L2/W2 FLAT FTSM FTGR
(1)
The notation is as follows:
Av: coefficient of the bottom friction 13: linear change rate of the Coriolis parameter Do: upper layer thickness of the Pacific ocean f0: Coriolis parameter H: sea level difference /7: mean sea level difference L~: length of the strait r i : ratio of the thickness of upper layer in the strait, where relatively large velocity is found, to that of the Pacific ocean
WINTER
~
SPRING
.I/~
/
~
s
SUMMER AUTUMN
~
0,,,,.... ,.o.
S~A*T#.
" M ~'-w~sl
. ~,( ,
,., ,,
WINTER
SPRING
. SUMMER AUTUMN
in the inserted map.
et al., 1985), All the available data by the direct current m e a s u r e m e n t s in 192~1974 are plotted. The locations o f the two stations are shown by solid circles
FIG. 2. Seasonal change in the observed mean current velocity at two points in the Tsushima Strait, west strait (left) and east strait (right) (after |NO~
s0m
20 rn
/ / /
,.<
Seasonal variation in in- and outflow volume transport
273
r0: ratio of the similar thickness of upper layer in the marginal sea to that of the Pacific ocean W: width of the strait Y: latitudinal distance of the two straits (Y = Y2-Yl, cf. Fig. l(a)). Subscripts 1,2: quantities in the inflow strait (the Tsushima Strait) and the outflow strait (Tsugaru Strait), respectively. Letters SLD, FLAT, FTSM and FTGR: terms used in the discussion. The sea level difference H is non-dimensionalized by the mean sea level difference H, while H is non-dimensionalized by the relation of the Sverdrup balance in M&K. The interpretation of eqn (1) is similar to Ohm's law: the volume transport (electric current) is proportional to the pressure gradient represented by the sea level difference (voltage) shown in the numerator (SLD) and inversely proportional to the friction (electric resistance) in the denominator; the first (FLAT), second (FTSM) and third (FTGR) terms represent the friction in the Japan Sea, the Tsushima Strait and Tsugaru Strait, respectively (for details of eqn (1), see M&K). Although some parameters in (1) cannot be defined clearly, we put Y = 1215km, L~ = 500 km, L2= 100km, W~ = 100 km, I4/2= 35km, f = 1 0 - 4 S - l , fl = 10-13cm -I s -I and Av = 0.1 cm s-', as in M&K. B is assumed to be 50cm. Then, (1) becomes 2 x 10-5 Doll SLD ~b = 6.08 x 10-5 D0(1 + ro ~) + 5(r i-~ + r i-2) + 2.86(r~-' + r~-2) FLAT FTSM FTGR
(2)
The difference of the sea level H and thickness of the upper layer of the north Pacific Do are estimated by a numerical model. If the seasonal changes of the parameters r0, r~ and r2 are estimated by observational data in the four seasons, the seasonal change in the in- and outflow volume transport ~b is determined from eqn (2). 3. IN- AND OUTFLOW VOLUME TRANSPORT INTO THE JAPAN SEA The domain of the numerical model used to estimate the sea level difference H and the upper layer thickness Do in (2) is shown in Fig. 3. A two-layer model driven by the observed wind stress is considered (Fig. 4). The sea level difference H in (2) is estimated at the two points a,b shown in Fig. 3. The basic equations under the Boussinesq,/~ and hydrostatic balance approximations are the same as in the previous paper of Sekine (SEKINE, 1986). We put fl = 2.0 x 10 -13 c m - I s - I , g* = gAp/p (reduced gravity) 2.0 cm s -2 and the coefficent of horizontal eddy viscosity Ah = 107 c m 2 s - I . The monthly mean wind stress over 1961-1983 compiled by KUXStrWADAand TERAMOTO(1987)is used (for details, see SEKn~Eand KUTSUWADA, 1989). Because the geostrophic balance holds good, the sea level anomaly is estimated by = f_0_~ + g- -*, 7
gDo
(3)
g
where ~' is the total volume transport function showing the barotropic transport in the upper and lower layer and ~/the interface deviation from the mean level of H (= 600 m) (Fig. 4).
274
Y. SEKINE
:::: .:
60 ~
J":lllllilllllll(llllll(I;llill(l(l'i'i'l[ :::::::::::::::::::::::::::::::
20 °
I
IO0°E
140°E
I
I
180°
I
125 Iw
10°N
14(~IY
FzG. 3. Domain of the numerical model (hatched region) to estimate the sea level difference between the two points a and b.
Figure 5 shows the calculated results. The volume transport of the subtropical circulation is maximum in winter and minimum in summer to autumn. There exists a clear latitudinal variation in the location of the subtropical circulation; the subtropical circulation is centered to the south of 30°N in winter, but at about 37°N in autumn. In contrast to this, no seasonal change in the thickness of the upper layer is clearly visible in the western boundary region (Fig. 5(b)), which indicates the predominance of the barotropic mode response of the ocean to the seasonal change in the wind stress. The results are essentially similar to other models developed so far (e.g. ANDERSONand CORR¥, 1985). Figure 6 shows the seasonal changes in the temperature and salinity at the two points in the Tsushima Strait. In winter, the mixed layer develops to about 150 m deep and the density stratification becomes very weak. On the other hand, warm and less saline water is found in summer to autumn and the density stratification is intensified. If the geostrophic balance holds good, these observational features agree with the vertical velocity fields shown in Fig. 2, in which small (large) vertical velocity shear in winter (summer to autumn) corresponds to weak (intensified) density stratification. These observations suggest that the baroclinic structure in summer is required to be included in the dynamics of the inflow. It is also indicated in Fig. 6 that the large inflow in summer is associated with the warm and less saline water, which is originated from the fresh river water discharged in the East China Sea.
H
h.I ~
I
I
0
h2
U~.,.~.LAYER
P*~P LOWER LAYER
FIG. 4. Schematic representation of the two-layer model, P and p + Ap, and h~ and h 2 denote the density and thickness of upper and lower layer, respectively.
Seasonal variation in in- and outflow volume transport
275
a f10N T H
MONTH
JAN,
JULT
o
•
120:[ t40:
160:
160:
160:
..............
MONTH
MAT
i8o;
160:
~ t
t4o:w
tso:
..................~'":~ "
t20:E t~O:
160:
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i,o.
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t6o;
t 2 0 : [ 140:
d40"~
.
t2o:~ t4o;
to:
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190°, 160:
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,o
~
t
t2o:~: t 4 o :
t6o'.
MONTH
NOV ,
o
:
teo;
t6o'.
" ~'~. . . . . . . . . . . . . . . .
140;w
12O*.E 140;
t4o:w
~ i ! + ! i
160", 180", 160:
t4O:u
b MONTM
JAN .
MONTH
J ' T ~ i ~ " ' : " " : ' " ' : ' " ' ~ 40"W 6~
JULT ~ " ~ ~ ' " " ' " ' " " ~
30"
30"
:
..t t0~
20" ............... t20.'E 140 T t60".
~.. . . . . . . . . . . . l e o : t60*.
t,to:w
. . . . . . . . . . . .L . . ~ . . . . t20:C t40: IS0: tS0".
L.,.,+-x:~....L,A.I. aI 0 : t60: t40:W
MAT
leO'.
t60".
'. 120".£ t40:
MONTH
. 120:g 140 ~, 160:
160:
t4o'u
MONTH SEP.
MONTH MAR.
MONTH
t20:Z 140:
180", 160:
160". 180:
12/j o
10:
160 ~. t40:~
NOV .
30 140".W
13:
)jl,o: 120".f" 140;
160:
180"
160:
140;u
FIG. 5. Seasonal change in the volume transport function (a) and upper layer thickness (b). The contour interval in (a) is 10 Sv. Regions with negative volume transport function (cyclonic circulation) are stippled. The contour intervals in (b) are 25 m.
Figure 7 shows the estimated value of ro, rt and r2 (hereafter referred to as the thickness parameters). According to the geophysical fluid dynamics, when the mixed layer reaches the bottom, the thickness parameters turn out to be underestimated if defined as the ratio
276
Y. SEKINE
a J F PIAPI J J A S O N D
b
J
J F PJiAPIJ J A S O N D J "
l~l
e4,.i
i
!,
"tl/I
.,,,..,
/
om
i i i$
i~
is
it
i?
ii
ii
I'
ii
I
"
'
ii.S
345
.J F M A M J J A S O N D J
J FMAPIJ JASONDJ
so iS 4~
ioo
~"
)is
:,?
ISo
3.~ ? ~:...-
!
ill
)ol
I00
FIG. 6. Seasonal variations in (a) temperature and (b) salinity in the Tsushima Strait East strait (34004 , N, 129032 ' E) (upper panel) and the West strait (34050 ' N, 129°19 ' E) panel) near the two points shown in Fig. 2 (after INoi.~ et al., 1985).
at the (lower
of the depth of the strait to the upper layer thickness of the ocean. If the mixed layer does not reach the bottom, the thickness parameters are estimated so as to be proportional to the vertical average of the vertical stability. Because the stability is strongest in summer to autumn, the thickness parameters reach a maximum in September. As the Tsushima Strait is rather shallow (100-300 m) in comparison with other regions, r~ has the largest seasonal variation. Figure 8 shows the seasonal variation in the intensity of the inflow volume transport. The details of the estimation by eqn (2) are tabulated in Table 1. If the thickness parameters are assumed to be constant similarly to M&K (Case I), the inflow volume transport is a function of H and D. Since the seasonal change in D is very small, the term i
l
!
I
l
!
!
°/
!
\
/
,i
/
\
;
L
o.
~
°.
ol";'"'r,,
l
•
/"
0,5
)
I
....•. " - \ h
r :
/'
, , , ,
J FNAPIJ FIG. 7. S e a s o n a l v a r i a t i o n
i
J
J
J ASOND in e s t i m a t e d r o, r i a n d r 2 .
Seasonal variation in in- and outflow volume transport
277
••" ~
Case I I
I
I
I
-' J ' F 'M A H J
~/
I
I
i
J A S 'O'N'D'
FIG. 8. Estimated seasonal variation in the normalized volume transport qb, Case I (open marks) and Case II (closed marks).
FLAT is almost constant in time (see Table 1). Therefore, the variation in ~b exclusively depends on H in the SLD term in eqn (2), which is large in winter and minimum in autumn. This tendency represents the seasonal variation in q~. In particular, the SLD term becomes negative in October to November, resulting from the northward shift of the subtropical circulation (Fig. 5), which gives rise to the higher sea level at the point b. On the whole, the result in Case I is quite different from the observed evidence shown in Fig. 2, in which the maximum exists in summer and the minimum in winter. If the seasonal change in the thickness parameters are included (Case II), the peak of in winter is not as dominant as in Case I, although the SLD term is the same as in TABLE 1. ESTIMATEDVALUESIN (2) FOR TrtE TWO CASES
Month
r0
rI
r2
SLD
FLAT
FTSM
FTGR
I
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
1/4 1/4 1/4 1/4 1/4 1/4 1/4 I/4 1/4 1/4 1/4 I/4
1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
1/8 1/8 1/8 1/8 1/8 1/8 I/8 1/8 1/8 1/8 1/8 1/8
235.9 264.6 233.1 110.6 14.0 24.8 31.1 20.7 11.0 -25.9 -26.9 52.2
18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1
360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0 360.0
205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7 205.7
40.4 45.3 39.9 18.9 2.4 4.3 5.3 3.5 1.9 -4.4 -4.6 8.9
II
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
0.23 0.21 0.19 0.21 0.24 0.28 0.31 0.34 0.38 0.34 0.28 0.25
0.10 0.06 0.05 0.30 0.50 0.70 0.80 0.93 0.95 0.80 0.30 0.20
0.15 0.12 0.10 0.15 0.18 0.20 0.23 0.28 0.30 0.24 0.18 0.13
235.9 264.6 233.1 110.6 14.0 24.8 31.1 20.7 11.0 -25.9 -26.9 52.2
19.6 21.1 23.0 21.1 18.7 16.7 15.3 14.2 13.0 14.2 16.7 18.3
550.0 1472.2 2100.0 72.2 30.0 17.4 14.1 11.2 10.8 14.1 72.2 150.0
209.5 420.6 600.0 82.5 47.6 34.7 28.0 21.2 19.6 26.8 68.8 131.9
30.3 13.8 8.6 62.9 14.6 36.1 54.3 44.4 25.3 -47.0 -17.0 17.4
$ ( x 10 -2)
278
Y. SEKINE
Case I. Because of the change in the thickness parameters, the FLAT, FTSM and FTGR terms vary seasonally (Table 1). It should be noted that the FTSM and FTGR terms are very sensitive to the thickness parameter rl and r 0, respectively, due to the inverse square part. Relatively large values of the FTSM term are found in winter. This is due to the small values of the thickness parameter rl which reflects the barotropic flow structure of the Tsushima Strait in winter. It is clear that the large FTSM term results in the small volume transport in winter. In contrast to this, the thickness parameters are relatively large in summer, and yield a peak of volume transport in summer. This result agrees with the observational features in Fig. 2. Two peaks are found in December to January and also in April. A prominent peak in April is due to the relatively large SLD term and the large thickness parameters (Table l). In April, the SLD term is relatively large corresponding to the last period of the winter peak in Case I and the thickness parameters are relatively large due to the development of the seasonal thermocline. Similarly, a peak in December to January is caused by the large SLD term and the relatively large thickness parameters, which are due to the incomplete development of the mixed layer in early winter. Thus increases in the early and late period of winter.
4. SUMMARY AND DISCUSSION Dynamics in the seasonal variation of the volume transport flowing into the Japan Sea has been discussed by MINATO and KIMURA (1980). In their model, the inflow volume transport is proportional to the sea level difference between the inflow strait and outflow strait. The inflow volume transport also depends on three thickness parameters, r0, rl and rE, which actually specify to what degree the flow crosses the geostrophic contour in the equivalent barotropic model. In the present study, a two layer numerical model driven by the observed wind stress is used to estimate the sea level difference between the Tsushima and Tsugaru Straits. The seasonal change in the density stratification in the straits is parameterized by the thickness parameter. The main results are summarized as follows: (1) It is shown from the numerical model driven by the observed wind stress that the sea level difference has a maximum in winter and minimum in autumn. The winter maximum is caused by the strong wind stress in winter, while the autumn minimum is caused by the northward shift of the subtropical circulation. (2) From the observed hydrographic data, the thickness parameter is shown to be largest in summer and smallest in winter. The inflow volume transport is sensitive to the thickness parameter in the strait rather than to the sea level difference. (3) The above results denoted in (1) and (2), show that the observed maximum inflow volume transport in summer is closely related to the large thickness parameter. Therefore, the development of the density stratification in the shallow strait is essential to the large inflow transport in summer. In contrast, the observed small transport in winter is caused by the barotropic structure in the strait, which means that the large sea level difference in winter is of secondary importance. (4) Because of the important role of the thickness parameter in the inflow intensity, the local oceanic phenomena should be more essential than the global oceanic variation. The observational data suggest that the warm and less saline water formed in the East China Sea takes an important role in the large inflow in summer.
Seasonal variation in in- and outflow volume transport
279
One of the shortcomings of the present study is the neglect of the thermohaline effect in the estimation of the sea level difference. Furthermore, the detailed local phenomena have not been included in the numerical model. If they could be included, the intensity of the in- and outflow could be calculated routinely from the model. Such a model will be developed in a near future study. Acknowledgements--The author wishes to thank Professor K. Takano of Tsukuba University for his critical reading of the manuscript and valuable comments. Thanks are extended to Dr T. Miita for his comment on the oceanic condition of the Tsushima Current. The numerical calculation was carried out on HITAC M200(H) of the computer center of the National Defense Academy. The author also thanks Mr M. Ootachi for his help in performing the numerical calculations.
REFERENCES ANDERSON, D. L. and R. Coggv (1985) Seasonal transport variations in the Florida Straits: A model study. Journal of Physical Oceanography, 15, 773-787. AOTA, M. and M. MATSUYAMA(1987) Tidal current fluctuations in the Soya Current. Journal of Oceanographical Society of Japan, 43, 276-282. GILL, E. G. (1982) Atmosphere-Ocean Dynamics. Academic Press, New York, 662 pp. INOUE, N., T. MIITA and S. TAWARA (1985) Tsushima Strait II: physics. In: Coastal Oceanography of Japanese Islands, H. KuNIsm et al., editors, Tokai University Press, 914-933 (in Japanese). KUTSUWADA, K. and T. TEgAMOTO (1987) Monthly maps of surface wind stress over the north Pacific during 1961-1984. Bulletin of the Ocean Research Institute, University of Tokyo, 24, 1-100. MINAMI, H. (1985) Sea conditions in the southern part of the Japan Sea. Umi to sora, 60, 77-88 (in Japanese). MINATO, S. and R. KIMURA(1980) Volume transport of the western boundary current penetrating into a marginal sea. Journal of Oceanographical Society of Japan, 36, 185-195. PEDLOSKY,J. (1979) Geophysical Fluid Dynamics. Springer-Verlag, New York, 617 pp. SEKINE, Y. (1986) Wind-driven circulation in the Japan Sea and its influence on the branching of the Tsushima Current. Progress in Oceanography, 17, 297-312. SEKIr,rE, Y. and K. KtrrsuwADA (1989) A numerical model for the wind-driven circulation in the north Pacific Subtropics (to be submitted to Journal of Physical Oceanography). STOMrCIEL, H. (1948) The westward intensification of wind-driven currents. Transactions of the American Geophysical Union, 29, 202-206. TOBA, Y., K. TOMIZAWA,Y. KURASAWAand K. HANAWA (1982) Seasonal and year-to-year variability of the Tsushima-Tsugaru Warm Current System with its possible cause. Lamer, 20, 40-51.