Calculation of the Kuroshio current South of Japan in May–June 1986

Prog. Oceanog. Vol. 21, pp. 503-514, 1988. Printed in Great Britain. All rights reserved.

0079-6611/88 $0.00 + .50 Copyright © 1989 Pergamon Press pie

Calculation of the Kuroshio Current South of Japan in May-June 1986 YUAN Y A O C H U , SU JILAN

and Z n o u W E I D O N G

Second Institute of Oceanography, State Oceanic Administration, Hangzhou, China (Received 20 January 1988; in revised form 15 August 1988; accepted 20 August 1988) Abstract--Based on hydrographic data obtained in May-June 1986, the velocity field south of Japan is computed by the beta spiral method and the dynamic method. The Kuroshio increases its speed to 122.5-139 cm s-t between 135°E and 137° E. The speed there remains high down to 400 m depth. Below 400 m the axis of the Kuroshio shifts southward. Close to the Kuroshio there is a meso-scale anticyclonic eddy centered at 135° E, 30°45' N.

1. INTRODUCTION THEREHAVEbeen many studies on the Kuroshio south of Japan (e.g. THE 1977-1982 KER SUMMARY REPORT, 1985; TAKANO and KAWAI, 1970). Since the Kuroshio Current is basically in geostrophic balance, most of the computations of the Kuroshio Current south of Japan were based on the dynamic method. It is well known that one of the drawbacks of the dynamic method is the uncertainty of the level of no motion. The velocity values and the volume transport greatly depend on choice of the level of no motion. For example, the 1977-1982 KER StJM~ARVREPORT (1985) pointed out that the volume transport referred to 3000 db is about 1.5 times larger than that referred to 1000 db. Since the pioneer work on the beta spiral method by STOMMELand ScHorr (1977), there have been many attempts to modify their method to compute the reference velocity at some reference level. Recently, BIOG (1985) proposed a modified beta spiral method which gave good agreement with numerical model results obtained by Cox and BRYAN(1984). Like Stommel and Schott's method, his method also relies on the availability of accurate hydrographic data, especially in deeper levels. In this paper, Bigg's modified beta spiral method is used to compute the velocity field south of Japan, based on hydrographic data collected by the First Institute of Oceanography, SOA, in May-June 1986.

2. GOVERNING EQUATIONS The beta sprial method is a steady state dynamical technique. SrOMMEL and ScHorr (1977) assume that (1) there is no flow across the density surfaces; (2) the flow is geostrophic; (3) the vorticity satisfies a linear balance equation on a beta-plane. In Bigg's 503

504

Y. YUAN et at.

modified beta spiral method, assumption (1) is replaced by the convection-diffusion equation for the density p, i.e.

Op U-~x + V~yy+ W ~

O:p

/02p 02p)

(1)

where x, y and z are directed to the east, north and upward respectively. If (U0, Vo, W0) is the velocity at some reference level Zo, then the velocity (U, V, W) at level Z may be written as

U=Uo+U', v = Vo + v', w=

(2)

w0+ w',

where (U', V', W') is the departure of the velocity at level Z from the reference value. By definition, at level Z0 we have U'= V'= W'=0.

(3)

Substituting eqn. (2) into eqn. (1) and using the thermal wind and linear vorticity equations (BIoG, 1985), we obtain the modified beta spiral equation for (U0, V0, W0), ~p U0~x+ Vo[~ +' ~/ z~ ° p 'tL ~ -- Zo)] + Wo~-~Pz= . ,0p W'~Pz ADV02p " {0:P 02P'~, -- U ~xx -- V ' ~ + ~z2+ ADH~x2 + ~-~y2/ (4) where U', V', W' satisfy the relations: 0U'

dp

O---Z - r 0y'

(5)

0V' 0p 0z = -Y~xx'

(6)

w'

fl Vo(Z =?

W"

=?/~ f~ V' dz.

- Zo) + w " ,

(7)

(8)

Here Y = g/fPo, Po is some reference density. If eqn. (4) holds good at more than three levels, the matrix equation follows; A U = C,

(9)

where U = (Uo, Vo, I4"o)r and A and C are the discrete forms of the left and right hand sides of eqn. (4), respectively. This is an over-determined matrix system, and will be solved by the Moore-Penrose generalized inverse method (LANcZOS, 1961).

Calculation of the KuroshioCurrent

505

If matrix (A rA) has an inverse, the standard deviations of the reference velocity are given by (BIGG, 1985) 6~=

"(ArA)kk , k = l ,

2, 3

(10)

where R is the sum of the squared residuals, N is the number of computation levels and (A rA)/;~ are the diagonal elements of the inverse matrix. The beta spiral method for the calculations of the Kuroshio Current south of Japan requires that the geostrophic relation is approximately satisfied there, i.e. the time varying terms and the nonlinear terms are much smaller than the Coriolis terms in the momentum equations. TAFT (1978) carried out deep-sea current measurements south of Japan in June-July 1971 and showed dominant low frequency fluctuations of about 20 days. TAIRA and TERAMOTO(1981) also moored current meters near the Izu Ridge in the upper layer of the Kuroshio from March 1977 to May 1979 and in the lower layer from May 1978 to February 1979, and showed that low frequency fluctuation with 33 days period was dominant in both layers with amplitudes of about 20 cm s-~. Temperature and current measurements in the Kuroshio south of Kyushu from 1979 to 1982 (TAKEMATSU, KAWATATE, KOTERAYAMA,StmARA and MITSUYASU, 1986) also showed dominant low frequency fluctuation with time scales of about 30 days. These observations suggest that periods of dominant fluctuations of the Kuroshio are longer than those of the Gulf Stream. If the scales T, L and U0 are taken to be 20 days, 200 km and 1 m s-~, respectively, and f = 7.51 x 10-Ss -I, the ratio of the time-dependent term to the Coriolis terms, (Tf) -~, becomes 7.5 x 10-3 and the ratio of the nonlinear terms to the Coriolis term, Uo/fL, to be 7 x 10 -2. Thus, the geostrophic relation is approximately valid in the Kuroshio Current south of Japan. In fact, TAFT (1978) pointed out that south of Japan the geostrophic profiles were adjusted to the 10-day average velocity component normal to the section where current meter data were available. In addition, SARKISYAN(1977) showed that in the Gulf stream region the relative differences between the flow velocities computed from the linear diagnostic equation and those from the nonlinear variant were 5-15%. Thus, the use of the beta spiral method in the Kuroshio region south of Japan seems to be justified. 3. COMPUTATION The bathymetry, the hydrographic stations, and the velocity mesh points are shown in Fig. 1. The velocity mesh points are in the center of four neighboring hydrographic stations. The vertical mesh points are at levels of 0, 5, 10, 20, 30, 50, 75, 100, 150, 200 m, and then at increments of 100 m thereafter. The deepest depth is 2500 m, and the shallowest depth is 800 m. In our computation we have used four different values of Aon (0, 105, 106, and 10 7 c m 2 S - I ) and three different values of Apv (0.1, 0.5 and 1 cm 2 s-J). Our computation indicates that the velocity is insensitive to AD., i.e. the horizontal diffusion term is not important, similar to Bigg's results (1985). It is also found that the velocity changes little with ADv ranging from 0.1 to 1 cm 2 s -j. The relative changes are less than 5%. The following discussion is confined into the result by Aov = 0.5 cm2 s -t. In the beta spiral method, the selection of computation levels is important for solving (U01 V0, W0) at reference level Z0. Here these levels are chosen below the upper boundary of the main thermocline. The upper boundary of the main thermocline was below 300 m

506

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at most of the hydrographic stations except at a few stations where it is between 100 m and 250 m. Four numerical experiments using different computation levels are carried out. The surface velocities at computation point No. 4 (see Fig. 1) based on four different computation levels are shown in Table 1. The speed is significantly higher in case 1 than in cases 2 to 4, while the direction in cases 1 and 2 is significantly different from that in cases 3 and 4. Note that the upper boundary of the main thermocline for the four hydrographic stations around mesh point No. 4 is at 500, 500, 400 and 300 m, respectively. This indicates that the computed velocities are stable when the computation levels are taken below the upper boundary of the main thermocline. The GEK-measured surface currents around mesh point No. 4 in May-June 1986 were about 15-95 cm s-' directed to the north (JAPANESEMARITIMESAFETYAGENCY, 1986, hereafter referred to as JMSA). TABLE

Case 1 2 3 4

1.

THE

SURFACE VELOCITIES AT POINT

The computation levels >i 300 I> 400 >/500 >/600

m m m m

No. 4

Speed

at surface Vs (cm s - ' )

Direction*

51.55 43.75 41.79 42.64

307 ° 328.2 ° 19.88 ° 19.65 °

*Measured clockwise from due north.

Calculation of the Kuroshio Current

507

At mesh points where the main thermocline was shallower than 300 m, the differences between computed velocities among all the four cases are not large. For example, at point No. 17 the upper boundary of the main thermocline of the neighboring hydrographic stations is 100, 100, 200 and 250 m, respectively. The surface velocity there is 7.07 cm s-l (164.2 °) in case 1 and 6.57 cm s -~ (171.1 °) in case 3, respectively. The largest difference in computed surface velocities among the four experiments occurs at point No. 12, where the difference betweeen cases 3 and 4 is 11.9 cm s-~ in speed and 40.6 ° in direction. One reason of such a striking difference is that the main thermocline is deeper ( > 500 m) around point No. 12. In addition, the equations used in the beta spiral method are in differential forms, so that the results are sensitive to data noise, especially in deeper levels. On the other hand, the equations used in the inverse method (WtrNSCH, 1977, 1978) are in integral form, which smoothes out small scale eddies to better represent the large-scale mean flow. Comparison of the two methods is, however, out of the scope of the present study. For most of the mesh points the difference of computed velocities between cases 3 and 4 are small. In subsequent discussion only results with computation levels at 500 m and below are used. The results obtained from the beta spiral and dynamic methods are compared in Table 2. The reference level for the dynamic method is chosen to be 800 m, because the minimum vertical extent of hydrographic data obtained by the cruise is 800 m. The reference level for the beta spiral method is chosen to be the deepest measurement depth at each point. Results in strong current regions (mesh points Nos 8 and 18) as well as the region of the deepest measurement depths (point No. 10) are tabulated. Compared to the velocities derived from the beta spiral method, the dynamic method tends to overestimate the surface speed. At all the three points, the 800 m level is not a level of no motion, but rather a level with a countercurrent. The existence of countercurrents at deeper levels does not mean, however, the existence of a level of no motion, because the absolute velocity spirals with depth. Figure 2 shows the absolute velocity spirals at points Nos 10, 16 and 21. The 800 m level seems to be better than the other levels for point 10 (Fig. 2 (a)) when used as the zero-reference level for dynamical computation. In fact, at most of the points, speeds at levels from 800m to 1200m are estimated to be less than 10cm s -t by the beta spiral method. Only at seven points is the speed greater than 10cm s -~ at levels from 800 m to 1200 m (Figs 7 and 8). In other words, for most of the points, a level of 800 m - 1 2 0 0 m may be regarded as a zero-reference level for the dynamic method. The beta spiral method is also applied to a different set of hydrographic data for computing the velocity field south of Japan in October 1986. Because the maximum TABLE 2, THE COMPARISON

Method Dynamic method

OF THE RESULTS BY TWO METHODS

Variables

Vo (cm s-~ ) 0D* Surface V# (cms -I ) 0p* Beta spiral 800m U (cms -I ) method V(cms -I ) Standard 61 (cm s -l) deviation 62 (cm s-~ ) The referencelevel (m) *Measured clockwise from due north. J.P.O. 21-3/4--S

Surface

8

Computed points 18

l0

140.I 86.9° 122.5 87.5° -17.5 -2.1 3.0 1.6 800

148.6 93.9° 139.1 93.8° -9.5 0.9 1.0 0.3 800

18.36 50° 15.30 53° -1.8 -2.7 2.2 1.6 2500

508

Y. YUAN et al.

measurement depth is only 700 m during that cruise, the computed speeds are not reliable and in general less than the observed ones. This indicates that hydrographic data in deep layers are essential for the beta spiral method.

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Calculation of the Kuroshio Current

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FIG. 2(C) FIG. 2. Absolute velocity spirals. (a) point 10; (I : 2500 m, 2:1200 m, 3 : 1100 m, 4:1000 m, 5: 900 m, 6:800 m, 7:700m, 8:600 m, 9:500m, I0:400 m, ll:300m, 12:200m, 13:100 m, 14:50m, 15:0m) (b) point 16; (l:lS00m, 2:1000m, 3:800m, 4:700m, 5:600m, 6:500m, 7:400m, 8:300m, 9:200m, 10:100m, ll:50m, 12:0m) (c) point 21; (l:1500m, 2:1200m, 3:l100m, 4:1000m, 5:900 m, 6:800 m, 7:700 m, 8:600 m, 9:500 m, 10:400 m, 11:300m,~12:200 m, 13:100m, 14:50 m, 15:0m).

4. C O M P U T E D R E S U L T S A N D D I S C U S S I O N When the Kuroshio flows out of the East China Sea through the Tokara Strait, it flows northeastward into the region south of Toimisaki, makes a cyclonic meander, and then enters a region south of Shikoku and Honshu. The variation of the Kuroshio south of Japan is complex. There are five types of flow patterns of the Kuroshio south of Japan (TH'E 1977--1982 K E R SUMMARY REPORT, 1985). Special attention is paid now to the Kuroshio path south of Japan, and to its subsequent journey to the east of Japan. The computed results are shown in Figs 2 to 8.

4.1. The Current south of Japan Figures 3 to 5 show that the Kuroshio flows northward or northeastward near the 133° E section. The surface speeds are moderate, ranging from 33 to 45 cm s -t. The GEKmeasured surface velocities are 15-95 cm s -~ to the north (JMSA, 1986). The Kuroshio turns clockwise to the east to the south of Ashizurimisaki and is intensified to the southwest of Shionemisaki. The computed surface velocity near 135 ° E, 32°45'N is 122.5 cm s -t (0p = 87.5 °) and the GEK-measured surface velocities there are in the range 100-245 cm s -t to the east (JMSA, 1986). The speed of the Kuroshio continues to increase to 139 cm s -~ (0a = 93.8 °) near 137 ° E, 32°45 ' N, as compared with GEK-measured nearby surface velocities of 100-245 cm s -t to the east (JMSA, 1986). The intensification of the

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~3t* 13z¢ 133" la4* 135" ~ * ~37" ~ma* ~9" 140" 141" FIG. 3. The distribution of horizontal velocity (z = 0).

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K u r o s h i o Current between 135 ° E and 137 ° E is consistent with the convergence o f at isopleths there from 75 m to 600 m levels (Fig. 9). It is also consistent with the observations from 1956 to 1964 (TAFT, 1970) s h o w i n g that the K u r o s h i o is intensified east o f 135 ° E. Southwest of Shiosaki and southeast o f D a i o z a k i , velocities d o w n to 400 m depth remain strong, as seen in Figs 4 and 5 and Table 3. The speeds are quite small at the 600 m level o f the strong current region ( N o s 8 and 18), Countercurrents occur below 700 m at these points (Fig. 7). At the neighboring southern points N o s 9 and 19 n o countercurrents occur except below 1000 m depth (Fig. 8). This s h o w s that the main axis o f the K u r o s h i o shifts southward, which is evident particularly below 400 m (Figs 5 to 7). The existence o f this

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l 142°

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145°

Calculation

of the Kuroshio Current

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o f h o r i z o n t a l velocity (z = 400 m).

countercurrent may be related to the shallow water depths near the Izu Ridge. However, no data are available to compute velocities near the Izu Ridge• Figures 3 to 6 also showed that south of the Kuroshio axis there is an anticyclonic eddy centred at 135 ° E, 30°45 ' N with scales o f about 450 km in the east-west direction and 190 km in the north-south direction• It extends vertically from the surface to 600 m depth. The GEK-measured surface current (JMSA, 1986) also shows the existence o f this eddy. Enclosed isotherms with cold core located at 135 ° to 136 ° E and 30 ° to 31 °30' N are seen from the surface to 200 m (Fig. 9). However, the temperature range o f this cold water is not large. Below 300 m warm water appears and the horizontal temperature

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gradient becomes larger. This causes a local minimum of ~°Hp dz near the center of the eddy. 4.2. The Kuroshio Current east of Japan Figures 3 to 6 show that after passing over the Izu Ridge the Kuroshio flows northward at the 141°E section and then turns eastward away from the Japan coast. This flow pattern coincides with the GEK-measured surface currents (JMSA, 1986) and the o t distribution at the 200 m level (Fig. 9). The values of current speed at points 3~

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Calculation of the Kuroshio Current

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N o s 26 to 28 east of Japan are shown in Table 3. Water depths at these three points range from 2000 m to 4000 m. Figures 3 to 8 and Table 3 show that the maximum velocity is greater than 50 cm s-' from the surface to the 200 m level, much less than the Kuroshio speed south o f Honshu. The current speeds at the 6 0 0 m level at these three points are small and a weak countercurrent occurs at point N o s 26 and 28 from the 800 to 1000m levels. However, at point N o . 27 no countercurrent appears d o w n to the 1000m level. N o data are available on the current condition in deeper levels.

TARLE 3. C u R a r e

s P m ~ AT SELECm~ POIm'S S O t r m w ~ r oF SHIOSAKI AND SOUTHEAST OF DAIOZAKI AND EAST OF JAPAN (eros -t)

Point no. Level (m) 0 100 200 400 600

8

18

26

27

28

122.5 106.4 86.0 35.2 1.9

139 113.8 87.4 37.2 4.5

47.4 53.8 52.8 31.4 11.7

51 37 27.2 18.7 3.8

47.3 42 34.5 17.3 4.6

514

Y. YUAN et al.

5. SUMMARY Based on the May-June 1986 hydrographic data, the velocity is computed by the beta spiral method and the dynamic method. It is found that: (1) The beta spiral technique is a useful and effective method for the computation of the velocity field in deep oceans such as the Kuroshio south of Japan. This method gives good results if the computation levels are chosen below the upper boundary of the main thermocline. In our study area, the computation levels are deeper than 500 m. The beta spiral method is free from the shortcomings of the dynamic method resulting from the somewhat arbitrary choice of the reference level. Because the absolute velocity profile spirals with depth, there is in general no reference level where the velocity is zero. At most of the computation points there are zero-reference levels between 800 to 1200 m where the velocity is very weak (< l0 cm s-t). The differences between the results by the beta spiral and the dynamic methods are small at these points provided that the level of no motion is chosen within this depth range. (2) During May-June of 1986, the Kuroshio south of Japan flows near the coast, showing four small-scale meanders. At first, the Kuroshio makes a cyclonic meander south of Toimisaki, then turns clockwise to the east to the south of Ashizurimisaki. After passing over the Izu Ridge, it makes a cyclonic meander and turns to the north around 141 ° E, and finally, again makes an anticyclonic meander near Inubozaki. (3) The Kuroshio Current is intensified between 135° and 137° E. The maximum surface velocities are 122.5-139 cm s -~ down to 400m depth. Below the 400m depth the axis of the Kuroshio shifts southward. Immediately south of the intensified part of the Kuroshio there is a meso-scale anticyclonic eddy centered at 135° E, 30°45 ' N with a vertical extent of 600 m. The density in this eddy is minimum locally at all the levels from 300 m to 1500 m.

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