Variation of the Kuroshio in the Tokara Strait Induced by Meso-Scale Eddies

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1 Journal of Oceanography, Vol. 57, pp. 55 to 68, 001 Variation of the Kuroshio in the Toara Strait Induced by Meso-Scale Eddies KAORU ICHIKAWA* Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fuuoa , Japan also; Frontier Observational Research System for Global Change, Toyo, Japan (Received 1 May 000; in revised form 31 August 000; accepted 13 September 000) Temporal variations of the Kuroshio volume transport in the Toara Strait and at the ASUKA line are decomposed by phase-propagating Complex EOF modes of highresolution sea surface dynamic topography (SSDT) field during the first tandem period of TOPEX/POSEIDON and ERS-1 (from October 199 to December 1993). Both variations are dominated by a mode with nearly semi-annual cycle, which indicates a series of interactions between the Kuroshio and meso-scale eddies. Namely, northern part of a westward-propagating meso-scale eddy at 3 N is captured into the southern side of the Kuroshio at the south of Oinawa, then it moves downstream along the Kuroshio path passing the Toara Strait, and reaches to the ASUKA line where it merges with another eddy propagating from the east at 30 N. The variation at the ASUKA line is, however, less dominated by this mode; instead, it includes the SSDT variations in the south of Shiou and the east of Kyushu which would be directly affected by eddies from the east without passing the Toara Strait. On the other hand, the same analysis for movements of the Kuroshio axis in the Strait indicates that they are governed by short-term variations locally confined to the Kuroshio in the East China Sea without being induced by meso-scale eddies. This results, however, seem to depend strongly on a time scale of interest. It is suggested that the long-term movements of the Kuroshio axis in the Strait would demonstrate coincidence with SSDT variation in the south of Japan. Keywords: Kuroshio, Toara Strait, ASUKA, complex EOF, TOPEX/ POSEIDON, ERS Introduction The Toara Strait between Kyushu and Nansei islands has long been a place to monitor variations of the Kuroshio since it is one of the most practical places to cross the Kuroshio current (Fig. 1). Plenty of studies on variations of the Kuroshio in the Strait such as its volume transport and movements of its axis have been made, including ones using long-term tide gauge records, frequent ferry boat observations and recent intensive field observations (e.g. Nagata and Taeshita, 1985; Kawabe, 1995; Feng et al., 000). Apart from those descriptive studies, many theoretical and experimental investigations on the Kuroshio in the south of Japan were carried out based on the Kuroshio volume transport in the Toara Strait (e.g. White and McCreary, 1976; Masuda, 198; Yasuda et al., 1985; Yoon and Yasuda, 1987; Aitomo et al., 1991, 1997; Masuda et al., 1999). * address: ichiawa@riam.yushu-u.ac.jp Copyright The Oceanographic Society of Japan. Comparing with numbers of studies on the possible effects of the Toara Strait to the Kuroshio in the south of Japan, causes of the variations are less well understood. Variations of the Kuroshio in the Toara Strait are considered to be originated from variations of the Kuroshio in the East China Sea where downstream propagation of signals is often observed (e.g. Qiu et al., 1990; Ichiawa and Beardsley, 1993). Interannual variations of the Kuroshio volume transport in the East China Sea seem to be originated from the upstream region of the Kuroshio (17 1 N), and to be induced by wind stress changes to the far east (Aitomo et al., 1996). Recently, higher-frequency variations of the Kuroshio volume transport in the east of Taiwan are suggested to be coincident with westward-propagating meso-scale eddies (Zhang et al., 000). However, detailed understanding of the response of the Kuroshio in the Toara Strait to meso-scale eddies has not been achieved at this stage. In addition, Feng et al. (000) found no significant coincidence in the upstream sea surface dynamic topography (SSDT) with longterm meridional shift of the Kuroshio axis in the Toara 55

2 Fig. 1. Locations of the tidal stations used in the present study. Also, location of the ASUKA line and schematic position of the Kuroshio axis are shown in the figure by a broen line and a broad arrow, respectively. Strait, which raises a question whether or not the volume transport and the position of the Kuroshio are related. Moreover, it is necessary to establish how the variations of the Kuroshio monitored in the Toara Strait would represent for the downstream areas. Therefore, it would be essential to investigate characteristic responses of the Kuroshio to meso-scale eddies in both up- and downstream areas of the Toara Strait. Use of altimetry data has shown a great progress in studies of meso-scale eddies in this decade (e.g. Ichiawa and Imawai, 1994; Ebuchi and Hanawa, 000; Yasuda et al., 000). Nevertheless, comparing with the previous studies of rings detached from the Gulf Stream or the Kuroshio that are based on in situ observations, surface drifters and satellite infrared imagery (e.g. Richardson, 1983; Koshlyaov, 1986; Yasuda et al., 199), interaction of meso-scale eddies with the Kuroshio is not well described by altimetry data. One of the reasons is their low temporal and spatial resolutions. In order to obtain horizontal map of the SSDT from along-trac altimetry data, spatial and temporal interpolation is required, so that fast moving small-scale variations that are frequently observed in the interaction with rings and the Kuroshio would be eliminated (Ichiawa and Imawai, 1994). Since October 1993, altimeters on U.S./French satellite TOPEX/POSEIDON (T/P) and European ERS-1/ have been operated at the same time. Combined use of these altimeters would provide denser observations, so that better description of interactions with meso-scale eddies and the Kuroshio current would be expected. In the present study, therefore, high-resolution SSDT field obtained from both T/P and ERS-1 altimetry data are used to study effects of meso-scale eddies onto variations of the Kuroshio in the Toara Strait. Also, eastward volume transport data at the ASUKA line (Fig. 1) are used to investigate their effects in the downstream of the Strait. The analysis in the present paper is based on decomposition of the Kuroshio variations by complex empirical orthogonal function (CEOF) modes that can describe phase-propagating meso-scale eddy field very well. Data sets of altimetry SSDT and tide gauge records used in the present analysis are described in Section, followed by a short description of the CEOF analysis method in Section 3. The results are described in Section 4 which consists of two parts; one is on the variation of the Kuroshio volume transport (Subsection 4.1) and the other on the position of the Kuroshio in the Toara Strait (Subsection 4.). Discussions and concluding remars are summarized in Sections 5 and 6, respectively.. Data In order to account for effects of meso-scale eddies to variations of the Kuroshio in the Toara Strait, the offshore SSDT anomaly determined from altimetry data were used. In the present analysis, they are compared with estimated variations of the volume transport and the position of the Kuroshio in the Toara Strait based on the local tide gauge records. The SSDT anomaly from its temporary mean is determined for every 10 days on a 0.5 grid from AVISO altimetry data (Le Traon et al., 1995; AVISO, 1996; Le Traon and Ogor, 1998) by an optimal interpolation for the first tandem period of T/P and ERS-1 satellites (from October 199 to December 1993). The study area, 34 N and E, is selected in order to include both up- and downstream regions of the Toara Strait. The area east of 137 E is excluded from the present analysis since very large meander of the Kuroshio from April to August 1993 may distort CEOF mode decomposition. During the study period, both altimeters were in operation so that observations are denser in both space and time. The optimal interpolation used in the present study is similar to Yasuda et al. (000), but signal and error covariance functions are modified to include area dependency of the magnitudes of signal and error. We use the Gaussian function for the signal covariance W(R 1,R ) between two observations as 56 K. Ichiawa

3 W R1, R St r1 St r exp ( )= ( ) ( ) x y t Lx L y Lt where R = (r,t) = (x,y,t), x, y, t are longitude, latitude and time of the observation, respectively, x, y, t are their differences, L x, L y, L t their decorrelation scales, and S t (r) the root-mean-squared (rms) magnitude of sea surface dynamic height variations at the position r with time scales longer than L t. Meanwhile, the noise covariance function used in the present study consists of three terms as ψ( R1, R)= σaltδ( R1 R) 4 r + 0( r1) 0( r) exp t E E l l r t 4 r + ( r1) ( r) exp t Et Et short short L L r t where r = x + y, δ the delta function, σ alt the rms magnitude of each altimeter s instrumental noise, E 0 (r) the rms magnitude of short-term (say, much less than T/P cycle) sea surface height variations at the position r, and E t (r) the rms magnitude of the sea surface dynamic height variations with time scale longer than l t but shorter than L t, which are treated as noise in the present interpolation. The first term comes from altimeter s noise, and both second and third come from height variations with time scales shorter than L t. All those S t (r), E 0 (r), E t (r) and σ alt are estimated from temporally lagged covariance of alongtrac TOPEX, POSEIDON, ERS-1 and ERS- altimeter data provided by AVISO. Parameters L x, L y and L t would better to be determined based on a sampling pattern of an altimeter in order to obtain almost uniform estimation error (Ichiawa and Imawai, 1996). In the present study, it was chosen that L x = 90 cos(y) m, L y = 11 cos(y) m and L t = 17.5 days, which are based on ERS-1 sampling pattern in order to increase spatial resolution rather than temporal one. Parameters for the error covariance are set somewhat arbitrary as l r = a R (y m )/, l t = 0.1 day, L r short = a R (y m ) and L t short = 0.1L t, where a R (y m ) is the internal Rossby radius determined from Emery et al. (1984) at the mean latitude y m = (y 1 + y )/. Although these parameters in the noise covariance are arbitrary, the results are not sensitive to them since E 0 (r) and E t (r) are generally smaller than S t (r) in the present study area. In addition, areas are excluded in the further analysis to avoid uncertainty when the estimation error exceeds 99% of S t (r); they are generally limited on the coastal boundaries where less altimetry data are available. Temporal variations of the surface volume transport in the Toara Strait, or surface geostrophic velocity integrated over the Toara Strait, can be qualitatively estimated from variations of the sea level difference between Naze and Nishinoomote; the location of the tide gauges are plotted in Fig. 1. Temporal variation of the position of the Kuroshio axis is also qualitatively estimated from tide gauge records as Kuroshio position index (KPI) which is defined by X + 50 cm KPI = Y cm where X is the anomaly of the sea level difference of the Naanoshima minus Nishinoomote from the long-term average, and Y is the same as X but for Naze minus Nishinoomote (Kawabe, 1995). The KPI is defined to increase (or decrease) when the Kuroshio axis moves northward (or southward) in the Strait. The sea level data at the tide gauge stations Nishinoomote, Naanoshima and Naze are provided by the Japan Oceanographic Data Center at Hydrographic Department of the Maritime Safety Agency, Japan. Tidal signals are first removed by a 48-hour tide iller filter from the hourly sea level data (Hanawa and Mitsudera, 1985), then the sea level is averaged over the same 10 days as the altimeter SSDT data. Time series of the eastward volume transport of the Kuroshio at the ASUKA (Affiliated Surveys of the Kuroshio off Cape Ashizuri) observational line, or the western boundary current array PCM5 of WOCE (World Ocean Circulation Experiment), located downstream of the Toara Strait (Fig. 1) are used in this study. The data are based on intensive in situ observations and T/P alongtrac altimetry data and represent eastward volume transport up to 1000 m depth north of 30 N (Imawai et al., 1997). 3. Method Since propagation of meso-scale eddies are nown to be distinct in the study area, CEOF analysis, a complex extension of ordinary EOF, was applied; while the EOF analysis interprets signals by combination of standing waves, CEOF analysis uses traveling waves to decompose the signals (e.g. Barnet, 1983; White et al., 1987). In CEOF analysis, the SSDT z(x,t) at a given location x and time t is decomposed by N phase-propagating orthogonal complex modes C j (x,t) ( j = 1,..., N); namely, where N { j } ( ) ( ) z x, t Re C x, t, j Kuroshio Variations Induced by Eddies 57

4 iψ j( x) iϕ j( t) C x, t A x e B t e, j ( )= ( ) ( ) j in which A j (x) and ψ j (x) indicate amplitude and phase variations of space-dependent component of z(x,t), respectively, and B j (t) and ϕ j (t) are those of time-dependent component. Since those modes are orthogonal each other, so-called contribution ratio, R j, or the ratio of the variance of a given mode j to the total one, is defined as R j = = N Cj x, t dxdt z x, t dxdt Aj x dx Bj t dt. A x dx B t dt ( ) ( ) ( ) ( ) ( ) ( ) By adopting a normalization condition A j (x)dx = 1 for any mode j, this can be simplified as R j = N () Bj t dt. B t dt In addition, a local contribution ratio at a given location x 0 for a given mode j, R j L (x 0 ), can be defined as () j R j L ( x )= 0 = ( ) ( 0 ) ( ) Rj ( ) Cj x0, t dt z x, t dt Aj x0 N A x0 which would be useful to spot locally trapped variations without strong dependency on the choice of study areas (Ichiawa and Kaneda, 001). Similarly, a temporal contribution ratio at a given time t 0 for a given mode j, R j t (t 0 ), is defined as ( ) 0 R C t d t j x, 0 x Rj ( t0 )= z ( x, t0 ) dx Bj ( t0 ) = N, B t ( ) Fig.. Contribution ratio R j of each CEOF mode accounting for the variance of the SSDT in the study area., Fig. 3. Time series of the temporal contribution ratio, R j t (t 0 ), for the major 4 CEOF modes. The mode numbers are illustrated besides the lines. The numbers on the upper axis indicate 10-day cycle numbers of TOPEX/POSEIDON. The values for the CEOF modes higher than 5 are not plotted since they are less significant. 58 K. Ichiawa

5 which would be used to estimate temporal variation of the mode intensity. Furthermore, any temporal variation y(t) can be expressed by combinations of those CEOF modes using the harmonic analysis; namely, unnown sensitivity factor F j and phase constant θ j in an estimate ỹ (t) are determined by minimizing (y(t) ỹ (t)) dt, where N i ϕ j()+ t θ j yt ()= Re FB j j() te. j ( ) Similarly to the definition of the local contribution ratio R j L (x 0 ), it is possible to introduce a ratio index R j y for a given mode j as R y Fj Rj j = N F R which indicates the relative coincidence of each CEOF mode j to the variations of y(t) (Ichiawa and Kaneda, 001). In the present case, the first 8 modes explain more than 95% of the total variance. Contribution ratios R j of each mode are shown in Fig. ; note that the mode is numbered in the order of larger R j. The CEOF 1st mode explains 40% of the overall variance, and its phase appears to change with an annual cycle. The characteristic period, for the phase is approximately 6 months for the nd mode, 3 5 months for the 3rd and 4th modes and about 3 months for modes higher than the 4th. Meanwhile, temporal variations of the mode intensity can be examined by the temporal contribution ratio R j t (t 0 ) plotted in Fig. 3. For example, the intensity of the nd mode is relatively wea during periods from December 199 to March 1993 and in October and November The 3rd and 4th modes, in turn, tend to strengthen during those periods, especially in late Spatial distribution of local contribution ratio R j L (x 0 ) for the first 8 modes is plotted in Fig. 4. In general, lower modes occupy wider areas of large local contribution ratios, but some local exceptions can be seen in up to 7th mode. For example, more than 50% of the variance at 31 N, 130 E is explained by the 7th mode, which accounts only 3% of the overall variance as shown in Fig.. 4. Results 4.1 Kuroshio volume transport Time series of the Kuroshio volume transport (hereinafter, abbreviated as KVT) in the Toara Strait and at the ASUKA line is plotted in Fig. 5. Both data show similar variations with a period of approximately 6 months. At the middle of the study period, variation at the ASUKA line seems to be delayed by about one month; for example, local maximum of the KVT in the Toara Strait occurs in June 1993, while that at the ASUKA line is in late July. This temporal lag, however, does not hold for the other periods, such as in late 1993 when both KVT data Fig. 4. Distribution of the local contribution ratio of CEOF 1st mode at each location, R 1 L (x 0 ) (a), and that for nd (b), 3rd (c), 4th (d), 5th (e), 6th (f), 7th (g) and 8th mode (h). Contour interval is 10% and areas with higher ratios are heavily shaded. Kuroshio Variations Induced by Eddies 59

6 Fig. 5. Time series of the Kuroshio volume transport anomaly in the Toara Strait indicated by daily sea level difference between tidal stations A and C in Fig. 1 (dots) and its temporally low-pass (10-day running mean) filtered values (thic line); the left axis indicates sea level differences in meter. Eastward volume transport observed at the ASUKA line is also plotted in the figure (broen line) with an adequate scale shown in the right axis in 10 6 m 3 /s unit; the eastward volume transport is determined at every 10 days indicated by star mars. Horizontal arrows at the bottom indicate the period plotted in Fig. 8, while those at the top in Fig. 13. change almost coincidently. It should be noted that the amplitude of the KVT variation in the Toara Strait is larger in mid 1993, while the variation at the ASUKA line remains almost the same during the whole period. Before decomposing these time series by the CEOF modes, cross correlation between the KVT in the Toara Strait and the offshore SSDT variations was examined in order to illustrate general relationship. Figure 6 shows spatial distribution of the cross correlation coefficients between the KVT in the Strait and the SSDT anomaly with different temporal lags; in the figure, statistically insignificant values suggested by t-test with 95% confidence level are mased. Positive correlation at 3 N, 19.5 E in Fig. 6(a) means that, for example, when SSDT at this particular location is higher (or lower), the KVT in the Toara Strait tends to increase (or decrease) 60 days later. The area of positive correlation at 3 N moves westward as the temporal lags decreased (Figs. 6(a) and (b)), and it becomes a long band of positive correlation elongated along the southern side of the Kuroshio from the south of Oinawa (5 N) to the south of the Toara Strait (8 N; Fig. 6(c)). The northern bound of the long band of positive correlation covers the southern side of the Toara Strait in the contemporary cross correlation (Fig. 6(d)), and the center of the positive correlation seems to move downstream of the Toara Strait when correlation is taen with the SSDT later in time (Figs. 6(e) and (f)). These tendencies at 3 N and around the Toara Strait are also found for the negative correlation. Temporal variations of the KVT in the Toara Strait and at the ASUKA line in Fig. 5 are then decomposed by CEOF modes. Figure 7 shows the contribution ratios R j KVT of each CEOF mode to account for the KVT variations. As clearly indicated in the figure, the CEOF nd mode, which also corresponds to phase variations of 6-month periods, largely contributes especially to the variation in the Toara Strait. In order to exhibit the SSDT pattern corresponding with the variation of the KVT, time series of the SSDT anomaly for the nd mode is shown in Fig. 8 for every 0 days during the period indicated in Fig. 5; the period covers almost one cycle of the nd mode variations with larger intensity explaining more than 30% of the total variance (Fig. 3). The features at 3 N and around the Toara Strait seen in the cross correlation analysis (Fig. 6) are also confirmed in Fig. 8. For example, a mesoscale eddy with positive SSDT anomaly at 3 N propagates westward with a speed of 8 cm/s during April and May 1993 (Figs. 8(a) (c)). When it moves further westward in June and early July, northern part of the eddy becomes elongated along the Kuroshio path and reaches to the Toara Strait (Figs. 8(d) and (e)). Coincidently, the KVT in the Toara Strait plotted in Fig. 5 increased due to the coverage of the positive SSDT anomaly at Naze tide gauge station. 60 K. Ichiawa

7 Fig. 6. Spatial distribution of cross correlation coefficients between the volume transport in the Toara Strait and the SSDT anomaly 60 days before (a), 40 days before (b), 0 days before (c), at the same time (d), 0 days later (e) and 40 days later (f). In the figures, statistically insignificant values at 95% confidence level are mased and locations of the Toara Strait and the ASUKA line are indicated by thic lines. Contour interval is 0. and areas with positive (or negative) correlation are indicated by red (or blue). Fig. 7. Contribution ratios R j KVT of each CEOF mode to account for the variance of the Kuroshio volume transport in the Toara Strait (a) and at the ASUKA line (b). The stretched positive SSDT anomaly moves further downstream along the southern side of the Kuroshio path, and about a month later of passing the Toara Strait, it reaches to the ASUKA line at which it merged into another meso-scale eddy with positive SSDT anomaly propagated from the east at 30 N to form a larger SSDT anomaly (Fig. 8(f)). The merged eddy crosses the ASUKA line by its northern part only, so that the eastward KVT at the ASUKA line increases coincidently (Fig. 5). The merged eddy moves northeastward in August (Figs. 8(g) and (h)) and seems to separate into two, as indicated by eddies in the previous cycle in Figs. 8(a) and (b). The same description holds for meso-scale eddies with the negative SSDT anomaly and decrease of the KVT. It is noted that the negative SSDT anomaly along the Japanese coast in Figs. 8(e) and (f) is originated from the merged eddy at the ASUKA line in Figs. 8(b) and (c), and they results in enhancing the increase of the KVT caused by meso-scale eddies with positive SSDT anomaly. After the possible interaction with the Kuroshio at the area south of Oinawa in late June (Fig. 8(d)), the meso-scale eddy with positive SSDT at 3 N eeps westward propagation with its center moved to the south by about 1, probably depending on the bottom topography. Consistently with the loss of some portion of the eddy captured in the Kuroshio, the zonal size of the eddy shrins to the west of 16 E, so that the propagation speed becomes slower (less than 7 cm/s). The meso-scale eddies east of Taiwan are also nown to affect the KVT at Kuroshio Variations Induced by Eddies 61

8 Fig. 8. Time series of the SSDT anomaly for the CEOF nd mode during the period indicated in Fig. 5; namely, on 14 April (a), 4 May (b), 4 May (c), 1 June (d), July (e), July (f), 11 August (g) and 31 August, 1993 (h). Contour interval is 5 cm and negative values are heavily shaded. In the figures, locations of the Toara Strait and the ASUKA line are indicated by thic lines. WOCE PCM1 line at 4 5 N (Zhang et al., 000). Although their effect in the East China Sea is not very prominent, they can be recognized in Fig. 8 as a long band of positive (or negative) SSDT anomaly in the East China Sea stretching from the east of Taiwan in the panel (c) (or (g)). It is also interesting to note that the strength of the eddies at 3 N suddenly increases at 133 E (Figs. 8(c) and (f)) where they cross the zonally extended Oi-Daito Ridge. 4. Position of the Kuroshio axis Time series of the Kuroshio Position Index is plotted in Fig. 9. In the figure, the KPI is dominated by variations with 0 60 days periods, which is obviously different from variations of the KVT shown in Fig. 5. Since the temporal resolution of the SSDT anomaly is 10 days and some sort of temporal smoothing is enforced by the optimal interpolation, considerable portion of the KPI variation might be lost in the later analysis. 6 K. Ichiawa

9 Fig. 9. Time series of daily Kuroshio Position Index anomaly (dots) and its temporally low-pass (10-day running mean) filtered values (thic line). The periods plotted in Figs. 1 and 13 are also indicated by horizontal arrows at the bottom and top, respectively. Fig. 10. Spatial distribution of cross correlation coefficients between the Kuroshio Position Index anomaly and the SSDT anomaly 0 days before (a), 10 days before (b), at the same time (c), 10 days later (d), 0 days later (e) and 30 days later (f). In the figures, statistically insignificant values at 90% confidence level are mased. Contour interval is 0., but lines only for 0.4 and 0.4 are seen in the figure except for a line of 0.6 south of Shiou in the panel (f). Colorings and thic lines in the Toara Strait and at the ASUKA line are same as Fig. 6. Kuroshio Variations Induced by Eddies 63

10 Nevertheless, spatial distribution of the cross correlation coefficients between the KPI and the offshore SSDT anomaly exhibits remarable features (Fig. 10). First of all, the SSDT variations corresponding to the contemporary KPI changes (Fig. 10(c)) is found to be locally limited to the northern part of the Toara Strait and indicated as a small area of positive correlation. This result is consistent with the past studies that movement of the Kuroshio temperature front in the Toara Strait is bounded to the north of Naanoshima (Nagata and Taeshita, 1985). This area of positive correlation can be traced bac to the upstream of the Kuroshio at 30 N in the correlation with SSDT 10 or 0 days before (Figs. 10(a) and Fig. 11. Contribution ratios R j KPI of each CEOF mode to account for the variance of the Kuroshio Position Index. (b)). Meanwhile, the area is not the downstream of the Toara Strait but along the western coast of Kyushu where significant correlation with the 10-day later SSDT is found (Fig. 10(d)). It is noted that all those areas with positive correlation are found to be negative in the panels lagged with 30 days ((f) for (c); (e) for (b); (d) for (a)). It suggests that the correlation in those areas is mainly responding to the KPI variations with approximately 60 days period. In addition, apart from those areas, westward shifts of corresponding areas of correlation can be observed at 30.5 N, 5 6 N and.5 N as the temporal lags decrease, similarly to ones seen in the correlation with the KVT (Fig. 6). The discrepancy between the KVT and the KPI is also confirmed in Fig. 11 in which contribution ratios R j KPI of each CEOF mode to account for the KPI variance are plotted. The largest contributions come from the higher 7th and 8th modes that have periods of a few months for phase variations, whereas the contribution is almost negligible for the nearly semi-annual nd mode that dominates the KVT variation. Considering that the sum of the 7th and 8th modes explains less than 5% of the overall Fig. 1. Time series of the SSDT anomaly for the sum of the CEOF 7th and 8th modes during the period indicated in Fig. 9; namely, on 5 January (a), 4 February (b), 13 February (c), 3 February (d), 5 March (e) and 15 March (f). Contour intervals, shading, and thic lines are same as Fig K. Ichiawa

11 variance (Fig. ), variation of the KPI is suggested to be caused by a local process that is somewhat independent from larger scale variations. The local contribution ratio in Fig. 4 also supports this interpretation that the larger contribution R j L (x 0 ) for both the 7th and 8th modes are bounded in the adjacent to the Kuroshio path in the East China Sea and at the exit of the Toara Strait. Time series of the SSDT anomaly for the sum of the 7th and 8th modes is plotted in Fig. 1 for every 10 days during the period shown in Fig. 9 when the large KPI variation is observed. The largest KPI, or the northernmost shift of the Kuroshio axis, occurs at the end of February In Fig. 1(d) corresponding to this period, Naanoshima is covered by the positive SSDT anomaly centered at 30 N, 19 E where the Kuroshio path typically meanders northward (Fig. 1). This positive SSDT anomaly seems to be originated from one at 31 N, 18 E in Fig. 1(b) whose diameter is approximately 150 m along the Kuroshio path. These values account for the propagation speed of approximately 9 cm/s downstream of the Kuroshio and wavelength of around 300 m, which agrees with typical values in the East China Sea estimated from in situ observations (Ichiawa and Beardsley, 1993). Meanwhile, as expected from the cross correlation analysis in Fig. 10(d), this positive SSDT anomaly seems to move northward in March 1993, rather than crossing the Toara Strait (Figs. 1(e) and (f)). The SSDT anomaly in the west of Kyushu may correspond to large shed-off of warm eddies often observed in the southwest of Kyushu (Qiu et al., 1990; Lie et al., 1998), but no clear dependency on the KVT variations as Qiu et al. (1990) suggested is found. Since the negative SSDT anomaly is also observed as in the same manner (Figs. 1(b) and (c)), they would correspond to variations of the Tsushima warm current rather than those intermittent shed-off; further studies are necessary to confirm this explanation. 5. Discussion The KVT variations both in the Toara Strait and at the ASUKA line are dominated by the CEOF nd mode that well illustrates their temporal lags in mid However, the nd mode fails to explain the coincident KVT variations in late This discrepancy should be related to the CEOF 3rd and 4th modes which have significant contributions R KVT j to the KVT variation at the ASUKA line (Fig. 7(b)), but less to that in the Toara Fig. 13. Time series of the SSDT anomaly for the CEOF 3rd mode on 31 August (a), 0 September (b), 9 October (c), 9 October (d), 18 November (e) and 8 December 1993 (f). Contour intervals, shading, and thic lines are same as Fig. 8. Kuroshio Variations Induced by Eddies 65

12 Strait (Fig. 7(a)). Since the intensity of the CEOF 3rd mode is stronger than that of the nd mode during periods from December 199 to April 1993 and in October and November 1993 (Fig. 3), the discrepancy between two KVT s would be magnified during such periods. This is clearly visualized in time series of the SSDT anomaly for the CEOF 3rd mode in late 1993 (Fig. 13). A westward-propagating positive meso-scale eddy at 30.5 N crosses the southern side of the ASUKA line in October 1993 (Figs. 13(c) and (d)). Then the eddy seems to be strengthened by merging with positive eddy propagating northeastward along the eastern side of Kyushu (Figs. 13(d) and (e)), leading the large KVT at the ASUKA line in November 1993 (Fig. 5). These meso-scale eddies affecting to the KVT at the ASUKA line come from the east of the Toara Strait so that no significant KVT change occurs in the Toara Strait for this mode. Considerable contribution from the CEOF 3rd mode is also found in the KPI variation (Fig. 11). The significance of the 3rd mode contribution can also be trailed in the cross correlation with the KPI (Fig. 10), as the areas of long-term significant correlations (at 30.5 N, 5 6 N and.5 N) are found to coincide with larger local contribution ratio of the 3rd mode R 3 L (x 0 ) in Fig. 4(c). During the period shown in Fig. 13, the KPI variation in Fig. 9 indicates that the Kuroshio too a long-term southern path in the Toara Strait in late October and early November Since the long-term southern Kuroshio axis in the Strait is suggested to be characterized by the positive SSDT anomaly east of Amamioshima at 7 N and the negative to the north of it (Feng et al., 000), the positive meso-scale eddy at 7.5 N in Fig. 13(e) approaching from the east to Amamioshima may be responsible for the long-term KPI variation. If this is the case, the longterm KPI and the KVT at the ASUKA line are correlated through the CEOF 3rd mode. In Fig. 13, the 3rd mode SSDT south of Shiou and east of Kyushu is found positive when the Kuroshio too the long-term southern path in the Toara Strait, which agrees with the negative correlation in the south of Japan in Fig. 10(f). The negative correlation between the long-term KPI and the Kuroshio variation in the south of Japan has been suggested also from tide gauge records and in situ observations (Kawabe, 1995; Feng et al., 000). On the contrary, the long-term KPI variation may lose significant correlation with the SSDT variations in the East China Sea where the highfrequency 7th and 8th modes dominate. It would partially be explained why no correlation with the upstream SSDT is found by Feng et al. (000). It might be noticed that the period of very large meander of the Kuroshio in mid 1993 (April August) is somewhat coincident with the period when the intensity of the CEOF nd mode strengthened (Fig. 3). This may suggest that the interaction between eddies and the Kuroshio shown in the nd mode itself is related to the large meander south of Japan, for instance, by supplying potential vorticity there from the lower latitude. Also, weaer intensity of the 3rd mode during this period may indicate some physical processes, such as blocing of westward propagation of meso-scale eddies north of 30 N by a large meander. The study period is, however, too short to assess those suggestions since it covers less than three cycles of the dominant KVT signal so that the conclusions would not be representative for the general ones. The shortage of the study period also prohibits to see physical causes of the CEOF modes. For example, the nearly 6-month period of the nd mode would be related to the modulations of the typical annual wind stress variations, which may be resonated with the Oi-Daito Ridge whose zonal length is similar to the half wavelength of the Rossby waves with the semi-annual cycle. However, the 15-month period is obviously too short to discuss such possibility. Therefore, for more generalized discussion, we may need to extend our study period, although high-resolution altimetry SSDT data that is essential for the present study can only be obtained for the tandem periods of T/P and ERS-1/. 6. Summary Effects of meso-scale eddies on temporal variations of the volume transport and the position of the Kuroshio in the Toara Strait are studied using 15-month altimetry data. Sea level difference between Naze and Nishinoomote is used to indicate variation of the Kuroshio volume transport (KVT) in the Toara Strait whereas variation of the position of the Kuroshio in the Strait is accounted by the Kuroshio position index (KPI) based on the ratio of the sea level difference between Naanoshima and Nishinoomote and that between Naze and Nishinoomote. Cross correlation of these variations is first taen with the high-resolution sea surface dynamic topography (SSDT) anomaly estimated from both of TOPEX/POSEIDON and ERS-1 altimetry data, then these KVT and KPI variations are decomposed by the complex empirical orthogonal function (CEOF) modes of the SSDT data. More than 71% of the KVT variance in the Toara Strait is explained by the CEOF nd mode whose period is almost semi-annual. In this mode, some portion of positive (or negative) SSDT anomaly propagating from the east at 3 N seems to be captured into the southern side of the Kuroshio at the south of Oinawa and passes the Toara Strait with increase (or decrease) of the KVT there. The captured eddy moves further downstream, and then merges with another eddy propagating westward at 30.5 N to mae larger (or smaller) KVT at the ASUKA line. Although the KVT at the ASUKA line is dominated by the nd mode, it also includes considerable contribu- 66 K. Ichiawa

13 tions from the CEOF 3rd and 4th modes. As an example, the 3rd mode clearly shows that meso-scale eddies to the east of the Toara Strait directly affect the KVT at the ASUKA line without passing the Strait. On the other hand, more than 58% of the KPI variance is explained by the minor 7th and 8th CEOF modes. These modes account less than 5% of the overall SSDT variance, and their local contribution ratios are bounded in the adjacent to the Kuroshio path in the East China Sea and at the exit of the Toara Strait. These results suggest that the KPI variation in the Strait is caused by a local process in the East China Sea, which is somewhat independent of the KVT variations. In the downstream of the Toara Strait, no systematic SSDT variations seem to be induced by the short-term KPI variation, but the SSDT southwest of Kyushu is found significantly correlated with the KPI variation in the upstream region. 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