Coastal Disturbance in Sea Level Propagating along the South Coast of Japan and Its Impact on the Kuroshio

Transcription

1 Journal of Oceanography, Vol. 61, pp. 885 to 93, 5 Coastal Disturbance in Sea Level Propagating along the South Coast of Japan and Its Impact on the Kuroshio AKIRA NAGANO* and MASAKI KAWABE Ocean Research Institute, The University of Tokyo, Minamidai, Nakanoku, Tokyo , Japan (Received 13 April 4; in revised form 31 January 5; accepted 1 February 5) The coastal sea level propagating westward along the south coast of Japan and the impact of the disturbance on the generation of the Kuroshio small meander have been examined. The propagation occurs in sea level variations for periods shorter than 1 days and is remarkable for periods of 4 6 days. Characteristics of the 4 6 day component have been studied using the extended empirical orthogonal function (EEOF). The first and second modes of EEOF are almost inphase throughout the south coast of Japan. The higher four modes of EEOF are significantly excited when the Kuroshio takes the nonlargemeander path, and propagate westward with phase speeds of 2.8 m s 1 (third and fourth modes) and 1.6 m s 1 (fifth and sixth modes) in the Kuroshio region west of Mera in the Boso Peninsula. The analysis shows that more than 7% of the small meanders generate in two months after a significant propagating disturbance reaches south of Kyushu when the velocity of the Kuroshio is high. This effect of coastal disturbance is examined by numerical experiments with a 2.5layer model in which coastal disturbance is excited by vertical displacement of the upper interface. The result is that offshore displacement of the Kuroshio occurs southeast of Kyushu only in the case of significant upward displacement of the interface under the influence of a high Kuroshio velocity. The significant coastal disturbance, which is associated with upward displacement of the density interface, and a high Kuroshio velocity can therefore be important factors in generating small meanders. Keywords: Coastal disturbance, south of Japan, Kuroshio small meander, tide gauge data, numerical experiments. 1. Introduction The Kuroshio, the western boundary current in the North Pacific, takes two longperiod paths alternately in the southern region of Japan with a dominant period of about years; the largemeander (LM) and nonlargemeander (NLM) paths (Yoshida, 1964; Masuzawa, 1965; Kawabe, 1987). The LM path is located offshore and makes a large detour to the south of Enshunada with a large cold eddy on the inshore side, whereas the NLM path is close to the coast west of Cape Shionomisaki and a little apart from the coast to the east of the cape (Fig. 1; Taft, 1972; Kawabe, 1985). Just before the Kuroshio large meander is formed, an offshore displacement of the Kuroshio path, called a Kuroshio small meander, occurs southeast of Kyushu, * Corresponding author. nagano@jamstec.go.jp Present address: Japan Agency for MarineEarth Science and Technology, 215 Natsushimacho, Yokosuka, Kanagawa 23761, Japan. Copyright The Oceanographic Society of Japan. propagating eastward to Cape Shionomisaki (Yoshida, 1961; Shoji, 1972; Kawabe, 198a, 5). The small meander is associated with an inshoreside cold eddy with a diameter of about 5 1 km. It occurs predominantly during the NLM periods (about twice a year), not only before the LM formation, slightly during the LM periods (about once per three years), and in total 42 times in 34 years from 1961 to 1995 (Nagano and Kawabe, 4). Half of the total small meanders propagate to the south of Shikoku, more than % of the total pass the Cape Shionomisaki, and a little more than 1% of the total bring about the LM formation and the transition from the nearshore NLM path to the offshore NLM path. The small meander is thus closely connected to the variations of path of the Kuroshio in the southern region of Shikoku and Honshu in Japan, and an elucidation of generation of the small meander is important to understand the variations of the Kuroshio. Three ideas have been proposed about the cause of the small meander. First, a significant increase of Kuroshio velocity has been considered as a factor. The 885

2 35 N 3 N Nishinoomote Kyushu 1 Naze Boso Pen. Honshu Shionomisaki Shikoku Japan LM Joban NLM North Pacific 25 N 125 E 13 E 135 E 1 E 145 E Fig. 1. Locations of tide stations and diagram of the typical Kuroshio paths: 1 Makurazaki, 2 Odomari, 3 Aburatsu, 4 Hosojima, 5 Tosashimizu, 6 Kochi (Kochi Yokohama), 7 Murotomisaki, 8 Shirahama, 9 Kushimoto, 1 Uragami, 11 Owase, 12 Toba, 13 Maisaka, 14 Omaezaki, 15 Minamiizu, 16 Oshima (Okada), 17 Mera, 18 Choshi (Choshigyoko), 19 Onahama. Sea level difference between Naze and Nishinoomote is used as an index of surface velocity of the Kuroshio. LM and NLM are the largemeander and nonlargemeander paths of the Kuroshio, respectively (Kawabe, 1985, 1995). sea level difference between Naze and Nishinoomote, an index of the Kuroshio velocity south of Kyushu, is at a peak when the small meander bringing about the large meander occurs (Kawabe, 1995). Numerical experiments conducted by Akitomo et al. (1991, 1997), Masuda and Akitomo (), and Endoh and Hibiya () examined responses of the Kuroshio path to shortterm variations of Kuroshio velocity, commonly showing that an increase of Kuroshio velocity produces positive relative vorticity and a small meander south of Kyushu. The positive vorticity is supplied from the noslip boundary condition at the south coast of Kyushu. Second, the mesoscale eddies in the offshore region of the Kuroshio have been supposed to create a disturbance forming a small meander when the eddies collide with the Kuroshio east of Kyushu (Ebuchi and Hanawa,, 1, 3). The eddies are generated east of the Izu Ridge and propagate westward between 24 N and 32 N south of Japan. This notion is based on data of sea surface height from the altimeter on the satellite TOPEX/ Poseidon. Following their analysis, Endoh and Hibiya (1) and Akitomo and Kurogi (1) injected a mesoscale eddy east of Kyushu in numerical models and examined an interaction between the eddy and the Kuroshio. Endoh and Hibiya (1) used a threedimensional model with realistic bottom topography and showed that a small meander is caused by cyclonic vorticity in the coastal water which is supplied by vertical stretching of the water column due to an anticyclonic eddy. Similar numerical experiments were conducted by Mitsudera et al. (1) and Waseda et al. (2). On the other hand, Akitomo and Kurogi (1) showed that a cyclonic eddy injected in the offshore region of the Kuroshio east of Kyushu forms a small meander, using a twolayer model with simple bottom topography. Thus there is a difference between Akitomo and Kurogi (1) and the other studies as to whether the effective eddy is cyclonic or anticyclonic. Third, a disturbance on the inshore side of the Kuroshio has been considered as a factor for the small meander. Moriyasu (1961) inferred that the upwelling southeast of Kyushu due to the winter monsoon causes a small meander. Yasuda et al. (1985) and Yoon and Yasuda (1987) examined the behavior of the Kuroshio in the case that a cyclonic eddy was artificially injected on the inshore side of the Kuroshio in numerical models. The transition from the NLM path to the LM path of the Kuroshio occurred when the cyclonic eddy had large spatial scale and large velocity. Nagano and Kawabe (4) showed that the small meander occurs from June to October more than in the monsoon seasons in winter and early spring, which suggests that other factors are associated with the small meander than just the upwelling southeast of Kyushu due to 886 A. Nagano and M. Kawabe

3 the winter monsoon. A candidate for the other factors in the third category may be a coastal disturbance propagating westward. Shoji (1961) and Isozaki (1969) reported a westward propagation of sea level along the southern coast of Japan. The propagation occurs in sea level variations for periods shorter than 1 days, especially for 4 6 days (Nagano and Kawabe, 4). The present paper examines the sea level variations with periods of 4 6 days and the associated coastal disturbance. The data and data processing are described in Section 2. Characteristics of the propagation of sea levels are investigated in Section 3 using the extended empirical orthogonal function (EEOF). In terms of the disturbance south of Kyushu due to the propagating sea levels, the relation to the small meander of the Kuroshio is studied by data analysis in Section 4 and numerical experiments in Section 5. It is concluded that the coastal disturbance possibly causes the small meander when the Kuroshio has a high velocity. The summary and conclusions are presented in Section Data and Data Processing Daily mean sea level data obtained at the 19 tide gauge stations from 1961 to 1995 on the southern coast of Japan were used. In addition, the sea level difference between Naze and Nishinoomote was used as an index of the surface velocity of the Kuroshio in the Tokara Strait (Kawabe, 198b, 1995). The locations and the names of the stations are shown in Fig. 1. The daily mean sea levels were obtained by averaging 24 hourly tide gauge data. The hourly data, except for Hosojima, were downloaded from the web site of the Japan Oceanographic Data Center. The daily mean data at Hosojima were obtained from the Tidal Record published by the Geographical Survey Institute, Ministry of Construction (currently Ministry of Land, Infrastructure and Transport), Japan. These daily mean sea levels were corrected for barometric pressure and removed 39 tidal components (Ssa, Mm, MSf, Mf, Q 1, ρ 1, O 1, MP 1, M 1, π 1, P 1, S 1, K 1, ψ 1, φ 1, J 1, SO 1, OO 1, 2N 2, µ 2, N 2, ν 2, OP 2, M 2, λ 2, L 2, T 2, S 2, R 2, K 2, 2SM 2, MO 3, M 3, MK 3, SK 3, M 4, MS 4, M 6, 2MS 6 ). We express the sea level at the ith station as u i (t) (i = 1, 2,..., M), where t is time and M is the number of the station, and the lagged covariance of sea level between the ith and jth stations as c i,j (δ), where δ is time lag taken between and T 1 days at an interval of one day. By using c i,j (δ), lagged covariant matrix C(δ) is defined as ( ) ( ) ( ) c11, δ c12, δ L c1, M δ c ( δ) ( δ) ( δ) 21, c22, L c2, M C( δ )=. M M O M c ( δ) c ( δ) L c ( δ ) M, 1 M, 2 M, M The case of δ = leads to the conventional empirical orthogonal function (EOF), as the kth mode of conventional EOF (k = 1, 2,..., M) is defined by the eigenvector e k and the eigenvalue λ k which satisfy ( ) = C e λ e. k k k The eigenvector is expressed by e k = { e i k }, i= 12,,..., M and the sea level at the ith station is expanded as M ui ()= t eik, Pk() t, k = 1 where P k (t) is time coefficient of the kth EOF mode. The conventional EOF expresses stationary modes and cannot detect a sea level propagation. To detect a propagation, the extended matrix R with dimension of TM TM is defined using the lagged covariant matrix C(λ), such as ( ) ( ) ( ) C C1 L C T 1 C() 1 C( ) L C( T 2) R =. M M O M C T 1 C T 2 L C ( ) ( ) ( ) The EOF for the matrix R is called the extended EOF (EEOF). The kth mode of the EEOF (k = 1, 2,..., TM) is expressed by the eigenvector Z k and the eigenvalue µ k satisfying RZ = µ Z. k k k The eigenvector Z k is composed of T vectors z δ+1,k (δ =, 1,..., T 1), such as where Z, = { z }, () 1 k δ + 1, k δ = 1,,..., T 1 z δ+ 1, k z δ M + i, k. i = 12,,..., M = { } As a result, the sea level variation is expanded by the TM modes of the EEOF as Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 887

4 TM ( )= () ( 2) u t + δ zδ, Q t, i M+ i k k k = 1 where Q k (t) is time coefficient of the kth EEOF mode. Using Eqs. (1) and (2), the orthogonal conditions for the EEOF such as Z k 1 Zl = ( k = l) ( k l) 3. Properties of Propagation of Coastal Sea Levels Westward propagation of peaks in sea level along the southern coast of Japan was found by Shoji (1961) and Isozaki (1969). The propagation occurs in the variations of sea level for periods shorter than 1 days, especially for 4 6 days (Nagano and Kawabe, 4). The sea level variations for periods of 4 6 days are different between the LM and NLM periods. The variance of the variations during the LM periods (1.52 cm 2 ) is much smaller than that during the NLM periods (1.94 are written as Q t Q t dt k () () = l µ k ( k = l) ( k l), a 1/27 HOS KUS CHO and 1/22 T 1 M k ()= δ M+ i, k i( + δ ). δ = i= 1 Q t z u t Time 1/17 1/12 The EEOF is useful to detect propagation of sea level (Weare and Nasstrom, 1982). For the calculation of the EEOF, the anomaly of sea level from the mean during was calculated, and then the variations in the sea level anomaly for periods of 4 6 days were extracted by a cosinelanczos filter. Maximum time lag (maximum δ) should be larger than the period (4 6 days), and was taken as nine days (T = 1). Missing sea level values were complemented with the mean sea levels at available stations, as in Nagano and Kawabe (4). b 1/7 1/2 1/27 1/ Distance (km) HOS KUS CHO 4. Time 1/17 1/ /7 Variance (cm 2 ) 1/2 5 1 Distance (km) Station Fig. 2. Variances of sea level variations along the south coast of Japan for periods of 4 6 days during the LM (dashed line) and NLM (solid line) periods between 1961 and The abscissa is the station numbers shown in Fig. 1. Fig. 3. Hovmöller diagrams of the sea level anomaly from the average between 1961 and 1995 for periods of 4 6 days in January 1987 (a) and October 1992 (b), which are typical of the LM and NLM periods, respectively. The abscissa is the distance along the coast from the westernmost station Makurazaki. The mark on the top of the panels shows the location of the tide stations. HOS, KUS, and CHO mean the stations at Hosojima, Kushimoto, and Choshi, respectively. Shading indicates negative values. Contour interval is cm. 888 A. Nagano and M. Kawabe

5 cm 2 ), in particular between Tosashimizu (station 5 in Fig. 1) and Kushimoto (station 9) (Fig. 2). The first mode of frequency domain EOF (FDEOF) with almost constant phase south of Japan is significantly larger for the LM period (accounting for.7% of the total variance) than the NLM periods (29.3%) (Nagano, 4). The sea level variations during the LM period therefore tend to be inphase throughout the south coast of Japan, while those during the NLM period propagate remarkably westward (Fig. 3). In order to examine the characteristics of the propagation exactly, the EEOFs are calculated for the 4 6 day variations during the NLM periods. The calculation concludes a pair of EEOF modes with nearly equal Mode: 1 ( 11.8%) Mode: 2 ( 11.1%) Mode: 3 ( 9.6%) Mode: 4 ( 9.4%) Mode: 5 ( 4.6%) Mode: 6 ( 4.5%) Fig. 4. Six lowest modes of the EEOF, Z k (k = 1, 2,..., 6) in Eq. (1), of sea level variations for periods of 4 6 days during the NLM period. The ordinate and abscissa are time lag δ (days) and eastward distance (km) from Makurazaki, respectively. The mark on the top of the panels shows the location of the tide stations. Thick and dashed contours indicate zero and negative values, respectively. Shading shows large absolute values more than.1. Contour interval is 5. The numeral in parentheses for each mode show the percentage of the variance accounted for by the EEOF mode. Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 889

6 Fig. 5. Difference (cm) in daily mean sea levels between Naze and Nishinoomote, which is an indicator of velocity of the Kuroshio in the Tokara Strait. The average between 1965 and 1995 is taken as the zero point. Positive values are colored black. Downward arrows indicate the times of occurrence of the small meander of the Kuroshio, reported by Nagano and Kawabe (4). 89 A. Nagano and M. Kawabe

7 Fig. 6. Square root of variance (cm) for 1 days of sea level variations at Odomari due to the 4 6 days components propagated by the third to sixth EEOF modes during the NLM period (solid line) and 1day means (cm) of the sea level difference between Naze and Nishinoomote (dashed line). Downward arrows indicate the times of occurrence of the small meander of the Kuroshio. Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 891

8 eigenvalues, i.e., equal percentages for the total variance, which has eigenvectors with a phase difference of 9, like sine and cosine functions (Fig. 4). This means that sea level expressed by one eigenvector leads by 9 or lags 27 behind the other eigenvector. The first and second EEOF modes are almost inphase throughout the southern coast of Japan, whereas the higher modes show westward propagation west of Mera (station 17), although they are inphase at Choshi (station 18) and Onahama (station 19) (Fig. 4). The inphase relation of the higher modes may imply that the variations of sea level occur in the region around Choshi and Onahama, probably due to the excitation by wind on the east coast of the Boso Peninsula (Kitade and Matsuyama, ) and the Joban coast. The phase speed west of Mera is 2.8 m s 1 for the third and fourth modes and 1.6 m s 1 for the fifth and sixth modes. The present estimates of phase speed are not affected by the first and second modes of EEOF, and are therefore smaller and more exact than those found by Shoji (1961) and Isozaki (1969). The propagation of sea level seeing the coast to the right is probably due to coastaltrapped waves, which are influenced by both the stratification and the continental slope in the upper layer above the main thermocline. The waves approach internal Kelvin waves as the width of the upper continental slope decreases (Kawabe, 1982). Since the continental slope in the upper layer is narrow south of Japan, the coastaltrapped waves may nearly be internal Kelvin waves with phase speed gh, where H is the depth of the main thermocline and g is the reduced gravity due to the density difference between the upper and lower layers. Near the coast of Japan, H ranges between 15 m and 3 m, and a typical value of g is 2.5 cm s 2. The phase speed therefore lies between 1.9 m s 1 and 2.7 m s 1. The phase speed of the third and fourth EEOF modes (2.8 m s 1 ) almost corresponds to the maximum speed of an internal Kelvin wave. The phase speed of the fifth and sixth EEOF modes (1.6 m s 1 ) is smaller than the minimum speed of an internal Kelvin wave and may be due to the second horizontal mode wave affected by the upper continental slope time lag (days) Fig. 7. Total number of occurrences of the small meander of the Kuroshio with respect to the time lag behind the significant value (larger than.6 cm) of amplitude of the sea level disturbance at Odomari shown with the solid line in Fig. 6. Thick and thin lines are the frequencies for the periods during which velocity of the Kuroshio is higher and lower than the average between 1965 and 1995, respectively. 4. Influence of the Sea Level Disturbance on the Kuroshio Path Kawabe (1995) pointed out that the small meander bringing about the large meander was generated at a peak of the Kuroshio velocity in dailymean time series. The relation was reproduced by numerical experiments which show that a pulselike increase of the velocity of the Kuroshio makes a small meander southeast of Kyushu (Akitomo et al., 1997; Masuda and Akitomo, ; Endoh and Hibiya, ). The relation to the surface velocity of the Kuroshio is then examined for all the small meanders, including those not related to the large meander generation (Fig. 5). Many small meanders certainly seem to correspond to peaks of the Kuroshio velocity, and most of the small meanders occur during periods of high Kuroshio velocity over the mean value. However, several small meanders are not related to velocity peaks, and most of the velocity peaks are not associated with a small meander. A high Kuroshio velocity in the Tokara Strait may therefore be a background condition for an occurrence of the small meander, and another factor may affect the generation of the small meander. A significant sea level disturbance propagates westward and reaches south of Kyushu during the NLM periods (Section 3), during which the small meander occurs predominantly (Nagano and Kawabe, 4). The square root of 1day variance of sea level at Odomari (station 2) due to the third, fourth, fifth and sixth EEOF modes (called amplitude of the sea level disturbance at Odomari hereafter) is shown by a solid line in Fig. 6. The amplitude of the sea level disturbance is modified with intraannual time scales, and the small meander occurred after a large amplitude sea level disturbance, for example in September 1967, October 197, July 1974, and January and May In these cases, the large amplitude of the coastal disturbance at the southern tip of Kyushu coming from the east may bring about an occurrence of the small meander southeast of Kyushu, somewhat lagging behind the disturbance. The total number of occurrences of the small meander for the cases of high and low velocity of the Kuroshio 892 A. Nagano and M. Kawabe

9 Fig. 8. As the solid line and downward arrows in Fig. 6. Crosses on the line show significant amplitudes (larger than.6 cm) of the sea level disturbance at Odomari at time when the velocity of the Kuroshio is higher than the average between 1965 and The downward arrow is encircled in case that the small meander of the Kuroshio occurs 6 days after the crosses. Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 893

10 are shown with respect to time lag after all the significant amplitudes (larger than.6 cm) of the sea level disturbance at Odomari (Fig. 7). The small meander tends to occur frequently 9 to days before a significant disturbance amplitude, when the Kuroshio has a lower velocity than the mean value. If the sea level disturbance causes the small meander, the generation of a small meander must lag behind the disturbance, and the time lag in Fig. 7 must be positive. Thus, the sea level disturbance may not cause the small meander when the velocity is low. On the other hand, when the Kuroshio has a higher velocity than the mean value, the small meander tends to occur frequently with a lag of 1, 1, and 5 6 days behind the significant disturbance. This suggests that the significant sea level disturbance leading by 6 days generates the small meander in case of high Kuroshio velocity. The significant amplitudes of the coastal disturbance during periods when the Kuroshio has a high velocity are marked by crosses on the time series of the amplitude of the sea level disturbance at Odomari (Fig. 8). The downward arrows, 42 in total and 38 for NLM, show the times of occurrence of the small meander. The small meander hardly occurs when there are few significant disturbances under high Kuroshio velocity, for example during October 1965 July 1966, August 1968 June 197, October 1971 May 1972, October 1973 April 1974, and July 1994 April Of the 38 (downward arrows) small meanders during the NLM periods, 28 (downward arrows with circles) small meanders occur 6 days after a significant amplitude of sea level disturbances under high Kuroshio velocity. In other words, more than 7% of the total small meanders during the NLM periods (28 out of 38) may be generated due to a significant coastal disturbance under high Kuroshio velocity, although the small meander does not always occur even if the two conditions are satisfied. The small meander occurs relatively frequently between June and October in a longterm integration (Nagano and Kawabe, 4). This may be related to seasonality of the Kuroshio velocity and significant coastal disturbance. The longterm average Kuroshio velocity is high between March and August with a maximum in July (Kawabe, 1988). Likewise, there is a high frequency of Kuroshio velocities above the mean between May and August (Fig. 9). There is a high frequency of significant sea level disturbance between July and November. As a result, the frequency of the significant disturbance under high velocity is relatively high between April and September, and it is especially high in July and August. This is similar to the seasonality of occurrence of the small meander shown in Nagano and Kawabe (4). This supports the possibility that many Kuroshio small meanders are generated due to the significant coastal 8 6 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Fig. 9. Monthly counts of the significant amplitude of the sea level disturbance at Odomari (thin line) shown with solid line in Fig. 6, large difference in sea level between Naze and Nishinoomote more than the average (dashed line) shown with dashed line in Fig. 6, and occurrence of both large sea level disturbance and high Kuroshio velocity (thick line) shown with crosses in Fig. 8. disturbance under high Kuroshio velocity. At least the remaining 1 small meanders must be generated due to other factors. Ebuchi and Hanawa (3) analyzed the TOPEX/Poseidon altimeter data and concluded that the small meander was generated due to an interaction of the Kuroshio with a cyclonic eddy in July 1993 and an anticyclonic eddy in May Mitsudera et al. (1) and Waseda et al. (2) show a similar eddy interacting with the Kuroshio, although the spatial scale of the eddy is much larger than that of Ebuchi and Hanawa (3). Some small meanders may be generated due to the interactions with offshore eddies. In addition, the small meanders in July 1966, April 197, March 1971, and April 1974 may be generated due to a large increase of Kuroshio velocity, as noted at the top of this section. Thus, at least a quarter of the small meanders are due to factors other than the coastal disturbance, such as an interaction with offshore mesoscale eddies and a large increase of Kuroshio velocity. 5 Numerical Examination of Influence of Coastal Disturbance We conducted numerical experiments in order to examine possibility of generation of small meander due to significant coastal disturbance and its dependence on Kuroshio velocity. 5.1 Description of the numerical model The numerical model is a 2.5layer primitive equation model on a beta plane, i.e., a threelayer model with two active upper layers and a lowermost resting layer. The interface between the first and second layers, called 894 A. Nagano and M. Kawabe

11 Japan y s y (km) 15 1 East China Sea y 5 North Pacific x (km) Fig. 1. Model geometry and coordinate system. The northwestern region is bounded by the isobaths of m. The zonal arrows at x = 36 km show the meridional distribution of zonal wind stress imposed in the present model. Interface displacement is injected in the meshed region of km < x < 3 km along the northern boundary of the model domain. the upper interface hereafter, represents the main thermocline. The second layer is active to allow for the baroclinic instability. The equations of motion and continuity for the first and second layers (i = 1, 2) are: 7 Kii P u t i ui ui + fk ui = pi + Ah ui + Fi, () 3 ρ hi t + ( h u )=, ( 4) i i 7 where F = ( τ ρ H, ), F = (, ), u = (u, v) is the velocity vector, t is time, p is the pressure, h and H are the thickness and the initial thickness of the layer, k is a unit vector in the vertical direction, A h is the coefficient of the horizontal eddy viscosity, f is the Coriolis parameter, ρ is the reference water density, and τ is the eastward wind stress. Note that operators and 2 are defined as = ( / x, / y) and 2 = = 2 / x / y 2, where x and y show the eastward and northward coordinates, respectively. The rest third layer gives the relation of gη + g η η3 =, g ( ) where η 1, η 2, and η 3 are the upward displacement of the surface, the upper interface, and lower interface, respectively, g is the gravitational acceleration, and g and g Fig. 11. Nearly steadystate of thickness (m) of the first layer in case of high velocity of the Kuroshio with the maximum velocity of 5 cm s 1 south of Kyushu and the Sverdrup transport of Sv. are the reduced gravity between the first and second layers and the second and third layers, respectively. The numerical computation of Eqs. (3), (4), and (5) is performed by using the spatial difference scheme of Holland and Lin (1975) with horizontal resolution of 1 km 1 km, and the leapfrogtrapezoidal scheme with time step of 7 seconds. The model domain is 2 km wide in the meridional direction and km long in the zonal direction, corresponding to the region of 18 N N, 125 E 166 E in the Pacific Ocean (Fig. 1). The origin of the x y coordinates is taken at the southwestern corner. The northwestern part of the model domain is bounded by the continental slope of the East China Sea and the Japanese coast. The model coastline is determined by the m isobaths, made by averaging the 1/12 Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 895

12 3 1 gridded bathymetric data of ETOPO5. A noslip condition is used along the coast from the west coast of Kyushu to the east coast of Japan. The other boundaries are assumed to be slip. The value of A h is 1 6 cm 2 s 1 in the region x < 3 km, increasing linearly eastward for x 3 km reaching 1 7 cm 2 s 1 at the eastern boundary to dissipate the potential vorticity carried by the Kuroshio to the eastern boundary region of the model. The values of H 1 and H 2 are 7 and 1 m, and the values of g, g, and g are 98, 1.5, and cm s 2, respectively. The Coriolis parameter is given by f = f + βy where f and β are the reference value and the latitudinal gradient of the Coriolis parameter, and are set to s 1 and 1 13 cm 1 s 1, respectively. The Kuroshio was driven by the zonal wind stress in the region 3 km < x < km, τ τ = τ ( y y ) ( ys y ) y< ys y y ( ) ( ) s, where τ is the maximum wind stress of the Westerlies, y shows the boundary between the Westerlies and the Trade Winds, and y s is the southernmost position of τ = τ (Fig. 1). The values of y and y s are taken as 1 km and km, respectively. The Kuroshio velocity south of Kyushu is changed by the value of τ which is con Y T E2 3 E th day E E th day 6 7 E E th day Fig. 12. Left: Thickness (m) of the first layer between the 13th and 29th days in case of upward displacement of the upper interface for high velocity of the Kuroshio (Case A). Right: The anomaly of the thickness (m) in Case A from that in Case B in which no disturbance is injected (Case A minus Case B). Shading indicates an anomaly smaller than m. Arrows in the left panels show offshore displacement of the contours in Case A. The letters E1, E2, and E3 in the right panels show cyclonic eddies described in the text. The letters Y and T on the left top panel show Yakushima and Tanegashima, respectively. 896 A. Nagano and M. Kawabe

13 nected to the Sverdrup transport as τ ( ) βvys y = L where V is the Sverdrup transport, and L is the zonal width of wind stress region being 1 km in this model. The period of the disturbance was assumed to be 1 days, because the sea level variations for periods shorter than 1 days propagate westward along the southern coast of Japan (Nagano and Kawabe, 4). The disturbance of 1day period with a phase speed of 2.8 m s 1 has the wavelength of about km. An interface displacement with an alongshore scale of 1 km was therefore injected to the upper interface every 1 days. The sea level variations are probably excited along the east coast of, the Boso Peninsula and the Joban coast. However, we imposed the disturbance along the northern boundary of the model domain (Fig. 1), since our purpose is to examine the effect of the coastal disturbance on the Kuroshio. We assumed that the coastal disturbance is carried by internal Kelvin waves, and the displacement of the upper interface η was given as η = η max ( ) 2π x x ξ sin exp, λ a where η max is a maximum displacement of the interface, ξ is the distance from the northern boundary, i.e., ξ = 2 km y, and x, λ, and a are the westernmost position, the wave length, and the efolding scale of the interface disturbance, respectively. The values of x, λ, and a are, E th day E E th day 7 6 E E3 1 29th day Fig. 12. (continued). Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 897

14 Fig. 13. Amplitude (left) and phase (right) in the first layer of the first and second CEOF modes of variations in thickness of the first and second layers in Case A: Shading in the right panel becomes darker every 9., and 6 km, respectively. The calculations were made in three cases of Sverdrup transport V = 12, 16, and Sv (1 Sv = 1 6 m 3 s 1 ), which correspond to the maximum velocity of the Kuroshio south of Kyushu of about 3,, and 5 cm s 1, called the cases of low, medium, and high Kuroshio velocity, respectively. In each velocity case, two kinds of the interface disturbance, η max = ± m were injected. The interface displacements almost correspond to 2 cm in amplitude of the sea level disturbance. A total of six cases of numerical experiments were examined. 5.2 Results and discussion The Kuroshio was produced in the model by spinning it up for 5 days from rest. The nearly steady state of thickness of the first layer for high Kuroshio velocity (V = Sv) is shown in Fig. 11. The flow concentrates in the first layer, reaching 5 cm s 1, while it is quite weak in the second layer, being at most of the order of 1 cm s 1. The model Kuroshio flows along the coast to the Kii Peninsula and separates from the coast to the east; it is similar to the offshore nonlargemeander path of the Kuroshio. Displacement of the upper interface was injected on the steady state in Fig. 11 every 1 days. The interface displacement propagates westward along the coast due to internal Kelvin waves. The firstlayer thickness values after the time integration of 47 days from the steady state are shown in Fig. 12. The th day corresponds to the day 47. The case of upward displacement for high velocity of the Kuroshio is called Case A, and the reference case without the interface disturbance for high velocity of the Kuroshio is called Case B. The left column of Fig. 12 shows Case A, and the right column is for the anomaly of Case A from Case B, i.e. Case A minus Case B. The internal Kelvin waves reach south of Kyushu twice, from the 11th day to the 15th day and from the 22th day to the 26th day, and are shown by negative anomaly clinging to the coast of Kyushu in the right columns of Fig. 12. Offshore displacement of the Kuroshio is found at the southeast of Tanegashima at the 13th day in Case A, as shown by an arrow, although its amplitude is much smaller than the small meander of the Kuroshio in the real ocean. The negative anomaly is most remarkable to the southsouthwest of Yakushima reaching a value smaller than 3 m, as marked E2, and secondary large southeast of Tanegashima, as marked E1. The offshore displacement of the Kuroshio corresponds to the significant negative anomaly E A. Nagano and M. Kawabe

15 time [days] Fig. 14. Amplitude of time coefficient of the second CEOF mode in Fig. 13 between the 6th and 3th days. Shading indicates periods of existence of the internal Kelvin waves propagating southeast of Kyushu. The offshore displacement of the Kuroshio shifts downstream to the east of Tanegashima at the 16th day, together with the negative anomaly peak E1. The large negative anomaly E2 propagates eastward to the southeast of Yakushima. The significant anomalies E1 and E2 propagate downstream to the east of Kyushu and south of Tanegashima at the 19th day, respectively. The significant anomaly E2 reaches southeast and east of Tanegashima at the 26th and 29th days, respectively, and are associated with the offshore displacement of the Kuroshio. It therefore takes about 18 days from the arrival of the internal Kelvin wave at the 11th day to the development of the offshore displacement southeast of Kyushu at the 29th day, which is consistent with the time lag of 6 days given in Section 4. The negative anomaly marked with E3 is generated due to the next disturbance southsouthwest of Yakushima at the 26th day and propagates to the south of Tanegashima at the 29th day. The situations at the 26th and 29th days are similar to those at the 13th and 16th days, respectively. Thus, the negative disturbance of the firstlayer thickness is propagated westward by internal Kelvin waves and strengthens greatly to the southsouthwest of Yakushima, and then the peaks of the disturbance propagate downstream (eastward) due to the Kuroshio. In association with the peak of the disturbance, offshore displacement of the Kuroshio occurs and propagates, and is clearly detected in the southeast and east regions of Tanegashima. In Fig. 13, the westward propagation of negative disturbance of the firstlayer thickness due to internal Kelvin waves is expressed by the first mode of the complex EOF (CEOF) for the variations in thickness of the first and second layers. The phase shows westward propagation with a speed of 2.3 m s 1, and the amplitude is confined to the internal radius of deformation (about km) from the coast. The second CEOF mode shows that a large negative disturbance exists to the southsouthwest of Yakushima and southeast of Kyushu, and the disturbance propagates eastward (downstream). This implies that the cyclonic eddy propagating downstream develops in the southeast region of Kyushu on average. Variations in strength of the cyclonic eddies are shown by the amplitude of time coefficient of the second CEOF mode, which expresses the cyclonic eddy component not including the disturbance carried by internal Kelvin waves (Fig. 14). The strength of the cyclonic eddies changes with a period of about 11 days, almost corresponding to the period of the disturbance; the eddies are weak between the 15th and 21th days during which internal Kelvin waves do not arrive at the southeast of Kyushu, and are relatively strong when the waves pass the southeast of Kyushu. The strength of the cyclonic eddies therefore seems to be associated with the disturbance carried by internal Kelvin waves. The distribution of relative vorticity is shown in Fig. 15. The right panels show that cyclonic and anticyclonic vorticities persist steadily southwest of Yakushima in Case B. The cyclonic vorticity is due to the velocity shear of the Kuroshio on the inshore side of the current axis southwest of Yakushima. The anticyclonic vorticity may be due to a block of the bottom topography and is located just north of the cyclonic vorticity. The effect of the disturbances propagating from east on the vorticities is shown in the vorticity distributions in Case A. At the 13 th day, when internal Kelvin waves are arriving, the anticyclonic (negative) vorticity strengthens shown by N, and the cyclonic (positive) vorticity extends eastward shown by P. The cyclonic vorticity shifts to the regions south and east of Tanegashima at the 16th and 19th days, respectively. Before internal Kelvin waves arrive, the cyclonic and anticyclonic vorticities rest south of Kyushu. When the internal Kelvin waves arrive, with upward displacement of density interface, the anticyclonic vorticity is strengthened due to the upward displacement of the upper interface by the waves through the conservation of potential vorticity, the cyclonic vorticity moves eastward, and then develops in the downstream region southeast of Kyushu, as shown in Fig. 13. The development of the cyclonic vorticity causes the offshore displacement of path of the Kuroshio, which may correspond to the small meander of the Kuroshio. Both the anticyclonic and cyclonic vorticities seem to play important roles in this process. As shown in Fig. 16, the anticyclonic (negative) vorticity at the 1th day is confined within 1 km from the northern end of the study line. When the internal Kelvin waves begin to arrive at the 11th day, the anticyclonic vorticity spreads southward and intensifies, and the cyclonic vorticity shifts southward by 1 km (one grid interval). The southward shift of the cyclonic vorticity is associated with the increase of the cyclonic vorticity at a distance of 3 km and km. A vorticity balance shows that the increase of Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 899

16 N P 13th day 13th day P 16th day 16th day P 19th day 19th day Fig. 15. Distribution of relative vorticity in the first layer in Cases A (left) and B (right). An interval of contour is 1 5 s 1. Positive vorticity is shaded. Dark shading shows large relative vorticity more than 1 5 s 1. The positive vorticity extending eastward is indicated by the letter P, and the intensified negative vorticity located southwest of Yakushima at the 13th day is indicated by the letter N. The meridional line below the letter N in the upper left panel shows the location where vorticity distribution is examined in Fig. 16. the cyclonic vorticity is due to the southward advection of positive vorticity. The southward shift of the cyclonic vorticity is therefore due to nonlinear interaction with the anticyclonic vorticity. The intensification of the anticyclonic vorticity and the southward shift of the cyclonic vorticity are continued until the 13th day. The maximum of the cyclonic vorticity shifts km southward between the 1th and 13th days, and is located near the Kuroshio axis at the 13th day, so that the cyclonic vorticity is advected eastward. The cyclonic eddy develops southeast of Kyushu and causes the offshore displacement of path of the Kuroshio. This may be caused by the barotropic instability in the present calculation. Potential vorticity in the first layer changes in the direction across the Kuroshio. It reaches a minimum on the offshore side of the Kuroshio axis southeast of Kyushu where the second CEOF mode has maximum amplitude. The minimum of potential vorticity intensifies when the time coefficient of the second CEOF mode is large. On the other hand, the amplitude and its variation of the potential vorticity in the second layer are quite small. These satisfy the necessary condition for the barotropic instability that the minimum of potential vorticity exists only in the first layer (Pedlosky, 1987). In the cases of the disturbance with downward displacement of the upper interface and the cases of low and medium Kuroshio velocity, no significant displacement of the Kuroshio occurs. The disturbance with downward 9 A. Nagano and M. Kawabe

17 1 5 s Distance (km) Fig. 16. Meridional distribution of relative vorticity at the 1 th (thin line), 11th (thick line), and 13th (dashed line) days along the line shown in the upper left panel of Fig. 15. The abscissa is the distance from the northernmost grid point of vorticity at the line. displacement has cyclonic relative vorticity, and does not intensify the anticyclonic vorticity southwest of Yakushima. Low or medium velocity of the Kuroshio does not involve significant cyclonic vorticity on the inshore side of the current axis. This may explain why significant displacement of the Kuroshio does not occur in the other cases than that of upward displacement of the upper interface under high Kuroshio velocity. Thus, the small meander of the Kuroshio may be caused by the coastal disturbance with upward interface displacement under high Kuroshio velocity. The dependence on velocity of the Kuroshio agrees with the result of the observation data indicated in Section 4. However, the displacement in the present model is much smaller than the small meander in the real ocean. Past numerical experiments suggest that the baroclinic instability is important for growth of the small meander to the east of Kyushu (e.g., Endoh and Hibiya, 1). A reason for insufficient development of the path displacement may be that the baroclinic instability is not effective in the present model. 6. Summary and Conclusions The coastal disturbance in relation to westward propagation of sea level for periods of 4 6 days during NLM periods has been examined in terms of generation of the small meander of the Kuroshio, using sea level data obtained from 19 tide gauges on the southern coast of Japan during The extended empirical orthogonal function (EEOF) analysis has been performed to investigate the propagation of the sea level. The first and second EEOFs are almost inphase throughout the south coast of Japan. The modes of the third to sixth EEOFs propagate westward in the region west of Mera at speeds of 2.8 m s 1 for the third and fourth EEOFs and 1.6 m s 1 for fifth and sixth EEOFs, and are inphase at Choshi and Onahama. This may imply that disturbances of the third to sixth modes are generated at the east coast of the Boso Peninsula and the Joban coast and propagate from there to the south of Kyushu. More than 7% of the small meanders during the NLM periods are generated 6 days after the significant coastal disturbance reaches south of Kyushu under high velocity of the Kuroshio. The contribution of coastal disturbances and Kuroshio velocity to generation of the small meander has been examined by numerical experiments using a 2.5 layer model. Upward and downward displacements of the upper interface with 1day period and low, medium, and high velocities of the Kuroshio are considered as the conditions in the numerical experiments, and a total of six cases have been computed. The interface displacement propagates westward along the Japanese coast due to internal Kelvin waves and causes coastal disturbance south of Kyushu. An offshore displacement of the Kuroshio path has been found to occur southeast of Kyushu only in case of the upward displacement of the upper interface with high Kuroshio velocity. No path displacement was found to occur in the other cases. The numerical experiments have shown the possibility that the coastal disturbances and high Kuroshio velocity contribute to generation of the small meander, and allow us to conclude that the coastal disturbances must be associated with the upward displacement of density interface, not the downward displacement. According to the sealevel analysis and the numerical experiments, three conditions in terms of coastal disturbances and Kuroshio velocity are important for generation of the small meander of the Kuroshio; 1) the coastal disturbances have significant amplitude, 2) the coastal disturbances have upward displacement of density interface, and 3) the Kuroshio has a high velocity. Significant coastal disturbances frequently occur between July and November. A high Kuroshio velocity frequently occurs between May and August. These two conditions are well satisfied from April to September, especially in July and August. This may cause the seasonality of occurrence of the small meander shown by Nagano and Kawabe (4). Significant coastal disturbances in autumn may be produced by atmospheric lows which pass over the Joban coast and the Boso Peninsula with periods of several days. The amplitude of the coastal disturbances with periods of 4 6 days increases significantly at intervals of several months. This may be a major reason why the small meander occurs with timescales of several months. The time interval of the small meander is increased more due to the observed fact that significant coastal disturbances Coastal Sea Level Disturbance Propagating South of Japan and Its Impact on the Kuroshio 91

18 do not always generate the small meander, even though Kuroshio velocity is high. This may be because some of the significant coastal disturbances are associated with downward displacement of the density interface. These may determine the timescales at which the small meander occurs to be approximately half a year during the NLM periods. Acknowledgements The authors would like to thank the Japan Oceanographic Data Center and the Japan Meteorological Agency for kindly providing the necessary data of sea level, barometric pressure, and tidal constants. The study benefited from teaching about numerical modeling techniques by Dr. Shinzou Fujio. This paper is part of the doctoral dissertation of the first author, and the authors thank the examiners, Drs. Yukio Masumoto, Masahiro Endoh, Toshiyuki Hibiya and Yukari Takayabu, for their valuable comments. Thanks are also due to the editor, Dr. Ichiro Yasuda, and the anonymous reviewers for helpful comments. References Akitomo, K. and M. 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