Long-term variability of the Kuroshio path south of Japan

Transcription

1 J Oceanogr (2013) 69: DOI /s ORIGINAL ARTICLE Long-term variability of the Kuroshio path south of Japan Norihisa Usui Hiroyuki Tsujino Hideyuki Nakano Satoshi Matsumoto Received: 1 April 2013 / Revised: 1 August 2013 / Accepted: 3 August 2013 / Published online: 31 August 2013 Ó The Oceanographic Society of Japan and Springer Japan 2013 Abstract This study investigates the long-term variability of the Kuroshio path south of Japan. Sensitivity experiments using a data-assimilative model suggest that the duration of the large meander (LM) strongly depends on the Kuroshio transport; specifically, low transport leads to a long duration of the LM. Actually, we find a good correlation between the duration of the past LMs and the Sverdrup transport estimated by a wind-driven linear baroclinic vorticity model. Then we explore favorable conditions for the LM and find a close relationship between the Kuroshio Extension (KE) state and the LM. That is, a precondition for the LM that the Kuroshio path on the Izu Ridge is fixed at a deep channel located around 34 N is achieved during a stable KE state. In addition, westward propagating signals with negative anomalies in the Kuroshio region and high sea-surface height (SSH) state east of Taiwan are key for generation of a small meander southeast of Kyushu that triggers a subsequent LM. The signals related to the above conditions change the upstream Kuroshio transport and velocity, which are consistent with features indicated by the former observational studies. Using reanalysis data, we construct long-time series of indices for the three conditions, which explain well the past LMs. The indices suggest that long-term non-lm states N. Usui (&) H. Tsujino H. Nakano Oceanography and Geochemistry Research Department, Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki , Japan nusui@mri-jma.go.jp S. Matsumoto Global Environment and Marine Department, Japan Meteorological Agency, Otemachi, Chiyoda-ku, Tokyo , Japan around 1970 and in the 1990s were attributed to a low-ssh state east of Taiwan and an unstable KE state, respectively. Keywords Kuroshio Large meander Long-term variability Kuroshio Extension Sverdrup transport Data assimilation 1 Introduction The Kuroshio, the western boundary current of the North Pacific subtropical gyre, originates from the northern branch of the North Equatorial Current (NEC) off the Philippines and flows into the East China Sea (ECS) through the passage east of Taiwan. It then goes northeastward along the continental slope in the ECS, turns east through the Tokara Strait and proceeds eastward along the southern coast of Japan (Fig. 1). After separating from the Japanese coast at the Boso Peninsula, it enters the Pacific basin as a free jet called the Kuroshio Extension (KE). The Kuroshio path south of Japan exhibits a remarkable bimodal feature: the large meander (LM) path and the nonlarge meander (NLM) path (Fig. 1). The NLM path is sometimes further classified into two paths, namely, the offshore NLM (onlm) and the nearshore NLM (nnlm) (Kawabe 1995). These paths are relatively stable and persist from one year to a decade (Kawabe 1987). Such a remarkable path variation is unique to the Kuroshio and is not observed in other western boundary currents such as the Gulf Stream. The particular bottom topography south of Japan, especially the existence of the Izu Ridge that lies along the meridian of 140 E and has two major gates, is considered to have a close relationship with the multiple paths of the Kuroshio. The northern gate of the Izu Ridge is a deep

2 648 N. Usui et al. Fig. 1 Bathymetry (unit in m) and three typical stable paths of the Kuroshio south of Japan: the large meander (LM) path, the offshore non-large meander (onlm) path, and the nearshore non-large meander (nnlm) path. Black closed circles indicate tide gauge stations for Aburatsu (AB), Naze (NZ), and Naha (NH) East China Sea PN line NZ Kyushu AB Tokara Strait Shikoku Kii Pen. LM Japan nnlm Izu Ridge onlm NH channel located around 34 N. The southern one is a shallow ridge rather than the gate and is located south of Hachijo-jima. The LM and the nnlm go through the northern gate and the onlm passes the southern one. The path transition from the NLM to the LM that is, the formation of the LM is preceded by eastward propagation of a small meander, which first appears off the southeast of Kyushu (e.g., Solomon 1978). It then grows up during the eastward propagation, resulting in the LM path. During the transition from the LM to the NLM, on the other hand, the LM path moves eastward while decreasing its amplitude. The onlm path is hence once established during the transition and then returns to the nnlm by further decreasing its amplitude. According to the previous theoretical and numerical studies (e.g., White and McCreary 1976), the LM path can be understood as a stationary Rossby lee wave excited pffiffiffiffiffiffiffiffiffi behind Kyushu with a wavelength scaled by U=b, where U is the current velocity of the Kuroshio and b is the meridional gradient of the Coriolis parameter. This means that the zonal scale of the LM depends on the velocity (or transport) of the Kuroshio. Since the zonal scale is restricted by the zonal width of the Shikoku basin from Kyushu to the Izu Ridge, it is expected that there is a relationship between the path selection and the Kuroshio transport. That is why a number of previous studies have addressed the relation of the LM to the Kuroshio transport. By looking into current velocity and hydrographic observations across the Kuroshio in the region off the southern coast of Japan, Nitani (1975) pointed out that the volume transport of the Kuroshio south of Japan was low during the LMs in 1950s and the1960s. On the other hand, Kawabe (1995), who investigated the relation between the upstream Kuroshio transport in the ECS and the Kuroshio path variations south of Japan using long-time series of both hydrographic observations and tide gauge data, concluded that the LM path tends to occur when the upstream Kuroshio transport is in large or medium range. The above results seem to conflict with each other but it should be noted that the Kuroshio transport focused on by Nitani (1975) is the one south of Japan while Kawabe (1995) looked at the upstream one in the ECS. This might imply that the Kuroshio transports in the upstream ECS and in the region south of Japan should be distinguished. Early modeling studies using inflow-outflow models have argued the sensitivity of the Kuroshio path to some parameters such as the Kuroshio transport and the inclination of the southern coast of Japan (e.g., Chao 1984; Yasuda et al. 1985; Yoon and Yasuda 1987; Akitomo et al. 1991). Their results show that there is a transport range, socalled multiple equilibrium regime, in which both the LM and NLM paths can exist. The existence of the multiple equilibrium regime was firstly presented by Masuda (1982), who showed using the path equation that the Kuroshio path can possess nonunique steady solutions under the constraints that the current is compelled to flow through two assigned points corresponding to the Tokara Strait and the northern gate of the Izu Ridge. Kurogi and Akitomo (2003) suggested that the pressure gradient along the

3 Long-term variability of the Kuroshio 649 southern coast of Japan originating from the large-scale wind stress field determines whether the multiple equilibrium regime can exist or not. Besides, they indicated that the actual wind stress field belongs to the multiple equilibrium state. This implies that other factors should also be considered as well as the Kuroshio transport for the actual Kuroshio path variations. The importance of several other factors has been suggested. Observational studies with a satellite altimeter have shown that mesoscale eddies propagating westward in the Kuroshio recirculation region interact with the Kuroshio southeast of Kyushu and sometimes trigger subsequent Kuroshio meanders (Ebuchi and Hanawa 2001, 2003; Mitsudera et al. 2001). Contribution from the upstream ECS has also been pointed out. That is, disturbances traveling from the ECS, which are induced as a result of interaction between mesoscale eddies and the Kuroshio east of Taiwan, give rise to the small meander southeast of Kyushu (Ichikawa 2001; Akitomo and Kurogi 2001; Kobashi and Hanawa 2004; Usui et al. 2008a). These should be taken into account together with the Kuroshio transport. In addition, this study focuses on a relationship between the LM and the dynamic state of the KE jet, which has not been investigated so far. The KE jet has a bimodal feature: stable and unstable states. These alternately appear on decadal timescales (Qiu and Chen 2005). According to previous observational studies using satellite altimeter data, there is a close relationship between the latitudinal position of the Kuroshio path on the Izu Ridge and the dynamical KE state (Qiu and Chen 2005; Sugimoto and Hanawa 2012). As described before, the typical Kuroshio paths south of Japan are also closely related to the Kuroshio position on the Izu Ridge. These imply a relationship between the bimodal KE state and the Kuroshio path south of Japan. Modeling studies using high-resolution models during this decade have revealed local dynamics responsible for the path transition among the typical Kuroshio paths, especially formation of the LM. According to them, the LM path is caused by baroclinic instability, which is usually triggered by mesoscale eddies (Endoh and Hibiya 2001; Miyazawa et al. 2004; Tsujino et al. 2006). Although individual path transitions are controlled by such short-term stochastic phenomena, long-time series of the southernmost latitude of the Kuroshio path south of Japan shown in Fig. 2 exhibits significant low-frequency variability. The LM frequently occurred in the late 1970s and into the 1980s, while the NLM path continued for a decade before and after the frequent LM period. Its predominant timescale is about 20 years (Kawabe 1987). This long-term variability is suggestive of a relationship with the largescale field. However, there is no study that explains the relation between the long-term behavior of the Kuroshio path and the large-scale field. Considering the results of the previous studies cited above, to clarify the cross relationship between the local dynamics governing individual path transitions and the large-scale field such as the Kuroshio transport and dynamic states of the Kuroshio in its upstream and downstream regions would be key to understanding the long-term variability of the Kuroshio path. Our previous studies provide implications on the relationship between the Kuroshio transport and the local dynamics. Tsujino et al. (2006) conducted a free-simulation experiment using a high-resolution ocean general circulation model (OGCM) and found that slow propagation speed of the small meander during its development is an important condition to achieve the stationary LM path, implying that a weak Kuroshio state is favorable for the LM formation. Usui et al. (2011) examined the decay mechanism of the LM in and suggested a possibility that low Kuroshio transport leads to a long duration of the LM. The recent study of Tsujino et al. (2013) succeeded for the first time at reproducing the longlived LMs in 1950s and 1970s in a long-term historical Fig. 2 Time series of the southernmost latitude of the Kuroshio path south of Japan ( E). The time series depicted by the thin line is based on monthly data obtained from the web site at data.kishou.go.jp/kaiyou/shindan/b_2/kuroshio_stream/kuro_slat.txt, and the thick line denotes the 13-month running mean values. Shades indicate LM periods. The periods since 1975 are identified by the criterion proposed by Yoshida et al. (2006), and that for the LM is based on Kawabe (1995)

4 650 N. Usui et al. OGCM simulation, and showed that features of the simulated Kuroshio path variability were consistent with the above implications. They also discussed contribution of wind-induced positive sea surface height (SSH) anomalies in the upstream region of the Kuroshio and mesoscale eddies from the Kuroshio recirculation to the formation of the simulated LMs. Kawabe (2005) proposed conditions for the LM. Those are based on local features of the Kuroshio such as the axis position at the Tokara Strait and behavior of the cold eddy associated with the small meander. Their relation with the large-scale field is, however, still unclear. Hence, our understanding of the long-term variability of the Kuroshio path, especially its underlying mechanism, is so limited at the present stage. One reason for this issue is that it is still difficult even for state-of-art OGCMs to reproduce the long-term behavior of the Kuroshio path (Tsujino et al. 2013). To defeat this difficulty, it would be better to use a data assimilation system that combines observations and a dynamical model to extract the statistically best estimate. In this study, we therefore utilize data assimilation techniques for the purpose of elucidating the long-term variability of the Kuroshio path south of Japan. We firstly perform sensitivity experiments using an ocean data assimilation system in order to clarify the relationship between the Kuroshio transport and the LM. Then, using long-term ocean reanalysis data we discuss key factors other than the Kuroshio transport that are considered to have a close relationship with the LM, and try to explain the long-term variation of the Kuroshio path using a newly proposed index representing the potential for the LM occurrence. This paper is organized as follows. Section 2 provides brief descriptions of the assimilation system and reanalysis data used in this study. Results of the sensitivity experiments are presented in Sect. 3. Section 4 estimates longtime series of the Sverdrup transport from the wind stress field and investigates the relationship between the Kuroshio transport and the LM. In Sect. 5, we propose three favorable conditions for the LM formation and statistically evaluate the conditions. We then argue about a relationship between the three conditions and variations in the Kuroshio velocity and volume transport according the former observational studies in Sect. 6. Summary and discussions are given in Sect Assimilation system and reanalysis data In this study we use an ocean data assimilation system called Meteorological Research Institute Multivariate Ocean Variational Estimation system (MOVE; Usui et al. 2006). Two varieties of the MOVE system are used: western North Pacific and global versions (MOVE-WNP and MOVE-G). The MOVE system consists of an OGCM and data assimilation scheme. The ocean model used is MRI Community Ocean Model (MRI.COM; Tsujino et al. 2010). MRI.COM is a multilevel model that solves primitive equations under the hydrostatic and the Boussinesq approximation. MOVE- WNP employs a western North Pacific model (model WNP). The model domain spans from 117 E to 160 W zonally and from 15 to 65 N meridionally. The horizontal resolution is variable: it is 1/10 in E (15 50 N) in the zonal (meridional) direction. There are 54 vertical levels with interval increases from 1 m at the surface to 250 m near the bottom. Oceanic states at the side boundaries are obtained from a North Pacific model with a horizontal resolution of 1/2 9 1/2. A biharmonic operator is used for horizontal mixing of tracers with a coefficient m 4 s -1. For the horizontal momentum a biharmonic Smagorinsky viscosity (Griffies and Hallberg 2000) is applied. The vertical viscosity and diffusivity are determined by the turbulent closure scheme of Noh and Kim (1999). More detailed descriptions of the model WNP are given by Tsujino et al. (2006). MOVE-G employs a near-global ocean model (model G) that covers from 75 S to 75 N excluding the Arctic Oceans. The horizontal resolution is except for the equatorial region (15 S 15 N), where the grid spacing in the latitudinal direction is 0.3 within 6 S 6 N and varies between 0.3 and 1 in 6 15 N(S). It has 50 levels in the vertical direction. The model G adopts isopycnal diffusion (Redi 1982) and isopycnal thickness diffusion (Gent and McWilliams 1990). The model by Noh and Kim (1999) is also used as the surface mixed layer model. The analysis scheme used in the MOVE system is based on a three-dimensional variational (3DVAR) scheme using vertical coupled temperature and salinity empirical orthogonal function (EOF) modal decomposition (Fujii and Kamachi 2003). The estimated temperature and salinity fields by the 3DVAR are inserted into the model state by the incremental analysis updates (Bloom et al. 1996). In this study two kinds of reanalysis data (MOVE-WNP RA and MOVE-G RA) produced with MOVE-WNP and MOVE-G, which are summarized in Table 1, are used in order to estimate the past ocean state. The periods of the reanalysis data for MOVE-WNP and MOVE-G are and , respectively. In-situ temperature and salinity profiles, and gridded sea surface temperature (SST) are used for both reanalysis data of MOVE- WNP and MOVE-G. In addition, MOVE-WNP assimilates satellite-derived SSH anomaly data, which is available since MOVE-G does not assimilate the satellite SSH anomaly data to prevent an artificial jump in the reanalysis data between before and after the satellite altimeter era.

5 Long-term variability of the Kuroshio 651 Table 1 Descriptions of the ocean reanalysis data used in this study Name Ocean model Period Forcing Observation MOVE- WNP RA MOVE-G RA Model WNP JRA-25/ T S profile JCDAS 1/10 9 1/10 SST L54 SSH Model G NCEP/ T S profile NCAR 1 9 1, L50 SST 15-member ensemble run assimilation TAU year TAU10 15-member ensemble run TAU08 15-member ensemble run Fig. 3 Schematic diagram of the sensitivity experiment The in-situ profile data are collected from the World Ocean Database 2001 (Conkright et al. 2002) and the Global Temperature Salinity Profile Program (Hamilton 1994). The gridded SST data used for MOVE-WNP is merged satellite and in situ data global daily surface temperatures (Kurihara et al. 2000) produced by JMA. That for MOVE-G is centennial in-situ observation-based estimates of the variability of SST and marine meteorological variables (Ishii et al. 2005), which is also compiled in JMA. The SSH observation used for MOVE-WNP is the alongtrack data from TOPEX/Poseidon, Jason-1/2, ERS-1/2, and ENVISAT, extracted from Ssalt/Duacs delayed-time multimission altimeter products (CLS 2004). The atmospheric reanalysis dataset of the Japanese 25-year reanalysis (Onogi et al. 2007) is employed as the external forcing for MOVE-WNP RA. For MOVE-G RA, the one produced by the National Center for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (Kalnay et al. 1996) is used. 3 Sensitivity experiment on the relation between the Kuroshio transport and the LM 3.1 Experimental setup In order to clarify the relation between the Kuroshio transport and the LM, we carry out sensitivity experiments using MOVE-WNP, which are summarized in Fig. 3. We firstly prepare three kinds of atmospheric forcing: One is a daily climatological data derived from the NCEP-Department of Energy (DOE) Atmospheric Intercomparisons project (AMIP-II) reanalysis (Kanamitsu et al. 2002), averaged over The others are produced by strengthening or weakening the climatological wind stress by 20 %, aiming to change the Sverdrup transport by 20 %. Other atmospheric conditions are common among the three datasets. Here we call these forcing data TAU12, TAU10, and TAU08. Using each forcing data, the model WNP is integrated for 25 years to get three basic states of the Kuroshio, that is, strong, normal, and weak states. These model integrations start from a common initial state obtained from the MOVE-WNP RA output on 1 January We then assimilate satellite-derived SSH anomalies into the model fields every year since year-11. The common SSH data observed in 2004, when the actual LM occurred, are used for the assimilation every year. The assimilation starts on 1 January each year and continues until the end of May to reproduce a Kuroshio small meander southeast of Kyushu. Then the model WNP is integrated for 19 months without assimilation starting from the assimilated field. Consequently, we get three sets of 15-member ensemble simulation results. 3.2 Results Figure 4 shows mean SSH fields and SSH variability in the 25-year free simulations. Here we regard the first 10 years as the spin-up or spin-down period, and hence exclude the period from the calculation for the SSH mean and variability. The mean SSH fields indicate that both the subtropical and subarctic gyres are spun up or spun down according to the wind stress fields. The SSH variability also changes due to the changes in the intensity of the wind stress. It is also worth noting that all the three mean states present a realistic Kuroshio path south of Japan while z- coordinate high-resolution OGCMs tend to have a defect that the Kuroshio path separates from the western boundary at the Tokara Strait south of Kyushu (Tsujino et al. 2006). It is clearly recognizable that TAU12 (TAU08) exhibits larger (smaller) variability than other cases in many areas such as the Kuroshio Extension and the subtropical frontal region (20 25 N). However, interestingly, in the area south of Japan TAU08 has slightly larger SSH variability than TAU10 and TAU12. In addition, taking a close look at the mean Kuroshio path south of Japan, we can see that TAU08 shows a somewhat meandering Kuroshio path in contrast to straight ones for TAU10 and TAU12. This implies that the strength of the Kuroshio has some influence on the path variations south of Japan. Figure 5 compares time evolution of the Kuroshio path in the ensemble simulations. We regard the SSH contour

6 652 N. Usui et al. (a) (d) (b) (e) (c) (f) Fig. 4 Mean (top) and standard deviation (bottom) of the SSH fields (unit in cm) for (left) TAU12, (middle) TAU10, and (right) TAU08. These values are calculated using the SSH fields during the last 15 years in the 25-year free simulations line of 5 cm as the Kuroshio axis. The initial state of each member presents a small meander southeast of Kyushu, which is reproduced by assimilating altimeter-derived SSH anomalies observed in The small meander then develops while moving eastward and a meandering path is once established in each case. Paying attention to the zonal position of the meandering path in 3-month, we can see that the meanders for TAU12 are located more eastward and most members reach the Izu Ridge while those for TAU08 are still situated south of the Kii Peninsula. This means that a large Kuroshio transport leads to fast movement of the small meander. According to Usui et al. (2011), when the LM reaches the Izu Ridge, it tends to be weakened by causing coastal waves and by outflow of high potential vorticity (high-pv) water associated with the cyclonic circulation of the LM to the downstream through the southern gate of the Izu Ridge. That is why the meanders for TAU12 soon decay. In TAU10 several members maintain the LM-type path in 6-month although they are located close to the Izu Ridge. In contrast, all members for TAU08 keep the LM path in 6-month and their positions are more west than those for TAU10 and TAU12. Figure 6 displays the time series of the southernmost latitude of the Kuroshio path south of Japan in the ensemble simulations. The southernmost latitude for each Kuroshio path is determined between E. The meanders in TAU12 develop during June to August, but their amplitudes soon decrease in a few months. It should be noted that several members keeping somewhat large amplitude do not take the LM but rather the onlm path as seen in Fig. 5. The meanders in TAU10 also take maximal amplitudes in August, and then gradually weaken. If we regard 32 N as a threshold for identification of the LM (Yoshida et al. 2006), there are 7(4) members in TAU10 exhibiting the simulated LMs continue more than 6(12) months. On the other hand, the meanders in TAU08 are very stable and all members maintain the LM path until the end of the period. The above results indicate that the stability of the LM strongly depends on the Kuroshio transport. To evaluate the relation between the stability of the LM and the Kuroshio transport more quantitatively, we perform the vorticity analysis. Here we examine the depth-integrated vorticity balance represented as follows (Tsujino et al. 2006):

7 Long-term variability of the Kuroshio 653 (a) (b) (c) Fig. 5 Time evolution of the Kuroshio path in the ensemble simulation for a TAU12, b TAU10, and c TAU08. The SSH contour line of 5 cm is regarded here as the Kuroshio axis of int og ot ot curlðu; vþj g 2 Z g curl ¼ bv þ 1 q 0 J p b ; H 2 þ curl4 Z g H V h ðuþ; V h ðvþ 4 H ðaðuþ; AðvÞ 3 Þdz5 3 dz 5 þ curl s s curl s b ; q 0 q 0 ð1þ where g is the surface height, (u, v) is the horizontal velocity, V is the depth-integrated meridional velocity, b is the meridional gradient of the Colioris parameter, p b is the bottom pressure, H is the local depth of the ocean, q 0 is the reference density, s s is the surface wind stress, and s b is the bottom friction. Operators A and V h denote the advection and the horizontal viscosity, respectively. The terms on the right-hand side represent the planetary beta effect, the bottom pressure torque, the curl of the advection of the horizontal momentum, the curl of the horizontal viscosity of the horizontal momentum, the wind stress, and the bottom friction. The Jacobian operator is represented by J. The beta term arises from the Coriolis force term, and the bottom pressure torque term arises from the pressure gradient term (Mertz and Wright 1992). The second term on the left-hand side is much smaller than the first term and is omitted from diagnostic calculations. Figure 7 compares the vorticity balance of the Kuroshio meanders in the ensemble simulations. The three major terms, the tendency, advection, and planetary beta terms are depicted. The vorticity analysis is applied to 5-day mean fields of each member during 4 8 August (TAU12), 9 13 August (TAU10), and September (TAU08), when the Kuroshio meanders have the maximal amplitude

8 654 N. Usui et al. Fig. 6 Time series of the southernmost latitude of the Kuroshio path south of Japan in the ensemble simulations for a TAU12, b TAU10, and c TAU08. The Kuroshio southernmost latitude between 136 and 141 E during the first 12-month is shown (a) (b) (c) (see Fig. 5). Then we take the ensemble mean for each term in the vorticity equation. The tendency term for TAU12 has prominent signals around the Kuroshio axis, strongly reflecting the advection term. That is why the meanders in TAU12 cannot maintain for a long time. The excess of the advection term can be also seen in TAU10, although it is somewhat mitigated compared with the result in TAU12. In contrast, there is no significant signal in the tendency term of TAU08. This means that the typical vorticity balance of stationary Rossby waves between the advection and the planetary beta is established for TAU08, resulting in the long-lived LM path. It is also noticeable that the shape of the Kuroshio meanders is different among the three cases. The Kuroshio for TAU08 takes a winding path with relatively large meridional displacement (see Figs. 5, 7). In contrast, the meander for TAU12 is somewhat zonally elongated, meaning a long wavelength. We consider here a possible cause for the difference in the meander shape from the point of view of the vorticity balance. The advection term in the vorticity equation includes the effect of vortex induction due to the curvature of the Kuroshio path, which essentially arises from the centrifugal force (Cushman-Roisin 1994). Since large Kuroshio transport strengthens the centrifugal force, it leads to enhancement of the vortex induction. That is probably why the shape of the Kuroshio meander is sensitive to the transport and the winding Kuroshio path can be established under the condition of low transport. In addition, the difference in the meridional displacement of the meanders would also be related to the above curvature effect. This is because large curvature is necessary to form a Kuroshio meander with large meridional displacement within the Shikoku basin, whose zonal width is limited between Kyushu and the Izu Ridge. The time evolution of the Kuroshio meanders for TAU12 in Fig. 5a shows that the troughs of the meanders tend to move quickly eastward because of enhanced vortex induction, leading to longer wavelengths. It is consistent with the relation between the Kuroshio transport and the wavelength of the LM proposed by the previous theoretical studies as described in the introduction. Thus, a longer zonal scale is necessary for the Kuroshio in TAU12 to take a meandering path with large

9 Long-term variability of the Kuroshio (a) 655 (b) (c) Fig. 7 Comparison of the depth-integrated vorticity balance of the simulated Kuroshio meanders for a TAU12, b TAU10, and c TAU08. Dominant terms in the vorticity equation, (top) time change of the relative vorticity, (middle) advection, and (bottom) planetary beta are depicted. The vorticity analysis is applied to 5-day mean fields of each member during 4 8 August (TAU12), 9 13 August (TAU10), and September (TAU08). Then we take the ensemble mean for each term. Contour lines indicate 5-daily SSH fields with an interval of 10 cm averaged over ensemble members meridional amplitude as TAU08, but this may never achieved due to the limitation for the zonal width of the Shikoku basin. Besides, the large meridional displacement causes large westward tendency by the beta effect, which counterbalances the eastward tendency originating from the advection term. For those reasons, it is possible that the Kuroshio meanders for TAU08 easily establish the typical vorticity balance of stationary Rossby waves. the Kuroshio transport. To confirm this relation for the actual Kuroshio, in this section we firstly try to estimate a long-time series of the Kuroshio transport from the wind stress field, and then look into the relation with the past LM events. To infer the past Kuroshio transport, we calculate the Sverdrup transport using the 1.5-layer reduced gravity model (e.g., Qiu 2003) represented by 4 Estimation of long time series of the Kuroshio transport and its relation to the LM In the previous section, it was revealed from the sensitivity experiment that the stability of the LM strongly depends on 1 ow ow curls b ¼ ; ox q0 R2c ot ð2þ where w is the Sverdrup transport, R2c is the internal Rossby radius of deformation, and q0 is the reference density. Integrating (2) from the eastern boundary (xe) along the baroclinic Rossby wave characteristic, we obtain

10 656 N. Usui et al. wðx; y; tþ ¼w x e ; y; t þ x x e þ 1 b Z x x e c R curls x 0 x x 0 ; y; t þ dx 0 ; c R ð3þ where c R (=b R c 2 ) is the westward phase speed of the long baroclinic Rossby waves. Taking w(x e, y, t) = 0, we perform a hindcast calculation using the monthly wind stress field derived from the NCEP/NCAR reanalysis data. Figure 8 shows the time series of the estimated Sverdrup transport averaged over E and N. To evaluate the estimated transport, we compare it with the Kuroshio throughflow transport derived from MOVE-WNP RA results during Here we define the throughflow transport as an averaged net Kuroshio transport from 132 to 140 E. The net Kuroshio transport is calculated from the surface to 1000 dbar at each meridional section from 132 to 140 E with an interval of 0.1, based on the same method as Sugimoto et al (2010). A comparison of the two time series shows that the estimated Sverdrup transport largely follows the throughflow transport from the MOVE-WNP result, although there are a few discrepancies, which might arise from errors in the westward phase speed of the long baroclinic Rossby waves prescribed in the linear model. Both time series indicate a significant transport change in association with the LM event of The Kuroshio transport decreased in prior to the LM formation. Then it rapidly recovered in the end of the LM period, resulting in a high transport state. Taking a close look at the variations in the Sverdrup transport during the other LM periods, we can see that for many LM events the transport increases in the last half of the periods as that of the LM in In order to make clear the variations in the Sverdrup transport during the past LMs, we extract all LM periods and compare them in Fig. 9. It should be noted that the horizontal axis in Fig. 9 denotes time normalized by each LM period. The figure indicates that the Sverdrup transport actually tends to increase in the last half of the LM period except for a few exceptions. It is especially noticeable for the LM events in 1975 and According to the sensitivity experiment in the previous section, it is possible that the increase in the Sverdrup transport leads to the enhancement of downstream movement of the meander, resulting in the decay of the LM. The exceptional events in Fig. 9 such as the case in 1959 might be due to errors of the estimated Sverdrup transport, or decay of these LMs might be caused through a process, not related to changes in the Kuroshio transport, such as detachment of a cold core eddy associated with the LM (Usui et al. 2011). The sensitivity experiment in the previous section indicated that low Kuroshio transport leads to a long duration of the LM. To confirm this relation for the past LMs, we plot a scatter diagram in Fig. 10 between the LM duration and the Sverdrup transport averaged over each LM period. It shows a very clear relation between them with a correlation coefficient of -0.93, which is consistent with the result of the sensitivity experiment. The intercept of the linear regression line in the scatter diagram is 50.5 Sv, which can be regarded as the upper limit of the Sverdrup transport for the LM. In fact, all the past LMs occurred when the transport was below the upper limit, and many of them decayed when the transport increased to around the upper limit. Therefore, the duration of the LM depends on when the Sverdrup transport comes up to the level of the upper limit. In the case with lower transport during the first half of the LM period, such as the LM in 1975, it takes longer time until the transport increases to the upper limit. That is probably why the duration of the LM has a close relationship with the mean Sverdrup transport during the LM period. Fig. 8 Time series of (black line) the Sverdrup transport estimated by the linear model and (red line) the Kuroshio throughflow transport above 1000 dbar calculated from the MOVE-WNP RA results. The Sverdrup transport are averaged over ( E, N) (color figure online) Sverdrup transport (Sv) Kuroshio throughflow transport (Sv)

11 Long-term variability of the Kuroshio 657 Sverdrup transport [Sv] Norimalized LM period [year] Fig. 9 Time evolution of the Sverdrup transport in the Kuroshio region ( E, N) during each LM period. The horizontal axis denotes the normalized LM period Sverdrup transport [Sv] r = Large meander duration [year] Fig. 10 Scatter plot between the duration of the LM and the Sverdrup transport in the Kuroshio region averaged over each LM period. The correlation coefficient is As shown below, the linear relation between the Sverdrup transport and the duration of the LM explains well the behavior of the LMs in the sensitivity experiment. The Sverdrup transports at E and N calculated from the wind stress fields for TAU12, TAU10, and TAU08 are 58.9, 49.1, and 39.3 Sv respectively. The transport for TAU12 exceeds the upper-limit transport, resulting in the rapid decay of the meanders. For TAU10, duration of the LMs expected from the linear relation is about 10 months, which is in good agreement with the experimental results as described in the previous section. That for TAU08 is calculated to 6.7 years by the linear relation, and in fact all the LMs in TAU08 continued until the end of the simulation period (19 months). Here it should be noted that the above discussion does not take into consideration a lower limit of the transport for the LM, while the existence of the lower limit has been indicated by a number of past studies (e.g., Chao 1984; Yoon and Yasuda 1987; Akitomo et al. 1991; Akitomo and Kurogi 2001; Kurogi and Akitomo 2003). We agree with the existence of the lower limit of the transport because a certain amount of velocity (or transport) would be necessary to supply positive vorticity for the LM formation and its maintenance as pointed out by Akitomo et al (1991). Thus the important thing is whether the value of the lower limit is in the range of the actual transport or not. The LMs in the sensitivity experiment of TAU08 are most stable among the three cases even though the Sverdrup transport for TAU08 is 39.3 Sv that almost corresponds to the lowest value in the actual transport range (Fig. 8). Hence we infer that the lower limit of the transport in the actual situation is much lower than the actual transport range. From the above results, we can conclude that the duration of the LM, in other words, the stability of the LM, strongly depends on the Kuroshio transport. It should, however, be noted that the LM does not necessarily occur during low transport periods (Fig. 8). For example, in the early 1970s the LM did not occur even though the low transport state continued. It implies that other factors should also be considered for the occurrence condition of the large meander as well as the Kuroshio transport. Those will be discussed in the next section. 5 Favorable conditions for the LM formation In this section, using the reanalysis dataset we discuss three factors which are considered to be closely related to the occurrence of the LM. Firstly, we take a close look at a relationship between the LM and the KE state, which has not been argued so far. In addition to the KE state, we focus on westward propagating signals originating from the wind stress field, and variation of the SSH field in the upstream region of the Kuroshio especially east of Taiwan. The importance of these two factors for the Kuroshio path variations south of Japan have been pointed out by a number of previous studies, which will be briefly reviewed in this section. Finally, we construct long-time series of variables related to the three factors.

12 658 N. Usui et al. 5.1 Kuroshio Extension state It is well known that the KE jet exhibits a significant decadal variability (Qiu and Chen 2005), which is remotely forced by large scale wind stress field in the North Pacific (Qiu 2003; Taguchi et al. 2007). The wind-induced positive (negative) SSH anomalies strengthen (weaken) the southern anticyclonic recirculation gyre, resulting in a stable (unstable) KE jet. The stable and unstable KE states are well characterized by the path length of the Kuroshio axis (Qiu and Chen 2010a). Figures 11a and b display the time series of SSH anomaly in the region of the southern recirculation gyre ( E, E) and the KE path length integrated from 141 to 153 E. These are calculated from the MOVE- WNP RA result. For comparison, we also plot the altimeter-derived annual mean SSH anomaly in Fig. 11a (shown by red line). Comparing the assimilated SSH anomaly with the observed one, we see that the MOVE-WNP RA reproduces well the observed decadal variability in the intensity of the southern recirculation gyre. We also find that the time series of the KE path length compares well with observation (see Fig. 3 in Qiu and Chen 2010a). The KE jet was in the unstable state during and after 2006, whereas the stable state existed before 1994 and from 2002 to The transition between the stable and unstable KE states is largely synchronized with the variation in the intensity of the southern recirculation gyre. Actually, a correlation coefficient between the annual mean values for SSH anomaly in the southern recirculation gyre and the KE path length exhibits a relatively high value of -0.74, although a few discrepancies are found in Fig. 11a, b such as in To visualize this relation more clearly, we plot in Fig. 12 the yearly Kuroshio paths and SSH anomaly in typical stable and unstable years. Here the Kuroshio paths, which are defined by the 10 cm contour of the assimilated SSH, are plotted every 20 days. During the stable years, the KE path is very stable especially in E, and is accompanied with positive SSH anomalies in the southern recirculation region, indicating a well-developed anticyclonic recirculation. In contrast, during the unstable years, the KE path is spatially variable, and the SSH anomaly in the southern recirculation region is negative, meaning a weakening of the recirculation. Observational studies using satellite altimeter data have indicated that there is a close relationship between the KE path and the latitudinal Kuroshio position on the Izu Ridge (see Fig. 1 for geographical location) lying along the meridian of 140 E (Qiu and Chen 2005; Sugimoto and Hanawa 2012). The relation between the KE path and the Kuroshio position on the Izu Ridge can be found in Figs. 11 and 12. During the stable KE state, the Kuroshio path on the Izu Ridge is also very stable and its latitudinal position is fixed at the northern gate of the ridge located at Fig. 11 Time series of a SSH anomaly (unit in cm) averaged over the southern recirculation region ( E, N), b KE path length (unit in km) integrated from 141 to 153 E, c latitudinal position of the Kuroshio axis on the Izu Ridge. Black curves are based on 5-daily assimilated fields of MOVE-WNP RA. The red line in a presents the altimeterderived SSH anomaly for comparison. Shades denote the period for the LM (a) (b) (c)

13 Long-term variability of the Kuroshio 659 (a) Stable years (b) Unstable years Fig. 12 Yearly KE paths and SSH anomaly (unit in cm) in typical a stable and b unstable years. The KE paths are defined by the 10-cm contour of the MOVE-WNP-assimilated SSH about 34 N (see Fig. 1). On the other hand, during the unstable KE state, the Kuroshio path on the ridge is also variable and consequently in some cases its latitudinal position migrates southward to the southern gate. In addition, the latitudinal position of the Kuroshio path on the Izu Ridge is closely related to the typical Kuroshio paths south of Japan. As shown in Fig.1, the nnlm and LM paths go through the northern gate of the Izu Ridge, while the onlm path passes through the southern one. The transition cycle among these paths is shown in Fig. 13a based on observational facts indicated by Kawabe (1995). The important thing here is that the LM path is necessarily established by a transition from the nnlm path, and these two paths go through the northern gate on the Izu Ridge. This is probably because a developed Kuroshio meander cannot maintain due to outflow of high-pv water associated with the cyclonic circulation of it, leading to decay, when the Kuroshio goes through the southern gate of the Izu Ridge (Usui et al 2011). This means that when a LM occurs, the Kuroshio path on the Izu Ridge needs to be maintained at the northern gate for a long time prior to its formation. Since the Kuroshio path on the Izu Ridge tends to be stably maintained at the northern gate during the stable KE state (see Fig. 13b), we conclude that the stable KE state can be regarded as one of favorable conditions for the occurrence of the LM, or expressed in another way, the stable KE state acts as a precondition for the LM formation by fixing the latitudinal position of the Kuroshio path on the Izu Ridge. The time series of the KE path length and the Kuroshio latitude on the Izu Ridge in Fig. 11b, c actually indicate that the KE was in the stable state from 2002 prior to the LM formation in 2004 and the resultant Kuroshio path on the Izu Ridge was stably maintained at the northern gate. This stable maintenance of the Kuroshio path on the Izu Ridge can also be found in Fig. 12a. The figure indicates that the nnlm path continued from 2002 through 2004 before the LM formation, although a few onlm paths sporadically appeared. This long-lived nnlm path might also be due to the stable KE state. We finally infer the past KE state using the MOVE-G RA results. Figure 14 displays the time series of SSH anomaly in the southern recirculation region ( E, E). For comparison, altimeter-derived SSH anomaly is also plotted with a red line. It should be noted again that the altimeter data is not assimilated into MOVE-G RA and is thus an independent observation from MOVE-G RA. The

14 660 N. Usui et al. Fig. 13 Schematic figure representing the relations of the Kuroshio position on the Izu Ridge with a cycle of the Kuroshio variations among the three typical paths and b KE states (a) Cycle of the Kuroshio path south of Japan nnlm 1 month 4 months several months tlm Northern gate (34 o N) (b) KE state and the Kuroshio position on the Izu Ridge stable (several years) unstable (a few months) onlm Southern gate (32 o - 33 o N) (a few months a few Izu Ridge Fig. 14 Same as Fig. 11a but for the SSH anomaly (unit in cm) based on the MOVE-G RA result during (black line). For comparison, the red line shows the altimeter-derived SSH anomaly in the southern recirculation region. Shades indicate LM periods MOVE-G RA result reproduces well the observed decadal variability even though it employs a coarse resolution OGCM (see Table 1) and hence is not able to resolve the realistic KE jet structure and energetic mesoscale variability. The difference in the amplitude of the variability might be due to nonlinear effects such as advection and eddy-mean flow interaction, which are not fully resolved in MOVE-G RA. According to the above results, a positive SSH anomaly means a strong southern recirculation gyre, indicating that the KE jet is in the stable state, and vice versa. We find in Fig. 14 that many of past LM events occurred during the stable KE state. This result will be discussed again in Sect Westward propagating signals in the Kuroshio region As mentioned in the introduction, the transition from the nnlm path to the LM path is preceded by eastward propagation of a small meander, which firstly appears southeast of Kyushu and is sometimes called trigger meander. A number of past studies have indicated that the small meander southeast of Kyushu is generated by an interaction between the Kuroshio path and a mesoscale eddy propagating westward in the Kuroshio region (e.g., Ebuchi and Hanawa 2001; Waseda et al. 2003; Miyazawa et al. 2004). For a trigger meander that occurred in December 2003 and subsequently developed into the LM in 2004, our previous study (Usui et al. 2008a) also suggested that a cyclonic eddy approaching to the Tokara Strait hit the Kuroshio and as a result the trigger meander was formed. Figure 15a presents the SSH field of MOVE-WN RA in January A negative SSH anomaly corresponding to the trigger meander is found southeast of Kyushu. In addition, negative anomalies are widely distributed in the Shikoku Basin. Usui et al. (2008b) indicated that the remarkable negative SSH anomalies weakened the Kuroshio and consequently led to slow eastward movement of the trigger meander during the formation stage of the LM, which is considered one of the necessary conditions to establish a long-lived LM path. It was also suggested that the negative SSH anomalies were generated by wind stress curl anomalies at the central North Pacific and then propagated westward (Fig. 15c). To detect westward propagating signals originating from the large-scale wind stress field during the past LM periods, a Hovmöller diagram of the Sverdrup transport anomaly at N estimated from the linear vorticity model of (3) is shown in Fig. 16b. As can be found in Fig. 8, the long-term variability, especially a remarkable contrast before and after the late 1970s related to the climate shift, is emphasized in the time series of the estimated Sverdrup transport. For that reason, in order to extract signals on interannual timescales, we applied a

15 Long-term variability of the Kuroshio (a) 661 (c) (b) Fig. 15 SSH (contours) and its anomalies (shades) at the Kuroshio region in a January 2004 and b October c Hovmo ller diagram of the SSH anomaly along 30 N (unit in cm). These are based on the MOVE-WNP RA results high-pass filter in which 6-year running mean values are removed. The SSH anomaly of MOVE-G also seems suitable for the purpose of detecting the westward propagating signals. However, in that case, area-averaged values over the Kuroshio region corresponding to those in Fig. 16a reflect not only the westward propagating signals but also anomalies associated with the LMs. It is difficult to distinguish those signals included in MOVEG RA due to coarse resolution. That is why we employed the high-pass filtered Sverdrup transport anomaly for this analysis. The Hovmo ller diagram indicates that the estimated Sverdrup transport anomaly successfully captures the westward propagating signal corresponding to the negative SSH anomaly in Fig. 15. The diagram also indicates that the similar negative anomalies are frequently observed and the amplitude of the anomalies was relatively small in 1990s when the LM hardly occurred. In the next section, we will use the area-averaged value over the Kuroshio region ( E and N) as an index of the Kuroshio transport and the potential for the occurrence of trigger meander. (a) (b) Fig. 16 a Time series of the high-pass filtered Sverdrup transport anomaly averaged over the Kuroshio region ( E, N). b Hovmo ller diagram of the high-pass filtered Sverdrup transport anomaly at N. Gray shades in a denote LM periods. Units in Sv

16 662 N. Usui et al. 5.3 SSH field east of Taiwan The importance of the upstream region of the Kuroshio for the formation of a small meander southeast of Kyushu has also been pointed out by previous studies. Kobashi and Hanawa (2004) indicated that in addition to a cyclonic eddy propagating from the Kuroshio recirculation region, a Kuroshio front meander traveling from the ECS contributed to the formation of small meanders in 1994 and A similar propagation signal in the ECS was pointed out by Ichikawa (2001), who performed lagged correlation analysis between the Kuroshio transport at the Tokara Strait and altimeter-derived SSH anomalies. Akitomo and Kurogi (2001) demonstrated using a two-layer model that a small meander southeast of Kyushu is generated when an anticyclonic eddy is artificially imposed east of Taiwan. Usui et al. (2008a) showed a detailed formation process of the trigger meander for the LM in According to them, a cyclonic eddy approaching the Tokara Strait interacted with the Kuroshio path and as a result an initial cyclonic anomaly was formed southeast of Kyushu. Then, high-pv water brought by a disturbance propagating along the Kuroshio in the ECS was supplied through the Tokara Strait, resulting in enhancement of the cyclonic circulation there. In addition, they indicated that the disturbance in the ECS was formed by a strong anticyclonic eddy interacting with the Kuroshio path east of Taiwan in September 2003 (Fig. 17a) and propagated along the Kuroshio in the ECS with high-pv generated at the continental shelf edge by viscosity (Fig. 17b). Figure 17a shows the SSH field of MOVE-WNP RA on 8 September A strong anticyclonic eddy colliding with the Kuroshio is recognizable east of Taiwan. Usui et al. (2008a) indicated that the eastward flow in the northern part of the anticyclonic eddy pulled out the Kuroshio path eastward, and consequently a cyclonic anomaly was formed, which is found at around 26 N, 125 E in Fig. 17a. Figure 17b presents a Hovmöller diagram of PV anomaly on a 26.0 r h isopycnal surface along the Kuroshio axis in the ECS based on a prediction result of Usui et al. (2008a) initialized using an assimilated field on 1 August The figure exhibits the propagation of high-pv anomaly generated by the interaction between the anticyclonic eddy and the Kuroshio. A more detailed mechanism of this process is given by Usui et al (2008a). Miyazawa et al. (2008) pointed out that the trigger meander was redeveloped in April 2004 through a similar process, which was also caused by an anticyclonic eddy interacting with the Kuroshio east of Taiwan in February They also suggested that the anticyclonic eddy contributed not only to the redevelopment of the trigger meander but also to amplification of an anticyclonic circulation south of the trigger meander (see Fig. 15a) through advection of positive SSH anomaly by the Kuroshio in the ECS. The amplification of the anticyclonic circulation due to the supply of positive SSH anomaly from the upstream region was also shown in the free-model simulation of Tsujino et al (2013). In addition, Tsujino et al. (2013) also suggested that the existence of the developed anticycloninc circulation located south of the trigger meander promotes subsequent development of the trigger meander. Actually, during the formation stage of the 2004 LM, the developed anticyclonic circulation interacted with the trigger meander and consequentially induced baroclinic instability, resulting in the LM (Usui et al. 2008b). Fig. 17 a SSH (contour with an interval of 10 cm) and its anomaly (shade) on 8 September 2003 derived from MOVE-WNP RA. b PV anomaly on the 26.0 r h isopycnal surface along the Kuroshio axis in the ECS (unit in cm -1 s -1 ), which is adopted from Fig. 13c of Usui et al (2008a). The black square plots (A D) in a are located along the mean Kuroshio path in the ECS at regular intervals of 200 km (a) SSH on 8 SEP 2003 D C A B 21OCT OCT2003 1OCT SEP SEP2003 1SEP2003 (b) PV anomaly 21AUG AUG2003 1AUG2003 A B C D

17 Long-term variability of the Kuroshio 663 Fig. 18 Same as Fig. 14 but for the assimilated SSH anomaly east of Taiwan ( E, N) based on the MOVE-G RA (black line) and the altimeter-derived anomaly (red line) averaged over ( E, N). Units in cm Considering the importance of the contribution from the upstream region for the trigger meander formation indicated by the previous studies as reviewed above, we focus on the SSH field east of Taiwan. Figure 18 shows the time series of the area-averaged SSH anomaly east of Taiwan ( E, N) calculated from MOVE-G RA. To evaluate the MOVE-G RA results, we compare it with altimeter-derived SSH anomalies, whose averaging area is E and N. The averaging regions east of Taiwan for MOVE-G RA and the observation are determined so that amplitudes in the area-averaged SSH anomalies are comparable each other. The time series of the SSH field east of Taiwan in MOVE-G RA largely reproduces observed features although there are some discrepancies. Both time series show the highest SSH from late 2003 to early 2004 prior to the LM in In addition, the MOVE-G RA result indicates that a remarkable low-ssh state continued from the late 1960s to the early 1970s. The low-ssh state in this period can also be found from the Sverdrup transport calculated by the linear vorticity model and the sea level observed at the tide gauge station of Naha ( E, N), neighboring the region east of Taiwan (not shown). During this low-ssh period, the LM did not occur for a decade, implying that the low-ssh state is one of reasons for the long-term NLM state. 5.4 Evaluation of the proposed conditions The three conditions proposed above are mainly based on the analyses for the 2004 LM. Thus, in this subsection, using MOVE-G RA results we construct long-time series of indices related to the three conditions and try to statistically evaluate the proposed conditions. Figure 19a c show time series of the three indices. These are the same as Figs. 14, 16a, and 18 but each value is normalized by standard deviation. It should be noted that the sign of the high-pass filtered Sverdrup transport anomalyinfig.19b, representing westward propagating signals, is reversed because the indices are intended to be positive when the favorable conditions for the LM are satisfied. In addition, note that for the time series of SSH east of Taiwan in Fig. 19c wetakeintoconsideration of a time lag of one year between the SSH state east of Taiwan and the LM formation, according to the fact that as mentioned in Sect. 5.3, the highest SSH east of Taiwan appeared in August September 2003, which was about 1 year prior to the LM formation in the summer of The index I all shown in Fig. 19d is obtained by summing the three indices and renormalizing the result. The index shows a significant decadal variability. It is largely positive and relatively high in the early 1960s, in the late 1970s, in the late 1980s, and in the early 2000s, when the LM occurred. During the long-term NLM periods around 1970 and in the 1990s, by contrast, I all is largely negative. The three indices composing I all suggest that different causes contributed to the two long-term NLM states. As described in Sect. 5.3, the low SSH state east of Taiwan contributed to the NLM from the late 1960s to the early 1970s, while the NLM in the 1990s was due to the unstable KE state in the period. We next introduce a metric in order to evaluate the calculated indices. It is represented as follows: M 1 Z sgnðiðtþþi 2 ðtþdt T flm flm 1 Z sgnðiðtþþi 2 ðtþdt; ð4þ sgnðþ¼ I T NLM NLM 8 < 1 ði [ 0Þ 0 ði ¼ 0Þ : 1 ði\0þ; where I is an index, T flm and T NLM denote the formation period of the LM and the NLM period, respectively. Specifically, for each LM event, we define the formation period as 13 months consisting of 6 months before and after the formation month. The NLM period used in this calculation is during the NLM state excluding the formation period. The metric represents the difference of signed mean square values in the periods for the LM formation and the NLM. A positive value denotes that an LM tends to occur when the index is positive. Using (4), we calculate scores for all indices, which are summarized in Table 2. The score for I all is 1.178, which is statistically significant (p \ 0.01). That is, the difference of the signed mean

18 664 N. Usui et al. Fig. 19 Time series of the three indices: a KE state (Index 1), b westward propagating signals (Index 2), c SSH anomaly east of Taiwan (Index 3), and d the sum of the three indices (Index 1? Index 2? Index 3). Shades indicate past LM periods. Thin lines are based on monthly data and the thick line denotes the 25-month running mean values. Unit is nondimensional (a) (b) (c) (d) Table 2 Scores for the indices evaluated with the metric I 1 I 2 I 3 I all * * * * Indicates that the score is statistically significant (p \ 0.01) square values during flm and NLM is significant. This high score of I all is mainly attributed to index 1 and index 3, which also exhibit relatively high scores and are statistically significant as well as that for I all. In contrast, index 2, representing westward propagating signals, has the lowest score, which is not statistically significant although it is positive. As shown in Fig. 16b, westward propagating signals with negative anomalies, having an ability to generate small meanders southeast of Kyushu, are frequently observed even during the NLM state. Actually, the small meander is generated a few times a year on an average (Nagano and Kawabe 2004), and most of them attenuate in several months. That is why the score for index 2 is much lower than those for the other indices. In addition, due to the low score for index 2, the score for I all ismuch lower than that for index 3 alone. Nevertheless, index 2 is still important for the occurrence of the LM since the LM is necessarily formed as a result of the development of the small meander. From the above statistical evaluation, we conclude that the proposed three conditions for the LM are valid not only for the 2004 LM but also for many of the past LMs.

19 Long-term variability of the Kuroshio Relationship between the proposed conditions and variations in the Kuroshio velocity and transport In past studies, conditions for the LM have been argued in terms of variations in velocity or transport of the Kuroshio. Thus, in this section we look into a relationship between the favorable conditions for the LM proposed in the previous section and variations in the Kuroshio velocity and volume transport using the MOVE-WNP RA results. Kawabe (1995) inferred sea surface geostrophic velocity at the Tokara Strait using sea level difference across the Kuroshio. He pointed out that a maximum surface velocity tends to appear just before or at the time of the formation of the small meander southeast of Kyushu and the surface velocity then decreases and remains small for several months after the LM formation. In addition, Kawabe (1995) constructed time series of a proxy of the Kuroshio volume transport across the PN line in the ECS (see Fig. 1) using tide gauge observations around the Tokara Strait. He focused on transport variations on interannual timescales and found that the LM is formed when the volume transport across the PN line starts increasing and continues as long as the transport increases. According to Kawabe (1995), we plot in Fig. 20a time series of sea level difference between Naze and Aburatsu from 1993 to 2007 (see Fig. 1 for their locations). Two time series derived from MOVE-WNP RA results and tide gauge data are compared. We applied a 3-month running mean filter to each time series in order to remove highfrequency signals. The assimilated surface velocity compares well with the observation. As mentioned in the previous section, the trigger meander for the 2004 LM was firstly formed in December 2003 and was redeveloped in April Temporal intensification of the surface velocity in the summer-fall 2003 and in the spring 2004 is probably related to the trigger meander formation and its redevelopment, as pointed out by Kawabe (1995). The SSH anomaly in September 2003 (Fig. 17) shows that positive anomalies originated from the region east of Taiwan are advected along the Kuroshio and sea level at Naze becomes high. As a result, the surface geostrophic velocity at the Tokara Strait is intensified. Since this positive SSH anomaly east of Taiwan contributed to the formation of the trigger meander in December 2003 as described in the previous section, the temporal intensification of the surface velocity in summer-fall 2003 is considered to be related to the trigger meander formation. According to Miyazawa et al (2008), both the trigger meander southeast of Kyushu and the anticyclonic circulation southeast of the Tokara Strait (see Fig. 15a) formed after the trigger meander formation were amplified due to advection of positive SSH anomalies originated from a strong anticyclonic eddy east of Taiwan. This amplification for the trigger meander (the anticyclonic circulation) leads to a sea level drop (rise) at Aburatsu (Naze), resulting in Fig. 20 Time series of a sea level difference between Naze and Aburatsu, and b volume transport at the PN line (see Fig. 1 for the geographical location). Green lines indicate the values estimated from tide gauge data at Naze and Aburatsu based on a method proposed by Kawabe (1995). Red lines are derived from MOVE-WNP RA results. The black line in b is geostrophic transport referring to 700 db, estimated using hydrographic observations. Gray shadings denote the period for the 2004 LM. Two black arrows indicate the time for the trigger meander formation and its redevelopment (a) (b)

20 666 N. Usui et al. the second temporal intensification of the surface velocity at the Tokara Strait in April It should be noted that not only the advection of the positive SSH anomalies from the upstream but also westward propagating negative anomalies from the east contribute to the amplification of the trigger meander and the resultant sea level drop at Aburatsu (Fig. 15). Thus, the second intensification of the surface velocity is also related to the redevelopment of the trigger meander. The surface velocity then weakened and remained small for several months. This is also consistent with the finding of Kawabe (1995), although the tide gauge data indicate that another minor intensification of the surface velocity occurred just after the LM formation. The weakening of the surface velocity is probably related to eastward movement of both the trigger meander and the anticyclonic circulation. As shown in Fig. 15b, the sea level difference between Naze and Aburatsu decreases as a result of the eastward movement of the trigger meander and the anticyclonic circulation, resulting in the weakening of the surface velocity. In addition, a cyclonic eddy approaching the Tokara Strait brought about a further weakening of the surface velocity in October 2004 (Fig. 15b). Next, we look into interannual variations in the Kuroshio transport at the PN line. Figure 20b compares time series of volume transport anomalies derived from three datasets: MOVE-WNP RA, repeat hydrographic observations by the JMA Nagasaki Marine Observatory, and estimate from tide gauge observations at Naze and Aburatsu based on a statistical analysis of Kawabe (1995). The transports from MOVE-WNP RA and the hydrographic observations are calculated with reference to 700 db. The transport anomaly (T PN ) from the tide gauge observations is estimated by T PN ¼ 0:355g nz 0:213g ab ; ð5þ where g nz and g ab are sea level anomalies at Naze and Aburatsu, which are defined as deviations from the mean state from 1993 to The coefficients of and for g nz and g ab are taken from Kawabe (1995). The time series for MOVE-WNP RA, the hydrographic observations, and the estimated transport from the tide gauge observations are based on every 5-day, 3-month, and daily data, respectively. In order to look at interannual variations of the volume transport as Kawabe (1995), we applied a one-year running mean filter to MOVE-WNP RA and the estimate from the tide gauge data, and a running mean filter with a 15-month window was applied to hydrographic observations. The three time series are in good agreement with each other during the period from 1993 to 2000, whereas after 2000 there are some discrepancies between MOVE-WNP (or the estimate from the tide gauge data) and the hydrographic observations. One reason for the discrepancies might be difference of the sampling intervals. The transport variations for the three datasets during the period of the 2004 LM, nevertheless, show a common feature. That is, all the three time series exhibit an increasing trend of the volume transport during the LM period, although the timing when the transport for MOVE-WNP RA starts increasing delays several months compared with the other estimates. This is consistent not only with the features indicated by Kawabe (1995) but also with the results obtained from the linear model in Sect. 4. To explore causes for the interannual variations in the Kuroshio transport at the PN line, a correlation map between annual mean transport and SSH calculated using MOVE-WNP RA results is plotted in Fig. 21. There are two areas exhibiting positive correlation. One is at a latitude band corresponding to the PN line and the positive correlation extends to eastward, implying that westward propagating signals from the interior region of the subtropical gyre affect the transport variations at the PN line. The other area is located east of Taiwan, suggesting that a high SSH state east of Taiwan intensifies the Kuroshio in the ECS. In contrast, negative correlations are widely distributed to the west of the Kuroshio axis in the ECS and a part of them enters into the region southeast of Kyushu. This means that the small meander southeast of Kyushu tends to be formed when the Kuroshio transport in the ECS is large. In fact, the volume transport for MOVE-WNP RA exhibits a large transport anomaly from the late 2003 to the early 2004 when the trigger meander for the 2004 LM was formed and was redeveloped, while it is unclear for the Fig. 21 Correlation map between annual mean volume transport at the PN line and SSH field. Contour lines indicate the mean SSH field with an interval of 10 cm. The green line denotes the location of the PN line

21 Long-term variability of the Kuroshio 667 transport from the hydrographic observations probably due to the coarse sampling interval. To summarize the above results, many of the features for the surface velocity at the Tokara Strait and the Kuroshio transport in the ECS indicated by Kawabe (1995) are confirmed from the MOVE-WNP RA results. In addition, the causes for the variations in the surface velocity at the Tokara Strait and the Kuroshio transport in the ECS are related to the second and third conditions proposed in the previous section, that is, westward propagating signals and SSH field east of Taiwan. The short-term variations in the surface velocity at the Tokara Strait are mainly affected by mesoscale phenomena around the Tokara Strait such as mesoscale eddies and Kuroshio meanders. In contrast, the interannual variability in the volume transport at the PN line reflect the variations in the SSH field east of Taiwan as well as those originated from the interior region of the subtropical gyre. 7 Summary and discussion In this study, we have examined the long-term variability of the Kuroshio path south of Japan. Sensitivity experiments using an ocean data assimilation system with an eddy-resolving OGCM suggest that the duration of the LM strongly depends on the Kuroshio transport. Specifically, low Kuroshio transport leads to a long duration of the LM. This relation can also be found from the Sverdrup transport estimated using a linear vorticity model forced by the NCEP/NCAR reanalysis wind stress. The linear relation between the Sverdrup transport and duration of the LM suggests that the upper limit of the Sverdrup transport for the LM is 50.5 Sv. In addition, it is shown that the LM did not necessarily occur during low transport periods and hence other factors should also be considered for the occurrence of the LM. Then we discussed three factors considered to be closely related to the formation of the LM: the KE state, westward propagating signals in the Kuroshio region, and the SSH field east of Taiwan. The relationship between the KE state and the LM is newly proposed in this study. During the stable KE state, the Kuroshio path on the Izu Ridge is fixed at the northern gate around 34 N. In addition, considering the observational fact that the LM path is necessarily formed by a transition from the nnlm path and both paths go through the northern gate of the Izu Ridge, we concluded that the stable KE state is one of favorable conditions for the occurrence of the LM. In fact, the stable KE state and the resultant stable nnlm path, passing through the northern gate of the Izu Ridge, were maintained from 2002 to 2004 prior to the LM formation in The other two factors, which have been extensively examined in terms of their relationship with the Kuroshio path variations south of Japan by previous studies, are considered to have a close relation to generation of the trigger meander southeast of Kyushu. In order to statistically evaluate the proposed conditions for the LM, we constructed long-time series of indices related to the three favorable conditions. An index I all defined as the sum of the three indices shows a significant decadal variability and is well synchronized with the longterm variation of the Kuroshio path. That is, it is largely positive during the past LMs, and in contrast is negative during the long-term NLM periods such as those around 1970 and in 1990s. The index also suggests that an extremely low SSH state east of Taiwan mainly contributed to the long-term NLM path around 1970 and the NLM path in 1990s was attributed to the unstable KE state. Evaluation of I all using a metric indicates that a calculated score is statistically significant. We, therefore, conclude that the stable KE state, westward propagating signals with negative anomalies in the Kuroshio region, and positive SSH anomaly east of Taiwan are favorable conditions for the occurrence of the LM, which are schematically illustrated with SSH variability in Fig. 22. According to the findings of Kawabe (1995), we next look into variations in the surface geostrophic velocity at the Tokara Strait and the Kuroshio transport across the PN line in the ECS, and their relation to the proposed conditions for the LM. Many of the features indicated by Kawabe (1995) such as short-term variations in the surface geostrophic velocity at the Tokara Strait and interannual variations in the Kuroshio transport in the ECS are confirmed for the LM in That is, the surface velocity at the Tokara Strait was temporarily intensified in association with the trigger meander formation, then decreased and remained small for several months after the LM formation. The Kuroshio transport in the ECS exhibits an increasing trend during the period of the LM in 2004, which is consistent with the results from the linear model. The shortterm variations in the surface geostrophic velocity at the Tokara Strait are mainly caused by mesoscale phenomena around the strait such as mesoscale eddies and Kuroshio meanders. In contrast, the interannual variations in the Kuroshio transport at the PN line in the ECS reflect variations in the SSH field east of Taiwan as well as variations originated from the interior region of the subtropical gyre. The above causes for the variations in the surface velocity at the Tokara Strait and the Kuroshio transport in the ECS are closely related to the second and third conditions proposed in the previous section, that is, westward propagating signals and SSH field east of Taiwan. Since the variations related to the above two conditions meet together around the Tokara Strait (see Fig. 22), looking at the Kuroshio velocity or transport around the Tokara Strait is effective to

22 668 N. Usui et al. Fig. 22 Schematic diagram of the three favorable conditions for the LM. The background shadings indicate the standard deviation of the SSH field derived MOVE-WNP RA 1. Stable KE state 2. Westward propagating signal 3. Positive SSH anomaly east of capture the signals related to the favorable conditions for the LM. The favorable conditions indicate that the KE and the region east of Taiwan are key areas for the LM formation as well as the Kuroshio region off the south of Japan. It is worth noting that those are located in the downstream and upstream of the Kuroshio current, seen from the area south of Japan, and are two major areas exhibiting high SSH variability in the western North Pacific (Fig. 22). Considering the above, the three favorable conditions could be understood as a natural result. The three indices related to the favorable conditions for the LM were calculated on the basis of the long-term reanalysis data. Because the uncertainty of reanalysis data generally depends on the number of available observations, it is possible that the three indices also have somewhat larger uncertainties especially during the beginning of the analysis period. In this study, the index I all is defined as the simple summation of the three indices. Intrinsically, it might be better that a threshold is defined for each index and I all depends on whether each index satisfies the corresponding threshold or not. Such an approach would not be, however, appropriate for the long-term reanalysis data used in this study due to the uncertainty. Therefore, further improvement of the reanalysis data by refining the assimilative model and re-evaluation of the indices using the improved data should be addressed in future studies. This study focuses on the dynamic state of the KE jet that significantly affects the position of the Kuroshio path on the Izu Ridge. Although there are a number of studies addressing the decadal variability of the KE jet, the transition mechanism between the stable and unstable states of the KE jet is still controversial. Nakano and Ishikawa (2010) demonstrated using a high-resolution OGCM that the northward (southward) shift of the KE jet on decadal timescales is induced as a result of deepening (shoaling) of the thermocline in the recirculation gyre due to the windinduced baroclinic Rossby waves with positive (negative) SSH anomalies. The deepening (shoaling) of the thermocline accompanies weaker (stronger) instabilities, that is, the stable (unstable) KE jet. Qiu and Chen (2005) and Sugimoto and Hanawa (2012), on the other hand, have argued a possible dynamical effect of the Izu Ridge on the bimodal KE state. Clarification of this mechanism should thus be subject for future studies and by doing so we will obtain a deeper understanding of the relationship between the KE state and the Kuroshio path south of Japan. In this study we used the Sverdrup transport anomaly estimated by the linear model in order to detect westward propagating signals for long periods. Actually, the amplitude and pathway of westward propagating signals are modified by interaction with eddies or the recirculation gyre, which are not resolved in the linear model. Therefore, the altimeter-derived SSH data is obviously more suitable for future monitoring of those signals. For the third index, we employed the SSH field east of Taiwan. Since the region east of Taiwan is located in the latitude band of the subtropical countercurrent (STCC) region, it would be expected that the mesoscale eddy activity in the STCC has a large influence on the SSH field east of Taiwan. Qiu and Chen (2010c) investigated interannual changes in the mesoscale eddy field in the STCC and suggested that changes in the vertical shear between the surface eastward-flowing STCC and the subsurface westward-flowing NEC due to changes in the surface Ekman forcing cause interannual variability in the mesoscale eddy activity. As shown in Fig. 19, the SSH field east of Taiwan actually indicates prominent interannual