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Origins of the Kuroshio and Mindanao currents Background

The boundary currents off the east coast of the Philippines are of critical importance to the general circulation of the Pacific Ocean. The westward flowing North Equatorial Current (NEC) runs into the Philippine coast and bifurcates into the northward Kuroshio and the southward Mindanao Current (MC) (Figure 1; Nitani, 1972). The partitioning of the flow into the Kuroshio and MC is an important observable. Quantifying these flows and understanding bifurcation dynamics are essential to improving predictions of regional circulation, and to characterizing property transports that ultimately affect Pacific climate. Fluctuations in the Kuroshio and MC can significantly impact variability downstream. For example, the Kuroshio penetrates through Luzon Strait into the South China Sea and onto the East China Sea shelf. The Kuroshio front dramatically alters stratification and may impact internal wave climate. The study proposed here incorporates observation, theory, and modeling to make fundamental advances in our knowledge of the origins of the Kuroshio and Mindanao currents.

Figure 1. Region of study. The major currents of the region are identified: the North Equatorial Current (NEC), the Kuroshio, and the Mindanao Current (MC). 2

Figure 2. Tracks of drifters color-coded by instantaneous (6 hourly) speed.

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Drifter observations of currents at 15 m depth form a comprehensive dataset of direct observations . According to these observations (Figure 2), the roots of the Mindanao Current can be located at approximately 11° N, 1.5° south of the latitude at which the mean NEC takes a southward and a northward bend (Centurioni et al., 2004) while approaching the Philippine Archipelago. The Kuroshio however, appears to become a stable, detectable boundary current (with speeds in excess of 0.8 m s-1) between 16°N and 18°N. Although the drifter data are too sparse to allow a definitive picture of the annual cycle in the region, the available data suggest that the two-dimensional circulation pattern north of 11° N changes seasonally. A region of complex and highly variable near surface flow exists off the western (Philippines) boundary and north of the roots of the Mindanao Current, i.e. between 12°N and 16-18°N. Regions characterized by intermittently high speeds (Figure 2) extend eastward and away from the region’s western boundary from 24°N to 18°N and between12°N and 9°N. Those are also the regions of relatively large, seasonally variable , Eddy Kinetic Energy (EKE), while lower EKE is generally found between those two latitude bands.

North Equatorial Current and Bifurcation

The bifurcation of the NEC has been the subject of a number of studies, as its position varies seasonally and with depth (Kim et al., 2004: Qu and Lukas, 2003: Yaremchuk and Qu, 2004). The location of the bifurcation also depends on the data and models used in its definition. General statements are difficult to make, but the following description is supported by the weight of the published material. In the annual average, the bifurcation trends north with depth, with the surface expression near 14°N sloping to 17°N near 500 m. The bifurcation is at its northernmost position in the fall and at its southernmost position in spring, with an annual excursion of about 2° in latitude.

The mechanisms governing the excursions of the bifurcation and the strengths of the currents are topics of active research. Local wind forcing through the wind stress curl, and remote forcing through Rossby waves are both possibly important (Qiu and Lukas, 1996). Interannual changes may have some relationship to ENSO, shifting northward during El Niño years and southward during La Niña years. The interplay of local and remote forcing, and the rich array of time scales make this region an interesting site for study.

Kuroshio

The Kuroshio forms in the NEC bifurcation region (12° - 18°N), though energetic mesoscale eddy variability often obscures the current in region east of the Philippine Archipelago. Data availability limits understanding of Kuroshio formation, with the upstream Kuroshio having received far less attention than the regions to the northeast. Although observations reveal an increasingly distinct Kuroshio northward toward Luzon Strait, the formation mechanism remains unclear. Should the upstream Kuroshio be considered as an eddy- driven current or as a laminar boundary flow, and from where does it draw its source waters?

The Kuroshio typically flows northward with a slight westward incursion through the deep channels (2400 m sill depth) of Luzon Strait, but occasionally turns westward to form significant intrusions into the South China Sea. These intrusions modify Kuroshio structure through entrainment of South China Sea waters and impact mesoscale and internal wave 4 variability within the South China Sea. The region experiences intense, seasonally reversing wind forcing by the Asian Monsoon, with strong wintertime winds from the northeast, weaker summertime winds from the southwest and relatively calm intermonsoon periods. Although observational evidence remains scarce, Kuroshio loop current events appear more common during the winter monsoon (Wang and Chern, 1987). Competing theories attempt to explain the dynamics governing these intrusions, the simplest invoking westward Ekman transport produced by the winter monsoon to drive the Kuroshio through the Strait (Farris and Wimbush, 1996). Weak (strong) wintertime (summertime) density contrasts across the Kuroshio-South China Sea front may accelerate (retard) westward translation of the front (Chern and Wang, 1998). Numerical investigations suggest that strong meridional windstress curl gradients across Luzon Strait may generate sharp contrasts in thermocline depth and enhance Kuroshio penetration (Metzger and Hurlburt, 2001), but find little direct correlation between winds and loop current formation. Sheremet (2001) finds that inertia carries western boundary currents across gaps for strong flows, but at slower speeds  effect dominates, driving a westward turn. These dynamics exhibit several characteristics consistent with observed loop current formation, including preferential wintertime formation (when monsoon winds may weaken the Kuroshio) and lack of direct correlation with local winds, possibly the result of response hysteresis. Both observations and theoretical results feature energetic meandering and mesoscale eddy generation.

Though mesoscale variability complicates quantification of Kuroshio transports south of Luzon Strait, Gilson and Roemmich (2002) employ an eight-year record of repeated XBT surveys to characterize transports off the southern end of Taiwan, after interactions with the South China Sea but prior to passage over the Ilan Ridge. Annual mean volume transport was 22±1.5 Sv with 8±6 Sv seasonal variation, with the strongest currents confined close to the Taiwan coast, in the upper 700 m of the water column. Kuroshio transport is strongest in winter/spring and weakest in autumn, in phase with NEC seasonal variations. Kuroshio transport exhibits 12±6 Sv interannual variability, well in excess of its seasonal range. The Kuroshio often exhibits a dual-core structure east of Taiwan (Chern and Wang, 1998), collapsing to a single current prior to passing over Ilan Ridge. Analysis of historical hydrographic measurements suggests that this two-core structure is a consistent feature of the Kuroshio offshore of Taiwan (Lien, personal communication).

After leaving the Luzon Strait region, the Kuroshio flows along the east coast of Taiwan, eventually encountering the Ilan Ridge where it can enter the East China Sea though the East Taiwan Channel or turn northeastward along the east side of the Ryukyu Islands. East of Taiwan, the Kuroshio exhibits annual mean transport of roughly 20 Sv with large 10 Sv variations at timescales of days to months (Johns et al., 2001). The mean transport profile is significantly sheared in the upper 500 m, with 40% (60%) of the transport occurring in the upper 100 (200) m. Meanders induced by anticyclonic eddies impinging from the Philippine Sea drive strong transport variability at ~100 day timescales (Zhang et al., 2001). During strong transport periods, the Kuroshio passes through the East Taiwan Channel and enters the East China Sea, impacting circulation and internal wave variability within the marginal sea. Zhang et al. (2001) associate low transport periods with impinging eddies that steer the current toward the eastern side of the Ryukyu Islands. Mesoscale-induced transport variability exceeds seasonal fluctuations (Johns et al., 2001), and eddy interactions may thus exert a controlling influence on the Kuroshio’s interactions with the East China Sea. 5

Mindanao Current

The MC has not been as well observed as has the Kuroshio. The most extensive series of observations took place during 1987-1990 as part of two efforts: the Western Equatorial Pacific Ocean Circulation Study (WEPOCS) and a joint United States/People’s Republic of China Tropical Ocean Global Atmosphere (TOGA) program. Hydrographic and Acoustic Doppler Current Profiler (ADCP) measurements were made in a series of 8 cruises. These observations were synthesized by Wijffels et al. (1995), which found a remarkably steady MC. While the core of the MC was stable, the flows offshore of the MC were extremely variable. For example, recirculation indicative of the Mindanao Eddy was found in only 2 of the 8 cruises, and the northward flowing Mindanao Undercurrent (Hu et al., 1991: Qu et al., 1998) was not apparent in the mean. The possibility remains that the Mindanao Eddy is strongly modulated on seasonal or shorter time scales (Toole et al., 1990).

A single mooring observation of the MC was made over the period from 1999-2002 by Kashino et al. (2005). They reported that the existence of a strong shallow surface current with a speed of over 1.3 m/s at 100 m, with a remarkably low variability of less than 0.2 m/s. The velocity was highest during boreal summer, and the strength was apparently modulated by the onset of the 2002 El Nino. However, the mooring observations left open several unanswered questions. As with previous hydrographic observations, there was no evidence found of a northward flowing Mindanao Undercurrent. Furthermore, the deep western boundary current that should exist there in theory was left unobserved.

Predictability

The ocean processes over the shelf and slope water off the Philippines and Taiwan are

Figure 3. Currents from two ocean models: the Navy Coastal Ocean Model (NCOM) and the Hybrid Coordinate Ocean Model (HYCOM). 6 inherently multi-scale and pose a challenge to predictability. Fine resolution ocean models, forced with synoptic atmospheric fluxes or coupled to an atmospheric model, and configured using either large-scale domains or regional grids forced laterally with remote oceanic forcing from a large-scale simulation offer us a means to explore predictability issues. A data assimilative capability in these models further enhances such studies.

In the first instance it is necessary to determine if these models are able to produce the mean and variability of the regional ocean circulation. Mass transports through key passages, patterns and strength of the surface circulation, time evolution of mixed layer depth, and time and space scales are among other environmental keys that provide a gauge of the realism of these models. Mean model surface currents from a global and coastal model afford an assessment of potential predictability issues associated with this region (Figure 3). In particular, both models reveal swift currents off Mindanao and Luzon (and Kuroshio intrusion into the SCS), with a more quiescent region in between. In this relatively fallow zone both models show a NEC flow at approximately 12N and 17N, with a continuous northward coastal current linking the two. In a region of elevated variability offshore (of the high-resolution model) around 20N, there is a proliferation of eddies. Surprisingly, both models produce a double gyre in approximately the same location in this two-month mean field, however they differ in their representation of other smaller scale circulations in this region. The temporal and spatial (horizontal and vertical) structure and variability of this eddy region, as well as the sensitivity to atmospheric forcing are aspects to be pursued through data assimilation and coupled ocean/atmosphere model studies. Such efforts would lead to improved prediction of complex coastal regions influenced by multiple impinging currents. Specific model predictability studies guided by observations are suggested below.

Zhang et al. (2001) document the predictability of Kuroshio Current meanders off Taiwan. They found low transport events as measured by an array of current meters in the East Taiwan Channel (ETC) to be co-incident with the arrival of anticyclonic mesoscale eddies at the western boundary that had propagated westward from the basin interior. During these events, surface drifter tracks showed that the Kuroshio Current developed a large offshore meander to the east of Taiwan and then intruded into the East China Sea (ECS) to the northeast of Taiwan.

Niiler and Kim correlated the current meter transport time series of Zhang et al. (2001) with sea surface height anomaly (SSHA) from the AVISO altimetry product in the waters surrounding Taiwan. They obtained a maximum correlation of 0.7 just to the east of the island (123.32E, 23.82N) and found that low volume transports corresponded to periods of low SSHA. They formed composites of trajectories of surface drifting buoys at 15 m that coincided with low and high sea surface height anomaly events at this location. They found that the high sea level composite trajectories were more tightly packed adjacent to the continental shelf while during low sea level events the Kuroshio Current intruded extensively over the shelf into the ECS.

McClean and Kim used output from two eddy resolving ocean models to ascertain if these simulations were able to reproduce this predictable ocean response. They calculated Kuroshio Current volume transport anomalies through the ETC for the period 1994-2003 from 7 the global 0.1 Parallel Ocean Program (POP) forced with synoptic atmospheric fluxes. They released numerical drifters to the east of Taiwan during selected low and high transport anomaly events during that period. The outcome was that during the low transport event the Kuroshio Current meandered offshore of Taiwan and then intruded into the ECS while during the high transport event the drifter trajectories closely followed the continental shelf. The intrusions into the ECS however occurred further to the north than is observed. Consequently, they repeated the numerical drifter exercise using the global 1/12 Hybrid Coordinate Ocean Model/ Navy Coupled Ocean Data Assimilation (HYCOM/NCODA) output. During low sea level events the Kuroshio Current meandered offshore and then intruded further into the ECS and its intrusion location is closer to that observed. Predictability of the variability of the paths and strengths of the Kuroshio and Mindanao Currents can likewise be examined offshore of the Philippines. Science Questions

The region where the NEC terminates and the Mindanao Current and Kuroshio originate along the low-latitude North Pacific western boundary is where time-varying oceanic signals generated in the eastern interior Pacific, or locally in the Philippine Basin, ultimately accumulate. The incoming, time-varying signals are either forced by the time-varying surface wind stress forcing, or are a result of intrinsic instability of ocean circulation.

Existing observational evidence from satellite altimeter, repeat hydrography, and high- resolution XBT/XCTD measurements reveals that the NEC bifurcation region of 12N~18N corresponds to a dynamic transition zone: in the lower latitude domain (i.e, the southern half of the NEC), the observed oceanic variability has predominantly annual-to-interannual timescales and some of these signals can be understood and hindcast by wind-driven linear vorticity dynamics. Oceanic variability does increase in amplitude again along the NECC band existing further to the south.

In the northern NEC latitudes, the observed oceanic signals are dominated by intraseasonal mesoscale eddy variations. The source of the eddy variability is likely the baroclinic instability of the vertically-sheared NEC and STCC (Subtropical Countercurrent) system (Qiu, 1999: Roemmich and Gilson, 2001). As a consequence of the enhanced mesoscale eddy variability, the formation of the upstream Kuroshio is much less well-defined than that of the upstream Mindanao Current. Indeed, a relevant theoretical framework is needed that allows us to understand how the upstream Kuroshio forms and to predict the regional circulation variability in the NEC bifurcation region. These issues suggest the following scientific questions for focusing the proposed research program: 1. Rather than an inertial laminar WBC, should we consider the upstream Kuroshio as an eddy-driven, turbulent, confluence flow? 2. Do the incoming eddies interact to drive the time-mean boundary currents or to affect regional water mass properties? 3. Why is the MC apparently much more steady that the Kuroshio at similar distance from the bifurcation region? 4. Does the Luzon Strait opening impact Kuroshio structure either downstream or upstream. 5. How is potential vorticity conserved from the NEC, through the bifurcation region, and 8

upon establishment of the Kuroshio and MC. 6. What is the fate of the incoming eddies and anomalies: Do they transmit southward in form of Kelvin waves, or northward via mean flow advection, or westward into the SCS through the Luzon Strait?

Given a programmatic goal of applying new understanding of the NEC-MC-Kuroshio system to improve predictability, two additional questions provide integrative metrics of success: 7. Given observations of oceanic forcing to the east in the form of the NEC and westward propagating eddies, can numerical models predict fluxes in the MC and Kuroshio? 8. Can the program’s results suggest a design for an observational and predictive system?

Implementation

The objectives of this program include quantifying flows and water properties, improving understanding of the dynamics of a bifurcation region, and establishing predictability of the three major currents in the region. The observational approach will have two major thrusts: (1) quantifying the fluxes of mass, heat, and salt in the NEC, Kuroshio, and MC, and (2) establishing Lagrangian patterns of flow. To quantify the seasonal cycle and to obtain an initial measure of

Figure 4. Map of region including OKMC and other planned projects. Locations of observational components are sketched in color lines and boxes: glider lines (black), mooring arrays (red), float deployments (green), drifter deployments (yellow). Other planned projects include Taiwanese moorings (blue), IWISE (brown), and Typhoon Impact DRI/ITOP (light blue). 9 interannual variability, these observations will be sustained over a three-year period. The bifurcation region is an interesting target, but the stagnation point of a turbulent flow is not an easy quantity to observe. The sustained observations will provide a test for models of the regions, and at the same time will be available for assimilation in models.

The proposed observing system employs a suite of complementary platforms to meet the challenges posed by this vast, highly variable study area. Guided by previous studies and by directed analysis of historical data, long-endurance autonomous gliders will be tasked to collect repeat occupations of key sections across the NEC, MC and Kuroshio. Because previous observational programs show that the Kuroshio sometimes reaches nearly to the coast, where glider operations can be difficult and risky, small arrays of moored instruments will augment glider sections to resolve the nearshore regions. Drifters and floats will be used to illuminate the pathways by which the NEC ultimately forms the Kuroshio and MC. Numerical efforts will aid interpretation and explore the predictive capabilities of regional models.

Historical data analysis (Niiler, Centurioni, Lee)

Analysis of historical data will pave the way for the observational program. The combination of satellite sea surface height and drifter data yields a comprehensive surface topography. Subsurface observations include data available from NODC and Taiwan. Analysis completed during the first year will guide observations to follow.

Figure 5. Salinity (shading) and potential density (contours, 0.25 kg/m3 interval) sections crossing the Kuroshio through the Luzon Strait. The shallow salinity maximum includes water of southern origin. The western limit of the maximum marks the edge of the Kuroshio. The salinity minimum near 500 dbar is reminiscent of North Pacific Intermediate Water. The patchy structure in this minimum is indicative of stirring by mesoscale eddies. 10

Gliders (Rudnick, Lee)

Fluxes will be quantified using gliders at strategic locations (Figure 4). These locations are chosen because the currents are well established, and to define the eastern boundary conditions of the NEC. Locations along the western boundary are in the MC at about 8°N, at the northern tip of Luzon where the Kuroshio enters the Luzon Strait, at the southern tip of Taiwan where the Kuroshio exits the South China Sea, and off the east coast of Taiwan where the Kuroshio is well established. A glider line at 135°E defines the eastern boundary of the study region. Gliders will cycle from the surface to 1000 m, and will measure velocity, temperature, salinity, and optical water properties. Some recent glider sections show that autonomous observation of the Kuroshio is practical (Figure 5).

Moorings (Sanford, Lien, Jayne)

Moorings will complement gliders at some lines, with an emphasis on shallower regions with strong velocities. The Kuroshio off of Taiwan is expected to be covered by moorings set by Taiwanese scientists. The first priority for US moorings is the southern Luzon Strait. The next priority is a line near 8°N across the Mindanao Current. If resources are available, a line in the Ilan strait would complete the moored observations. Moorings will measure velocity, temperature, and salinity, and may include Pressure Inverted Echo Sounders (PIES).

Drifters (Centurioni, Niiler)

The Lagrangian component of the experiment will focus on identifying the pathways and patterns of flow from the NEC to the fully formed Kuroshio and MC. Drifters drogued at 15 m will be released in a broad region spanning the bifurcation region from the coast of the Philippines to 135°E. The best deployment option is from ships, especially considering the research vessel activity in the area. If an adequate deployment plan from ship is not possible, air deployments are possible.

Floats (Sanford, Lien, Qiu, Rudnick)

Profiling floats will be deployed in a band just west of 135°E. The floats, profiling from the surface to 500-1000 m, will provide displacements at depth and hydrographic measurements along their paths. As with drifters, ship deployments are the preferred mode, but air is possible. The floats and drifters, combined with satellite altimetry will allow a comprehensive description of circulation in the area.

Modeling (McClean, Cornuelle)

The combination of observations will prove a fertile test bed for studying the value and limitations of regional numerical models. Predictability experiments may involve using or withholding data from assimilating models, and comparing metrics such as fluxes and the partitioning of flow into the Kuroshio and MC. Patterns of variability from Lagrangian measurements are another target for prediction. CCSM (fine resolution), HYCOM (1/12 degree) results are available for analysis.

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Linkages

Taiwanese investigators have proposed a 3-year Kuroshio study with focus on the region between Ludao Island off the west coast of Taiwan and Ilan Ridge. The study area may be extended to south of Ludao if resources become available. Three mooring arrays are planned extending west, north, and east from Ludao. Each array will have ~5 subsurface ADCP moorings. One land-based radar on Ludao will monitor surface waves. Shipboard ADCP survey is also proposed. A zonal mooring array south of Ilan ridge, ~24 oN, may be implemented in 2010-2011, depending on the funding support. The West and North mooring arrays will be deployed in 2009, and the East mooring array in 2010. The potential Taiwanese mooring lines are colored in blue in Figure 4.

ONR-sponsored programs planned for the region in the same time frame include the Internal Wave in Straits Experiment (IWISE), the ONR Typhoon Impacts DRI and the Taiwanese Integrated Typhoon-Ocean Program (ITOP). The observations proposed here will provide a large scale context to IWISE and the two typhoon programs. Intense typhoon systems exert significant impact on the ocean variability in the Western Pacific. The combined data sets could be exploited to understand the impacts of typhoon forcing on NEC-MC-KC evolution.

References

Centurioni, L. R., P. P. Niiler, and D. K. Lee, 2004: Observations of inflow of Philippine Sea surface water into the South China Sea through the Luzon Strait. J. Phys. Oceanogr., 34, 113- 121.

Chern, C. S. and J. Wang, 1998: The spreading of South China Sea water to the east of Taiwan during summertime. Acta Oceanographica Taiwanica, 32, 97-109.

Farris, A. and M. Wimbush, 1996: Wind-induced Kuroshio intrusion into the South China Sea. J. Oceanogr., 52, 771-784.

Gilson, J. and D. Roemmich, 2002: Mean and temporal variability in Kuroshio geostrophic transport south of Taiwan (1993-2001). J. Oceanogr., 58, 183-195.

Hu, D. X., M. C. Cui, T. D. Qu, and Y. X. Li, 1991: A subsurface northward current off Mindanao identified by dynamic calculation. Oceanography of Asian Marginal Seas, K. Takano, Ed., 359-365.

Johns, W. E., T. N. Lee, D. X. Zhang, R. Zantopp, C. T. Liu, and Y. Yang, 2001: The Kuroshio east of Taiwan: Moored transport observations from the WOCE PCM-1 array. J. Phys. Oceanogr., 31, 1031-1053.

Kashino, Y., A. Ishida, and Y. Kuroda, 2005: Variability of the Mindanao Current: Mooring observation results. Geophys. Res. Lett., 32, -. 12

Kim, Y. Y., T. D. Qu, T. Jensen, T. Miyama, H. Mitsudera, H. W. Kang, and A. Ishida, 2004: Seasonal and interannual variations of the North Equatorial Current bifurcation in a high- resolution OGCM. Journal of Geophysical Research-Oceans, 109, -.

Metzger, E. J. and H. E. Hurlburt, 2001: The nondeterministic nature of Kuroshio penetration and eddy shedding in the South China Sea. J. Phys. Oceanogr., 31, 1712-1732.

Nitani, H., 1972: Beginning of the Kuroshio. Kuroshio: Its Physical Aspects, H. Stommel and K. Yoshida, Eds., University of Tokyo Press, 129-163.

Qiu, B., 1999: Seasonal eddy field modulation of the North Pacific subtropical countercurrent: TOPEX/Poseidon observations and theory. J. Phys. Oceanogr., 29, 2471-2486.

Qiu, B. and R. Lukas, 1996: Seasonal and interannual variability of the North Equatorial Current, the Mindanao Current, and the Kuroshio along the Pacific western boundary. Journal of Geophysical Research-Oceans, 101, 12315-12330.

Qu, T., H. Mitsudera, and T. Yamagata, 1998: On the western boundary current in the Philippine Sea. J. Geophys. Res., 103, 7537-7548.

Qu, T. D. and R. Lukas, 2003: The bifurcation of the North Equatorial Current in the Pacific. J. Phys. Oceanogr., 33, 5-18.

Roemmich, D. and J. Gilson, 2001: Eddy transport of heat and thermocline waters in the North Pacific: A key to interannual/decadal climate variability? J. Phys. Oceanogr., 31, 675-687.

Sheremet, V. A., 2001: Hysteresis of a western boundary current leaping across a gap. J. Phys. Oceanogr., 31, 1247-1259.

Toole, J. M., R. C. Millard, Z. Wang, and S. Pu, 1990: Observations of the Pacific North Equatorial Current Bifurcation at the Philippine Coast. J. Phys. Oceanogr., 20, 307-318.

Wang, J. and C. S. Chern, 1987: Warm core eddy in the northern South China Sea, Pt. 2, Simple mechanism for the establishment and development of the warm core eddy. Acta Oceanographica Taiwanica, 18, 104-113.

Wijffels, S., E. Firing, and J. Toole, 1995: The Mean Structure and Variability of the Mindanao Current at 8-Degrees-N. Journal of Geophysical Research-Oceans, 100, 18421-18435.

Yaremchuk, M. and T. D. Qu, 2004: Seasonal variability of the large-scale currents near the coast of the Philippines. J. Phys. Oceanogr., 34, 844-855.

Zhang, D. X., T. N. Lee, W. E. Johns, C. T. Liu, and R. Zantopp, 2001: The Kuroshio east of Taiwan: Modes of variability and relationship to interior ocean mesoscale eddies. J. Phys. Oceanogr., 31, 1054-1074.