Identification of different types of Kuroshio intrusioninto the South China Sea

Feng Nan & Huijie Xue & Fei Chai & Lei Shi &Maochong Shi & Peifang Guo

Received: 16 August 2010 /Accepted: 14 April 2011# Springer-Verlag 2011

Abstract Kuroshio intrusion into the South China Sea(SCS) has different forms. In this study, a Kuroshio SCSIndex (KSI) is defined using the integral of geostrophicvorticity from 118° to 121° E and from 19° to 23° N. Threetypical paths (the looping path, the leaking path, and theleaping path) were identified based on the KSI derived fromthe weekly satellite Absolute Dynamic Topography from1993 to 2008. The KSI has a near normal distribution.Using ±1 standard deviation (σ) as the thresholds, theleaking path is the most frequent form with the probabilityof occurrence at 68.2%, while the probabilities of occur-rence for the looping path and the leaping path are 16.4%and 15.4%, respectively. Similar analysis is also conductedon the daily Hybrid Coordinate Ocean Model (HYCOM)Global Analysis from 2004 to 2008. The results aregenerally consistent with the KSI analysis of the satellitedata. The HYCOM data are further analyzed to illustratepatterns of inflows/outflows and the maximum/minimumsalinity as representatives of the subsurface/intermediatewaters. The Kuroshio bending and the net inflow throughthe Luzon Strait reduce from the looping path to the leakingpath to the leaping path. However, the Kuroshio subsurfacewater intrudes farthest into the SCS for the leaking path.

Vorticity budget associated with the different intrusiontypes is then analyzed. The tilting of the relative vorticity,the stretching of the absolute vorticity, and the advection ofplanetary vorticity are important for the change of vorticity,whereas the baroclinic and frictional contributions are threeorders smaller.

Keywords South China Sea . Kuroshio intrusion .

Vorticity . Current loop

1 Introduction

The South China Sea (SCS) is the largest semi-enclosedmarginal sea in the northwest Pacific, connecting with theEast China Sea, Pacific, Sulu Sea, and Java Sea via the TaiwanStrait, Luzon Strait (LS), Mindoro and Balabac Strait, andKarimata Strait, respectively. Among the five passages, LS isthe deepest (∼2,500 m) and the main water exchange passagebetween the SCS and the western Pacific. It is about 360 km inwidth and consists of three narrow passages (Bashi Channel,Balintang Channel, and Babuyan Channel) separated bymany small islands in the strait (Fig. 1).

The Kuroshio with high temperature and salinity is themost important western boundary current in the NorthPacific. It flows northward along the east Philippine coast.When passing by the LS, a branch of the Kuroshio flowsnorthwestward into the SCS (e.g., Liang et al. 2003, 2008;Yuan et al. 2008) mainly through the Balintang Channel.Most of the Kuroshio water flows out of the SCSsubsequently through the Bashi Channel, but some waterintrudes into the SCS. The latter affects the temperature,salinity, circulation, and eddy generation in the northeasternSCS (e.g., Li et al. 1998; Xu and Su 2000; Wu and Chiang2007; Xiu et al. 2010).

Responsible Editor: Hua Wang

This article is part of the Topical Collection on 2nd InternationalWorkshop on Modelling the Ocean 2010

F. Nan (*) :H. Xue : F. Chai : L. ShiSchool of Marine Sciences, University of Maine,Orono, ME, USAe-mail: Feng_Nan@umit.maine.edu

F. Nan :M. Shi : P. GuoCollege of Physical and Environmental Oceanography,Ocean University of China,Qingdao, China

Ocean DynamicsDOI 10.1007/s10236-011-0426-3

Much work has been done on the Kuroshio intrusion,and some characteristics have been illustrated. TheKuroshio intrusion has a seasonal pattern with theintrusion being stronger in winter than in summer(Wyrtki 1961; Shaw 1991). The surface Kuroshio watercan intrude deep into the SCS especially in winter(Centurioni et al. 2004). In the LS, eastward and westwardflows appear alternately (e.g., Nitani 1972; Xu et al. 2004;Zhou et al. 2009). Estimates of the transport through theLS vary from a few Sv to more than 10 Sv (e.g., Xu andSu 2000; Giloson and Roemmich 2002; Qu et al. 2006;Tian et al. 2006; Yuan et al. 2008).

It is still a debated issue on how the Kuroshio intrudesinto the SCS. Based on the float measured currents andhistorical observations, Qiu et al. (1984) demonstrated thatin the northern part of the SCS, there exists a westwardcurrent on the continental slope with relatively high speedand steady direction. They speculated that the current is abranch of the Kuroshio and called it the South China SeaBranch of Kuroshio (SCSBK). Li and Wu (1989) suggestedthat there is a “Kuroshio Current Loop (KCL)” in the SCSand the loop can extend to 116–117° E. Yuan et al. (2006)analyzed satellite ocean color, sea surface temperature, andaltimeter data and demonstrated that the anticyclonicintrusion of the Kuroshio is a transient phenomenon ratherthan a persistent circulation pattern in the LS area. Carusoet al. (2006) depicted five different types of Kuroshiointrusion into the SCS, including a small anticyclonic bendin the LS, the SCSBK, the KCL, a detached anticycloniceddy, and a cyclonic loop northwest of the LS.

The KCL was reproduced in several models (e.g.,Farris and Wimbush 1996; Chern and Wang 1998;Sheremet 2001; Jia and Liu 2004; Xue et al. 2004; Wuand Chiang 2007; Chern et al. 2010; Sheu et al. 2010).Using a single-layer depth-averaged approach, Sheremet(2001) formulated an idealized model of a westernboundary current encountering a gap in a ridge. Multipleflow patterns (leaping the gap or penetrating the gap) existin such system, which were explained by variations in thebalance between the inertia and the β effect. Laboratoryexperiments of the gap-leaping western boundary currentwere conducted by Sheremet and Kuehl (2007) and Kuehland Sheremet (2009), and the results again showedmultiple flow patterns depending on past flow states. Theauthors also noted that the idealized model and thelaboratory experiments lack aspects of realism includingbathymetry, stratification, and mesoscale disturbances. Onthe other hand, several comprehensive models simulatedthe Kuroshio flowing by the LS in the presence ofcomplex bathymetry, seasonally evolving stratificationand wind forcing, as well as mesoscale eddies. The modelof Xue et al. (2004) depicted both the KCL and theSCSBK, and following a simplified vorticity balanceequation, Xue et al. (2004) also suggested that theoccurrence of the KCL or SCSBK depends on the speed,angle, and position of the intruding Kuroshio in the LS.The model of Wu and Chiang (2007) showed that theKuroshio tends to loop into the SCS more often in winter,while it tends to leap across the LS more often in summer.Sheu et al. (2010) concluded that these two distinct paths

Fig. 1 Topography in the vicin-ity of the LS and the sketchof three Kuroshio paths. Thedotted line, the gray solid line,and the black solid line repre-sent the looping path, the leak-ing path, and the leaping path,respectively

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of the Kuroshio are determined by the Kuroshio transportand the potential vorticity distribution.

In general, the Kuroshio paths discussed in the abovestudies have been descriptive and schematic. The purposeof this paper is to define an index that can be used todistinguish different types of Kuroshio intrusion quantita-tively. We decide that the index should be derived based onreadily available observations (e.g., satellite remote sensingdata) or credible ocean model data. Furthermore, thedefinition should be simple to use and can be applied tomultiple datasets consistently. Such index can then be usedto categorize the Kuroshio paths, which will then becomethe basis to address such questions as: how often dodifferent paths occur, how does the path change from onetype to another, and what is the cause?

The organization of this paper is as follows. Section 2describes the satellite and numerical model data as well asthe definition of an index for indentifying different types ofKuroshio intrusion into the SCS. Section 3 illustrates theresults of applying the index to the satellite and model data.Sensitivities to the threshold used to distinguish betweenthree paths (the looping path, the leaking path, and theleaping path) are discussed. Section 4 discusses thevorticity budget associated with the different types ofKuroshio intrusion. Finally, Section 5 summarizes thefindings and discusses their implications.

2 Data and methodology

2.1 Satellite and model data

The Absolute Dynamic Topography (ADT) data used inthis paper are produced by the French Archiving, Valida-tion, and Interpolation of Satellite Oceanographic (AVISO)data project. The merged data from the combination ofJason, Topex/Poseidon, Envisat, GFO, ERS, and Geosataltimeters (Dibarboure et al. 2010) are interpolated onto aglobal grid of 1/4° resolution and are archived in weeklyaveraged frames. The dataset covers the period fromOctober 1992 to present, while in this study, the data from1993 to 2008 are used. Although both tidal and sea levelpressure corrections are incorporated, the ADT data in shelfareas are still contaminated by aliases from tides andinternal waves (Yuan et al. 2006). Following Yuan et al.(2006), the data in areas where the water depth is less than200 m are excluded.

The Hybrid Coordinate Ocean Model (HYCOM)+NavyCoupled Ocean Data Assimilation (NCODA) Global 1/12°Analysis data are available for the period from November2003 to present at http://www.hycom.org/dataserver/glb-analysis. The horizontal dimensions of the global gridinclude 4,500×3,298 grid points resulting in ∼7 km spacing

on average. There are 32 vertical layers. Bathymetry isderived from the quality controlled DBDB2 dataset.Surface forcing is from the Navy Operational GlobalAtmospheric Prediction System that includes wind stress,heat flux, and precipitation. NCODA uses the modelforecast as a first guess in a Multivariate OptimalInterpolation scheme and assimilates available satellitealtimeter observations, satellite, and in situ sea surfacetemperature (SST) as well as in situ vertical temperatureand salinity profiles from Expendable Bathythermographs,ARGO floats, and moored buoys. Daily output is patchedfrom multiple runs. The legacy experiments contain threesegments, 11/03–12/06, 01/07–04/07, and 04/07–09/08,while the current experiments contain two segments, 09/08–05/09 and 05/09–present. Although there is no obviousdiscontinuity in the surface elevation, the subsurfacesalinity maximum jumps between the legacy experimentsand the current experiments (not shown). Hence, this studyuses only the output between 2004 and 2008.

2.2 Definition of the Kuroshio SCS index

Long-term and high-resolution sea surface informationfrom satellite is readily available. As the SCS water warmssignificantly in summer, it decreases the temperaturedifference between the Kuroshio and the SCS surfacewater, making it difficult to distinguish the two waters(Farris and Wimbush 1996). SST is thus not a goodindicator to distinguish the Kuroshio water from the SCSwater. It is also difficult to identify the Kurishio water andthe SCS water based on the SSH difference quantitatively.Based on previous studies (see Section 1) and our analysisof the geostrophic velocity derived from the weekly satelliteADT maps, the looping path, the leaking path, and theleaping path are the three distinctive forms of the Kuroshiointrusion into the South China Sea through the LS. Thelooping path is characterized with a strong anticycloniccirculation southwest of the Taiwan Island, while theleaping path is characterized with a strong cycloniccirculation west of the LS. The leaking path is anintermediate situation but a different path. The three pathswill be distinguished below in Section 3.1.

In this study, an areal integrated geostrophic vorticity,defined as the following,

KSI ¼ W � g=fð Þr2h� �

dA ð1Þ

is used as the KSI to differentiate Kuroshio paths in the LSand northern SCS. Here, η is the ADT or SSH; g is thegravity acceleration; and f is the Coriolis parameter.Stronger anticyclonic currents correspond to larger negativeKSI, while stronger cyclonic currents correspond to largerpositive KSI. By virtue of Green’s theorem, the KSI is

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equivalent to the velocity circulation along the contourbounding this area, and it could vary with the position ofthe contour, which must be chosen to best reflect the flowfeatures of interest. We inspected all the weekly geostrophiccurrent maps. The mean axis of the Kuroshio in the LS islocated at ∼121° E, and the KCLs are located southwest ofTaiwan almost always in the box from 118° to 121° E andfrom 19° to 23°. We did a number of trial calculations withdifferent areas of integration by moving the southernboundary between 18.5 and 19.5° N, the western boundarybetween 117.5 and 118.5° E, and the eastern boundarybetween 120.5 and 121.5° E (figures not shown). Althoughthere are small differences in KSI values by changing therange of the box, the impact on the separation of the paths(based on the magnitude and duration of peak/trough KSIvalues, see below) is insignificant. The area integral ofgeostrophic vorticity in the box 118–121° E, 19–23° N(referred to as the KSI box hereafter) is chosen as it resultsin clearly discernable Kuroshio paths in the northeasternSCS (see below).

3 Results

3.1 Types of the Kuroshio intrusion

The KSI derived from the weekly satellite ADT is shown inFig. 2 for the period from 1993 to 2008. It is mostlypositive with a mean (μ) of 1.18×105 m2 s−1 (the dash-dotted line) and standard deviation (σ) of 0.95×105 m2 s−1

(the dashed lines). Based on its variation, three categoriesare distinguished with values greater than μ+σ (bluepoints), less than μ−σ (red points) and between μ±σ(green points). Figure 3 shows the mean ADT andgeostrophic currents by averaging the weekly mapscorresponding to these three categories. The mean state ofall red points (Fig. 3a) shows that the Kuroshio water entersthe SCS in the middle and outflows in the northern part ofthe LS. It forms the KCL southwest of the Taiwan Island.Anticyclonic eddies may be shed from the current loop asobserved by Li et al. (1998). This category is defined as the“looping path” of the Kuroshio. The mean state of all greenpoints (Fig. 3b) shows that when passing by the LS, the

Kuroshio bends anticyclonically in the LS, and a portion ofthe Kuroshio water leaks into the SCS. A cyclonic gyre(Luzon Cyclonic Gyre) appears northwestern of the LuzonIsland. This category is defined as the “leaking path” of theKuroshio. The mean state of all blue points (Fig. 3c) showsthat the Luzon Cyclonic Gyre becomes stronger to the westof the LS, and the main body of the Kuroshio flows acrossthe LS and continues northward along the east coast ofTaiwan. This category is defined as the “leaping path” ofthe Kuroshio.

The different patterns associated with the three pathsseen in Fig. 3 suggest a dynamical interpretation of the KSIas follows. When the Kuroshio loops into the SCS, thecurrent is anticyclonic southwest of the Taiwan Island, andthe geostophic vorticity should be negative. When theLuzon Cyclonic Gyre becomes stronger, the current isstrongly cyclonic (i.e., larger positive vorticity) west of theLS. The Luzon Cyclonic Gyre appears to impede theKuroshio from entering the SCS. As a result, the main bodyof the Kuroshio leaps across the LS. When the LuzonCyclonic Gyre is weaker, more Kuroshio water enters intothe SCS, which is defined as the leaking path.

The KSI has a near normal distribution: at ±σ, theprobability of occurrence is 16.4% for category 1, 68.2%for category 2, and 15.4% for category 3 (Fig. 4a). Theprobability is almost the same for categories 1 and 3,decreasing from 32% at 0.5σ to 7% at 1.5σ, while theprobability for category 2 increases from 36% at 0.5σ to86% at 1.5σ. To test the sensitivity of division to the σthreshold, the areal integral of the squared geostrophicvorticity difference

R R ðzs 0 � zsÞ2dA� �

is compared withR R ðzsÞ2dA� �

for the three categories, respectively(Fig. 4b). Here, ζσ represents the geostrophic vorticity ofthe mean states defined using the threshold ±σ, while zs 0 issimilar to zs but with σ′ changing from 0.5σ to 1.5σ. Thevariations are small: 0–27% for category 1, 0–1% forcategory 2, and 0–10% for category 3. Between 0.9σ and1.1σ, the variations are less than 1.5% for all the threecategories. Compared with the three mean states shown inFig. 3, the mean states of the three categories separated usingthe threshold ±0.9σ or ±1.1σ have no obvious difference.However, the differences are significant with the leakingpath mixed in the looping and leaping paths at ±0.5σ

Fig. 2 Time series of theweekly KSI (unit: square metersper second) derived from thesatellite ADT in the periodfrom January 1993 to December2008. The dash-dotted linerepresents the mean, while thedashed lines represent ±σ

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or ±1.5σ. It is thus decided on ±σ as the divisions for thethree categories.

Another interesting aspect is the seasonal and inter-annual variations of the occurrence for the three categories.Figure 5a shows the monthly occurrence of the threecategories averaged from 1993 to 2008. Figure 5b is similarto Fig. 5a but for yearly occurrence from 1993 to 2008. Theleaking path is the dominant form with the occurrence atmore than 60% except in February and in 1994 and 1995.In general, the leaking path occurs more often in the secondhalf of the year, while the leaping path appears more in thefirst half of the year. The looping path is least frequent from

March to June. Either the looping path or the leaping path isno more than 25% in any given month. For the loopingpath, it is more frequent before 2001 except during thestrong El Niño in 1997∼1998. It is most frequent (>30%)right before (1996) and right after (1999 and 2000) the ElNiño years. For the leaking path, it is more frequent (>25%)in 2002 and 2005 and less frequent from 1996 to 2000.

3.2 Applying the KSI to the HYCOM global analysis

The daily KSI derived from the HYCOM predicted SSH inthe northeastern SCS is shown in Fig. 6 for the period from

Fig. 3 The mean ADT (unit:centimeters) and thecorresponding surfacegeostrophic currents associatedwith the three types of Kuroshiointrusion: the looping path(a), the leaking path (b), and theleaping path (c)

Ocean Dynamics

2004 to 2008. Since the HYCOM assimilates satellitealtimeter observations, the KSI variation (Fig. 6) is generallyconsistent with the one derived from the satellite ADT (seethe ending portion of Fig. 3), and the division of threecategories also corresponds well. The probability of occur-rence (not shown) for category 1 is 15.6%, a little lower thanthe result derived directly from the satellite ADT, while theprobability of occurrence for category 3 is 16.1%, a littlehigher. Similarly, the mean SSH and geostrophic currents

corresponding to these three categories are obtained byaveraging the daily maps accordingly, and they are shown inFig. 7. The transition of patterns from the looping to theleaking then to the leaping path is consistent to those derivedfrom the satellite ADT (Fig. 3) despite the fact that there arequantitative differences in both the inflows to and theoutflows from the SCS, part of which can perhaps beattributed to different resolutions and durations between thesatellite ADT and the HYCOM Global Analysis.

Fig. 4 a The percentage ofoccurrence as functions of thethreshold between 0.5σ and 1.5σfor the looping path (red), theleaking path (green), and theleaping path (blue). b Similarto (a) but for the ratio betweenthe areal integral of the squaredgeostrophic vorticity differenceand the areal integral of thesquared geostrophic vorticityat ±σ

Fig. 5 a Monthly probability ofoccurrence for each of the threeKuroshio paths averaged for theperiod from 1993 to 2008. RedThe looping path, green theleaking path, and blue the leap-ing path. b Similar to (a) but forthe yearly probability of occur-rence from 1993 to 2008

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It should not be a surprise that the KSI and the meansurface state associated with different types of Kuroshiointrusion derived from the HYCOM Global Analysis are

consistent with those derived from the satellite ADT asthe HYCOM assimilates the satellite data. The HYCOMGlobal Analysis, however, contains information from the

Fig. 6 Similar to Fig. 3 but forthe daily KSI derived fromthe HYCOM Global Analysisfrom 1 January 2004 to 31December 2008

Fig. 7 a–c Similar to Fig. 4 butfor the mean sea surface eleva-tion and the surface geostrophiccurrents derived from theHYCOM Global Analysisbetween 1 January 2004 and 31December 2008

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surface to the bottom and from other variables, whichcan be analyzed further to illustrate contrasts in otherflow characteristics.

3.3 More flow characteristics associatedwith the different Kuroshio paths

According to Sheremet (2001) and Xue et al. (2004), thebalance between the inertial and β effects controls theintrusion patterns; flow structures in the LS are firstcompared among the three different paths. Figure 8 showsthe mean velocity on meridional cross-sections at 120.5° Ein the LS. The flow patterns corresponding to the threeKuroshio paths are clearly different. The looping path isassociated (Fig. 8a) with the Kuroshio flowing into the SCSin the middle part of the LS and flowing out in the northernpart of the LS. The inflows of the leaking path (Fig. 8b) andthe leaping path (Fig. 8c) are much weaker than that of thelooping path (45 cm s−1) with the maximum velocity of 29and 24 cm s−1, respectively. The decrease of Kuroshioinflow from the looping to the leaking to the leaping pathresults in a corresponding decrease in the westwardtransport through the section from 19 to 15 to 14 Sv. Theoutflow of the leaking path is weaker with maximumvelocity less than 10 cm s−1, while the outflow of theleaping path in the northern part of the LS disappears.Outflows of the SCS water occur in the southern part of theLS as well as below the Kuroshio inflow in the middle ofthe LS. These outflows have lower salinity, ≤34.65 (notshown). The outflow of the SCS waters of the leaping pathbecomes stronger than the outflow of the leaking path dueto the stronger Luzon Cyclonic Gyre. Though very weak,the flow is again westward right next to the Luzon Island.Overall, the net transport of the three paths is different,which varies from 8 Sv for the looping and leaking paths to5 Sv for the leaping path. Furthermore, there exist seasonaland inter-annual variations of the occurrence for the threepaths (Fig. 5), which may be one reason that the observedtransport through the LS in different seasons or in the sameseason of different years is greatly different (e.g., Xu andSu 2000; Giloson and Roemmich 2002; Tian et al. 2006;Yuan et al. 2008; Zhou et al. 2009).

The maximum and minimum salinity of the subsurfaceand intermediate waters are good tracers to delineate theKuroshio and SCS waters since the maximum (minimum)salinity of the Kuroshio water is notably higher (lower) thanthose of the SCS water. The high salinity subsurfaceKuroshio water often appears in the interior SCS especiallyalong the northern shelf (Qu et al. 2000; Xu and Su 2000;Li et al. 2002). The maximum (minimum) salinity at alllocations are selected from the vertical profiles and shownin the left (right) panels of Fig. 9. The maximum salinity ofthe subsurface water in the Pacific is ∼34.90 at ∼200 m

depth while it is less than 34.70 at ∼150 m depth in theSCS. When the Kuroshio enters the SCS, the maximumsalinity of the subsurface water decreases, but it is stillhigher than that of the SCS water. For the looping path

Fig. 8 Cross-sectional distributions of the zonal velocity (unit: metersper second) at 120.5° E. Negative (positive) values represent westward(eastward) currents. a The looping path, b the leaking path, c theleaping path

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(Fig. 9a), the higher salinity water is mostly in thenortheastern corner of the SCS, which is consistent withthe current loop. The saline Kuroshio water also extendsinto the interior SCS along the northern slope. The 34.70isohaline reaches about 115° E. An anticyclonic eddy shedfrom the current loop was observed in September 1994 (Liet al. 1998). The maximum salinity at the center of thiseddy was 34.81, similar to the salinity in the current loopnear the LS (Fig. 9a). For the leaking path (the Fig. 9c) andthe leaping path (Fig. 9e), the area of higher salinitysouthwest of Taiwan is smaller especially for the latter. Thewestward intrusion of the saline Kuroshio water occursagain along the northern slope in both cases, and the 34.70isohaline reaches ∼112° and 116° E past the Xisha Atoll,respectively. Salty water from the Kuroshio with salinityhigher than 34.80 was observed along the northern slopein the September 1994 (Li et al. 1998) and in June/July1998 (Li et al. 2002). However, salty water did not pass119.5° E in November/December 1998 (Li et al. 2002),which may correspond with a leaping path.

The patterns are somewhat different for the intermediatelayer (the right panels in Fig. 9). The minimum salinity ofthe intermediate water in the Pacific is ∼34.25 at ∼550 mdepth and ∼34.45 at ∼500 m depth in the SCS. The

Kuroshio has an anticyclonic bending in the middle of theLS and the bending reduces from the looping path to theleaking path to the leaping path. It can be seen from Fig. 8that the current gets weaker in or below the intermediatelayer (∼500 m) than the subsurface layer (∼200 m).Correspondingly, the westward intrusion of the intermediatewater is more limited, which is consistent with the result ofQu et al. (2000). According to Chen and Huang (1996),there exists a “mid-depth front” near 122° E between 350and 1,350 m separating the SCS water from the Pacificwater. The intermediate water cannot easily flow into theSCS due to the shallower water depth (∼500 m) in the LS(120.25° E, 21° N; Fig. 1), which inhibits the formation ofthe current loop in the intermediate layers.

4 Vorticity budget associated with the three Kuroshiopaths

Based on the geostrophic vorticity, the KSI is defined andthree different Kuroshio paths in the northeastern SCS areidentified. As well, the three paths have distinct hydro-graphical characteristics. In this section, the vorticitybudget is diagnosed for each of the three types. The

Fig. 9 Subsurface salinity maximum (left panels) and intermediate salinity minimum (right panels) associated with the looping path of theKuroshio (a, b); the leaking path (c, d); and the leaping path (e, f)

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vorticity equation can be obtained by taking the curl of themomentum equation.

@z@t ¼ �ðu @z

@x þ v @z@yÞ � z þ fð Þr �~u�v @f

@y þ gr2

@r@x

@@y

R 0z rdz� @r

@y@@x

R 0z rdz

� �þ n @2z

@z2

A1 A2 B C D Eð2Þ

Here, ζ is the relative vorticity, f the planetary vorticity, ρthe density, p the pressure, and ν the kinematic viscosity setto 1.0×10−4 m2 s−1 (Wallcraft et al. 2009). The left-handside represents the rate of change of vorticity. The first twoterms on the right represent the tilting of the relativevorticity, which consists of the zonal (Term A1) andmeridional (Term A2) advection of the vorticity. Term Bmeasures the stretching of the absolute vorticity; Term C

the advection of planetary vorticity; Term D the barocliniccontribution to the change of vorticity; and Term E thediffusion of the vorticity.

All these terms are calculated using the HYCOM GlobalAnalysis. Figure 10 shows their distribution at 200 m depth.The three Kuroshio paths can be seen from distributions ofA1, A2, and C in the LS. The Kuroshio bending of thelooping path is in the middle of the LS, but in the northern

Fig. 10 Right-hand side terms of Eq. (2) at 200 m depth associated with the looping path (left), the leaking path (middle), and the leaping path(right)

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part of the LS for the leaking path. The Kuroshio bendingof the leaping path is the smallest. Terms A1, A2, and B areof the highest order, which would imply the importance ofnonlinearity. However, Terms A1 and A2 tend to canceleach other, and the sum is actually the same order as TermC. The contribution of stretching (Term B) comes largelyfrom the planetary vorticity as f is ∼2.5 times the relativevorticity. Overall, Term B is large near the islands due tostrong convergence and divergence that also dictate thenoisiness of this term. However, these large values ofconvergence and divergence might be artifacts of interpo-lating the HYCOM result from its native grid to thestandard depths, which tends to affect most near islands.Term C clearly shows the northward Kuroshio and thesouth(west)ward flows on the northern slope as the changesof β are small in this area. Terms D and E are three orderssmaller than the other terms; thus, the baroclinic andfrictional contributions are small. Terms E is again largernear the islands as Term B.

To show how the vorticity budget varies with depth, allthe terms on the right-hand side of Eq. (2) are integrated in

the KSI box, and these profiles are shown in Fig. 11 for thethree paths, respectively. The differences are obvious onlyin Terms A1, A2, and B. Again, A1 and A2 are mostlyopposite in sign. In particular, Terms A1 and A2 tend tocancel each other for the looping path. Most terms becomevery small below 1,000 m except for Term B due to largevalues near sidewalls of islands. The baroclinic term (TermD) has opposite signs above and below 900 m, but it isagain three orders smaller than the tilting and stretchingterms, so is the frictional term (Terms E).

The sum of all right-hand side terms is then integratedvertically from the surface to 1,000 m depth (left panels inFig. 12), equivalent to the rate of change of the integratedrelative vorticity according to Eq. (2). There are nownotable differences among the three paths especially in theKSI box from 118–121° E, 19–23° N, where the rate ofchange tends to have opposite signs between the loopingpath and the leaping path. For the leaking path, the patternis similar to that of the looping path in the LS, but it issimilar to that of the leaping path west of the LS albeit withsmaller magnitudes. It is also interesting when comparing

Fig. 11 Profiles of the terms in Eq. (2) averaged in the box (118–121° E, 19–23° N) from 0 to 2,000 m. Red the looping path, green the leakingpath, and blue the leaping path

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the vertically integrated @z=@t with the vertically integratedζ (the right panels in Fig. 12). It appears that the effect of@z=@t is to negate the existing ζ especially for the loopingpath and the leaping path, which implies that these twotypes cannot be sustained. This may be the reason for morefrequent leaking path, which tends to be the intermediatestate between transitions.

5 Summary and discussion

The weekly satellite data of 16 years and the daily HYCOMGlobal Analysis of 5 years are used to study the Kuroshiointrusion into the SCS. The areal integrated geostrophicvorticity in the box (118–121° E, 19–23° N) is defined asthe KSI that allows for the first time quantitativelydistinguishing among three types of Kuroshio intrusion.

& The looping path: when the KSI is less than its (μ−σ),the mean state shows clearly an anticyclonic currentloop with the Kuroshio flowing into the SCS in themiddle of the LS and flowing out in the northern part ofthe LS.

& The leaking path: when the KSI is greater than or equalto (μ−σ) but less than or equal to (μ+σ), the mean stateshows an anticyclonic bend in the northern half of theLS with a branch of the Kuroshio separating from thebend and intruding into the northern SCS along theslope.

& The leaping path: when the KSI is greater than its(μ+σ), the mean state shows that the bend becomessmaller and moves further to the north and that themajority of the Kuroshio traverses the LS without anyobvious branching into the SCS.

The analyses show that the leaking path is the mostfrequent form of the Kuroshio intrusion with the probabilityof occurrence of ∼68%, while the looping path and theleaping path split almost equally the remaining 32%. Thereare slightly more occasions of the looping path than theleaping path in the satellite data. In contrast, these areslightly less occasions of the looping path than the leapingpath in the HYCOM Global Analysis. In any given month,the probability of occurrence for the looping path or theleaping path is less than 25%. The leaking path occurs moreoften in the second half of the year, while the leaping path

Fig. 12 The vertically integrated (from 0 to 1,000 m) rate of changeof the relative vorticity (left panels, unit: meters per second),calculated as the sum of all terms on the right hand of Eq. (2) and

the vertically integrated (from 0 to 1,000 m) relative vorticity (rightpanels, unit: meters per second). a, b the looping path; c ,d the leakingpath; and e, f the leaping path

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appears more in the first half of the year. The looping pathis least frequent from March to June. Interannually, thereare more events of the looping path before 2001 exceptduring the strong El Niño in 1997∼1998. The analyses alsosuggest that the stronger and larger Luzon Cyclonic Gyremight set up a more favorable condition for the leaping pathby blocking the Kuroshio from entering the SCS.

Since the HYCOM Global Analysis includes variablesother than the sea surface elevation and additional infor-mation below the surface, this dataset is further analyzed todelineate other characteristics associated with the threeKuroshio paths. In the LS, the core of Kuroshio intrusionmoves northward, and the inflow speed decreases from thelooping path to the leaking path to the leaping path. Despitethe stronger inflow associated with the looping path, the nettransport through the LS is the same as that of the leakingpath, both at 8 Sv. This is because in the case of the loopingpath, the majority of the Kuroshio water entering the SCSflows out of the SCS via the Bashi Channel in the northernpart of the LS. On the other hand, the net transport throughthe LS for the leaping path is considerably smaller at 5 Svbecause there is more outgoing SCS water in the southernpart of the LS.

Intrusion of the subsurface and intermediate Kuroshiowaters into the SCS is depicted using the salinity maximumand minimum, respectively. It is clearly seen in Fig. 9 thatnot only the intrusion location shifts northward but also theintrusion angle (to the true north) becomes smaller from thelooping path to the leaking path to the leaping path.However, the high salinity water reaches the west mostlocation in the case of the leaking path.

Vorticity budget analysis suggests that the tilting of therelative vorticity, stretching of the absolute vorticity, andadvection of planetary vorticity are important for thechange of vorticity, whereas the baroclinic and frictionalcontributions are three orders smaller. Furthermore, thederived rate of change of vorticity seems to negate theexisting vorticity patterns, implying that the looping pathand the leaping path cannot be sustained and that in thetransition, the leaping path appears most frequently as theintermediate state.

It is interesting to note that from the looping path to theleaking path to the leaping path, the Kuroshio inflowbecomes weaker and shifts northward (Fig. 8), and theinflow angle gets closer to the true north (left panels inFig. 9). However, the Kuroshio intrusion into the SCS is acomplex process. The KCL can last from 2 to 3 weeks tooccasionally a couple of months (Fig. 2) with the loopenlarging and shrinking continually. The strength andextension also vary from loop to loop. In this study, wefocus on the mean state and choose ±σ as the dividers(Figs. 2 and 6). The actual separations between the loopingpath, the leaping path, and the leaking path are often vague

and subjective. In order to understand further how the threeKurishio paths are different in dynamics, detail progressesfrom one path to another need to be studied in futureresearches.

Acknowledgement The altimeter products were produced by Ssalto/Duacs and distributed by Aviso, with support from Cnes (http://www.aviso.oceanobs.com/duacs/). The 1/4° gridded data were downloadedfrom ftp.aviso.oceanobs.com/. The 1/12° HYCOM+NCODA GlobalAnalysis were obtained via OPENDAP at http://tds.hycom.org/thredds/dodsC/glb_analysis. This work was supported by the Programfor New Century Excellent Talents in University (NECT-07-0781), theNational Basic Research Program of China (No. 2011CB403500), andNSFC 90711006. The authors also thank Mr. Stephen Cousins at theUniversity of Maine for the help on data processing.

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