The Kuroshio Onshore Intrusion along the Shelf Break of the East China Sea: The Origin of the Tsushima Warm Current

a. General features of currents in the ECS

The current at the surface layer in the ECS (Fig. 2) shows a clear seasonal variation. East of Taiwan, the northward Kuroshio is strong in summer (August) and weak in winter (February), showing a similar seasonal variation to that observed (Tang et al. 2000). After impinging on the shelf break northeast of Taiwan, the Kuroshio turns northeastward and flows along the shelf break up to the area around 30°N, 129°E where it turns eastward and then exits the ECS through the Tokara Strait. The strength and width of the modeled Kuroshio in the ECS are about 1 m s⁻¹ and 100 km, respectively. The speed of the Kuroshio along the shelf break increases from winter to summer and decreases from summer to winter in response to the Kuroshio east of Taiwan. This can be inferred from the shaded area in Fig. 2.

Before further describing Fig. 2, we compare the model results and the observed data along a section across the Kuroshio to examine its modeled vertical structure. For the comparison, we choose the PN line (see Fig. 1b for its position), where long-term hydrographic data are available (Oka 2000). There is very good agreement between the observed annual mean absolute geostrophic current (Fig. 3a) and the modeled current (Fig. 3d) in terms of current strength, location of the strongest current, and horizontal and vertical gradients of current. Also, there is very good agreement between the observed and modeled mean potential water temperature (Figs. 3b,e) and salinity (Figs. 3c,f). The mean volume transport through the PN line is 24.44 Sv, which is also consistent with the value of 25.4 Sv calculated from the geostrophic velocity referred to 700 m (Hinada 1996). The appropriate representation of the vertical structure of the Kuroshio as well as of the bathymetry (Fig. 1) ensures a reliable cross-isobath intrusion of the Kuroshio in the model as discussed by Guo et al. (2003).

Returning to Fig. 2, we find that the current from the Taiwan Strait also flows strongly into the ECS. We refer to it as the Taiwan Warm Current, which flows in a northeastward direction initially but turns eastward around 28°N, 123°E. After further flowing eastward to 125°E, it turns northeastward following the local bathymetry and finally enters the Tsushima Strait. The Taiwan Warm Current is clearly strong in summer and weak in winter, which is consistent with the volume transport variation through the Taiwan Strait estimated by Fang et al. (1991).

The Taiwan Warm Current meets the Kuroshio water north of Taiwan (Fig. 2). During winter, the Taiwan Warm Current is weak and the intruded Kuroshio water dominates. From winter to summer, the Taiwan Warm Current intensifies gradually while the Kuroshio intrusion weakens. This results in the Taiwan Warm Current dominating north of Taiwan in summer. From summer to winter, the Taiwan Warm Current gradually weakens and the Kuroshio intrusion intensifies. This modeled seasonal variation of the onshore intrusion of the Kuroshio northeast of Taiwan is consistent with the observations of current (Tang and Yang 1993; Chuang and Liang 1994) and watermass distribution diagrams based on satellite infrared images (Chen et al. 1996).

In addition to the Kuroshio and the Taiwan Warm Current, a variety of interesting currents such as the Kuroshio countercurrent, the China Coastal Current, the West Korea Coastal Current, and the southward current along the western coast of Kyushu are found in Fig. 2. Among them, the China Coastal Current and West Korea Coastal Current have a close relation to the prevailed northerly wind in autumn and winter in the ECS and Yellow Sea (Guan 1994). Since these currents have little relation with the Kuroshio onshore intrusion across the shelf break, we leave discussions of them for future research.

The TWC, that is, the strong northeastward current in the Tsushima Strait, is clearly reproduced by model results (Fig. 2). Tsushima Island, located in the center of Tsushima Strait, divides the current into two branches. After passing the Tsushima Strait, the western branch of the TWC flows along the eastern coast of Korea and goes northward to around 37°N, while the eastern branch flows along the coast of Japan.

b. Distribution of volume transport in three layers

From a viewpoint of water budget, when discussing the origin of the TWC, it is better to use volume transport rather than velocity distribution at a given depth. For this purpose, we have calculated the volume transport through the lateral section of each grid point in three layers: the upper layer (from the surface to 50 m), the middle layer (50–100 m), and the lower layer (100–150 m) and present the seasonal variation of each layer in Figs. 4, 5 and 6. In the upper layer (Fig. 4), the Kuroshio and Taiwan Warm Current are clearly distinguished. In winter, the Taiwan Warm Current has a small volume transport and exists only in the eastern part of Taiwan Strait while the Kuroshio intrusion northeast of Taiwan is noticeable. After merging north of Taiwan, the intruded Kuroshio water and the water from the Taiwan Strait form a northeastward current over the continental shelf, nearly parallel to the Kuroshio. This current turns northward as it arrives at ∼30°N and forms a northward current west of Kyushu. The majority of the northward current west of Kyushu flows into the Tsushima Strait while a small proportion flows into the Yellow Sea. The volume transport of the northward current west of Kyushu is smaller than the eastward current around 28°N, 123°E indicating that a part of the intruded Kuroshio water northeast of Taiwan rejoins the Kuroshio main stream, or is absorbed in the middle layer.

From winter to summer, the volume transport of the Taiwan Warm Current increases as the current itself becomes stronger and wider. It reaches as far as 30°N over the continental shelf in summer before turning eastward. On the other hand, the intrusion of the Kuroshio northeast of Taiwan becomes weaker and an area with very weak transport appears between the Taiwan Warm Current and the Kuroshio. The weakened Kuroshio intrusion northeast of Taiwan suggests that the Taiwan Warm Current supplies most of the northward current west of Kyushu in the surface layer in summer. In autumn, although the volume transport of the Taiwan Warm Current decreases greatly, there is no clear decrease in volume transport of the northward current west of Kyushu and that of the TWC. Therefore, the Kuroshio onshore intrusion along the shelf break must be associated with a volume supply toward the continental shelf region in autumn.

The seasonality of the Taiwan Warm Current has been explained by the combination of monsoonal wind and topography forcing (Jan et al. 2002). The annual mean current in the Taiwan Strait is northward (Chuang 1985, 1986). The northerly wind in winter tends to produce a southward current in the strait (Ko et al. 2003), while the southerly wind in summer tends to produce a northward current in the strait. As a result, the monsoonal wind weakens (reinforces) the annual mean northward current in winter (summer). On the other hand, the blocking of a bottom ridge in the strait is stronger in winter than that in summer because of the strong barotropic structure of the current in winter and the strong baroclinic structure in summer (Jan et al. 2002).

In the middle layer (Fig. 5), seasonal variations are small. The Kuroshio intrusion northeast of Taiwan features a northward current west of Kyushu with the same strength as that in the upper layer. In the lower layer (Fig. 6), seasonal variations are unclear. The northward current west of Kyushu can still be identified and is fed likely by the separated northward branch of the Kuroshio southwest of Kyushu.

The volume transport distributions in the upper, middle, and lower layers suggest that the TWC is directly related to the northward current west of Kyushu. These distributions also suggest that the Taiwan Warm Current, the intruded Kuroshio water northeast of Taiwan, and the separated Kuroshio water southwest of Kyushu are three important sources of the northward current west of Kyushu. Because these three sources of water merge into one in the region southwest of Kyushu, local observations west or southwest of Kyushu cannot distinguish the three sources.

The contribution of waters in the middle and lower layers to the TWC is shown explicitly in Figs. 5 and 6 because it was not addressed in sufficient detail in previous studies (Fang et al. 1991; Lie and Cho 1994). The role of each layer can be seen clearly in the time series of volume transport through each layer of section EC between Cheju Island and Kyushu (Fig. 7). The mean volume transport through the middle layer of section EC is 0.93 Sv (Fig. 7b) and it is larger or at least the same order as the volume transport of 0.82 Sv through the upper layer (Fig. 7a). The lower-layer transport is 0.58 Sv (Fig. 7c). Thus, the volume transport through the middle and lower layers (1.51 Sv) is definitely larger than that through the upper layer.

The variation of volume transport in the three layers of section EC decreases with depth (Fig. 7). The short-term variation is stronger in the upper layer than the middle and lower layers. The seasonal variation pattern in the upper layer is different from that in the middle and lower layers. The volume transport through the upper layer increases from 0.5 to 1 Sv from March through September, decreases after September, and reaches its minimum (0.5 Sv) in January (Fig. 7a). The volume transports in the middle and lower layers show similar seasonality with the maximum in October and the minimum from winter to spring (Figs. 7b,c). During summer, the lower layer keeps a stable low transport but the middle layer shows a gradual increase in transport just like the upper layer.

The mean volume transport through the Cheju Strait is 0.69 Sv (Fig. 7d), which is not much different from the value of 0.59 Sv estimated by Teague et al. (2003) from ADCP data. Its maximum appears in October, almost at the same time as the middle and lower layers of section EC but about a month after the maximum of the upper layer of section EC.

c. Volume transport variations in the ECS

The water exchange in the ECS takes place in the Taiwan Strait (TAS), the section east of Taiwan (ET), the four sections along Ryukyu Islands (RK-1 to RK-4), the Tokara Strait (TOS), the Osumi Strait (OS), and the Tsushima Strait (TUS) (see Fig. 1 for location of these sections). The volume transport through these sections and their spectrums are shown in Figs. 8 and 9, respectively.

The time-averaged volume transport through the Taiwan Strait is 1.71 Sv and its standard deviation is 0.99 Sv (Fig. 8a). The seasonal variation is significant with a maximum (∼3 Sv) in July and a minimum (∼0.5 Sv) in January. This is consistent with the variability reported by Fang et al. (1991) on the basis of current meter data. But the minimum value (∼0.5 Sv) in winter is larger than a recent estimate (∼0.14 Sv) by Teague et al. (2003) on the basis of data from four moored ADCPs from October through December 1999. The difference might suggest the interannual variation of the throughflow. In addition to the seasonal and interannual variations, the short-term variations between 10 and 100 days also exist (Fig. 9a).

The time-averaged volume transport through section ET (i.e., east of Taiwan) is 23.83 Sv and the standard deviation is 2.73 Sv (Fig. 8b). The seasonal variation is weak. Instead, the short-term variation (10–100 days) and interannual variations are prominent in this section. The calculated mean transport corresponds to the generally accepted value of the Kuroshio mean volume transport into the ECS (Hsueh et al. 1992; Ichikawa and Beardsley 1993; Johns et al. 2001). The prominent short-term variations (10–100 days, Fig. 9b) in the Kuroshio transport east of Taiwan are consistent with the results of a 20-month moored current meter dataset (Zhang et al. 2001).

The time-averaged volume transports (and their standard deviation) through the four sections around the Ryukyu Islands are 0.73 (0.42) Sv for RK-1, −0.49 (1.63) Sv for RK-2, 0.97 (0.83) Sv for RK-3, and −0.62 (0.34) Sv for RK-4 (Fig. 8c–f), where the positive volume transport denotes an outward flow from the ECS. Among the four sections, RK-2 and RK-3 have the largest variation. Those are due to active mesoscale eddies around the Ryukyu Islands, which were reported by Ichikawa (2001) and reproduced in the present model.

The time-averaged volume transport through the Tokara Strait is 19.47 Sv and the standard deviation is 2.06 Sv (Fig. 8g). The mean transport is close to the climatological value of 20 Sv used by Teague et al. (2003), but it is a little smaller than the value of 23.4 Sv given by Feng et al. (2000). Like the volume transport through section ET, short-term and interannual variations are prominent in the volume transport through the Tokara Strait. The significant periods of 70 and 20 days in the spectrum of the volume transport (Fig. 9g) are consistent with the observations (Feng et al. 2000). There is a clear correspondence between the volume transports through sections ET, RK-2, RK-3, and the Tokara Strait particularly for the interannual variations. Ichikawa (2001) has reported the correlation between the mesoscale eddies around the Ryukyu Islands and the sea level variations at the Tokara Strait from observed data.

The time-averaged volume transport through the Osumi Strait is 2.46 Sv and the standard deviation is 0.49 Sv (Fig. 8h). Short-term variations of periods of about 70, 50, and 20 days are significant here (Fig. 9h), but interannual variations are weak (Fig. 8h).

The time-averaged volume transport through the Tsushima Strait is 3.03 Sv and the standard deviation is 0.59 Sv (Fig. 8i). The seasonal variability is the strongest among other signals, while the short-term variation of 20 days also exists (Fig. 9i). We note that the volume transport increases gradually from January to October. After attaining to its maximum in October, it starts to decrease and reaches its minimum in the following January. Although the mean transport of 3.03 Sv is slightly larger than the 2.7 Sv estimated by Teague et al. (2002), the seasonal march is consistent with the observation.

To summarize the above results, the averaged volume transports across some selected sections in the ECS are shown in Fig. 10. The volume transports through the channels that enclose the ECS are balanced. Since the volume transport through the Tsushima Strait is larger than that through the Taiwan Strait by 1.32 Sv, the residual must be supplied by the onshore flux across the shelf break. In Fig. 10, we have 1.46 Sv as the onshore volume transport across the 200-m isobath and a 0.14 Sv southward volume transport through a section west of Kyushu (WK in Fig. 1). As expected, the difference of these two values (1.46 minus 0.14 Sv) just explains the shortage of the volume transports between the Tsushima Strait and the Taiwan Strait.

d. Kuroshio onshore flux across 200-m isobath

Seasonal variability is the most significant signal in the time series of Kuroshio onshore flux across the 200-m isobath (Fig. 11). From October to November, the Kuroshio onshore flux reaches its maximum of about 3 Sv and then it begins to decrease gradually until reaching its minimum (<0.5 Sv) from June to July. The mean value is 1.46 Sv and the standard deviation is 1.17 Sv. It must be noted that the Kuroshio onshore flux across the 200-m isobath calculated from the results of zero-forcing experiment is around 0.02 Sv. Therefore, the results shown in Fig. 11 contain 0.02 Sv of uncertainty.

In Fig. 11, the daily difference between the volume transport through the Tsushima Strait and that through the Taiwan Strait is also shown, and is almost exactly the same as the daily Kuroshio onshore flux across the 200-m isobath. Teague et al. (2003), based on the difference between the observed volume transport through the Taiwan Strait and that through the Tsushima Strait, suggest a value of 3 Sv for the Kuroshio onshore flux across the shelf break of the ECS during October–December 1999. Our model result supports the result as well as the method.

In addition to the seasonal variability, short-term variations are also prominent in the time series of the daily Kuroshio onshore flux across the 200-m isobath (Fig. 11). The spectrum of the daily Kuroshio onshore flux across the 200-m isobath (not shown here) shows an energy peak at 17 days, which is consistent with the period of Kuroshio meanders in the ECS (Sugimoto et al. 1988; Qiu et al. 1990; James et al. 1999). Therefore we have plotted the daily Kuroshio path in the ECS and have confirmed the existence of the short-term Kuroshio meanders in NEST3. According to Fig. 11, the Kuroshio meanders cause transport variations of about 1 Sv across the 200-m isobath and results in a standard variation of 0.37 Sv. Because the standard deviation caused by the seasonal variation is 0.90 Sv, we conclude safely that the seasonal variation of Kuroshio intrusions is the most important factor controlling the Kuroshio onshore flux across the shelf break in the ECS.

The spatial distribution of the time-averaged volume transport across the 200-m isobath (Fig. 12) shows that the Kuroshio intrusion northeast of Taiwan is the major source of the mean Kuroshio onshore flux to the ECS. This is seen more clearly in the spatially integrated onshore flux starting from the coast of Taiwan (Fig. 12). The first 40 grid points (northeast of Taiwan) and the grid point 210 to 240 (southwest of Kyushu) are two major sections providing the onshore volume transport (see Fig. 1b for the location of grid point). The former section provides 5.6 Sv of the onshore flux and the latter provides about 1 Sv. We note that 4.6 Sv leaves as the offshore flux between the grid points 40 and 210, and 0.5 Sv leaves north of grid point 240. Thus, the total mean Kuroshio onshore flux is maintained at 1.5 Sv.

We use the standard deviation at each grid point to examine the spatial structure of the temporal variation of the Kuroshio onshore flux (Fig. 12). The standard deviation of the long-term variation (SD-L) in the first 80 grid points (northeast of Taiwan) and the grid points after 240 (southwest of Kyushu) is larger than that of the intermediate area, suggesting that the seasonal variation takes place mainly in these two areas. The short-term variation (SD-S) has the same order of magnitude and the same spatial distribution as the seasonal variation in these two areas, implying that the short-term and the seasonal variations are both strong there. However, in the intermediate area (i.e., shelf break), only the short-term variations are very strong and the long-term variations are weak. This indicates that the Kuroshio is stable without the seasonal variation along the shelf break, but the active frontal eddies perturb the Kuroshio frequently, causing Kuroshio meandering.

To clarify when and where the seasonal variation of the Kuroshio onshore flux takes place, we have calculated the monthly anomaly of the volume transport across the 200-m isobath at each grid point (Fig. 13). As expected from the distribution of the standard deviation (Fig. 12), the first 80 grid points show remarkable seasonal variation. These grid points can be further divided into three subgroups according to the seasonal variation pattern. The first 20 grid points and grid points 40 to 80 have similar seasonal variation but grid points 20 to 40 show an opposite seasonal variation. The former two subgroups show an onshore flux anomaly from October to February with a maximum in November and an offshore flux anomaly from March to September with a maximum in July. The same pattern of variability is found for the grid points beyond point 210. Grid points 20 to 40 show an onshore flux anomaly from April to October with a maximum in July and an offshore flux anomaly from November to March with a maximum in January.

e. Depth dependence of the temporal variation of the Kuroshio onshore flux

To study the vertical distribution of the Kuroshio onshore flux, we divide the 200-m isobath fluxes into four layers: a surface layer (0–50 m), two middle layers (50–100 and 100–150 m), and a lower layer (150 m to bottom) and show the time series of volume transport in each layer in Fig. 14.

The volume transport from the surface and lower layers contributes more than 80% of the mean Kuroshio onshore flux. Among the 1.46 Sv of the mean Kuroshio onshore flux, the surface layer contributes 0.68 Sv and the lower layer 0.52 Sv. The surface layer has the largest variation and its standard deviation is about 3 times larger than that in the other three layers. The increase of onshore flux from October to November is found in all four layers, while the decreasing phase is slightly different among four layers. In the surface layer, a negative onshore flux (i.e., an offshore flux) appears in summer although it is modified frequently by short-term variations. In contrast, the lower layer has little variation and provides almost 0.5 Sv of onshore volume transport throughout the year. The mean onshore flux in the two middle layers is small. Further examination shows that 1.6 and 1.0 Sv of onshore fluxes exist in the first 40 grids of the upper and lower middle layers, respectively, while 1.5 and 1.0 Sv of offshore fluxes exist from grid points 40 to 210 in the upper and lower middle layers, respectively. Thus, the net onshore fluxes through two middle layers become small as seen in Fig. 14.

a. Remote and local effects on the seasonality of Tsushima Warm Current and Kuroshio onshore flux

As suggested by Minato and Kimura (1980) and Ohshima (1994), the volume transport of TWC depends primarily on the sea level difference between the Tsushima Strait and Tsugaru Strait, which is determined by the large-scale wind-driven Sverdrup dynamics in the Pacific. Further, Ohshima (1994) suggested that the TWC also influences the northeastward currents along the shelves in the ECS and South China Sea. Following this notion, the sea level difference between the Tsushima Strait and Tsugaru Strait is expected to affect the volume transport through the Taiwan Strait and the Kuroshio onshore flux. However, this expectation is not supported by the results from the present study.

From January to September, the transport through Tsushima Strait (Fig. 19a) is in phase with the sea level difference between the Tsushima Strait and Tsugaru Strait (Fig. 19b). Both of them increase in general and both of them decrease in January, June, and September. This relation is broken after September. The sea level difference decreases largely from September to November but the transport still keeps increasing and attains a maximum in November. The inconsistency also happens in December when the sea level difference increases but the transport decreases. Therefore, although a positive sea level difference between the Tsushima Strait and Tsugaru Strait is kept throughout the year (Fig. 19b) and drives an annually positive transport from the ECS to Japan Sea through the Tsushima Strait, which is consistent with the results of Minato and Kimura (1980) and Ohshima (1994), the proportional relation of the transport of TWC to the sea level difference between the Tsushima Strait and Tsugaru Strait is not completely held in the seasonal variation.

Further examination of the transport through the Taiwan Strait and the total Kuroshio onshore flux across the 200-m isobath (Fig. 19a) shows that the transport through the Taiwan Strait is generally in phase with the sea level difference between the Tsushima Strait and Tsugaru Strait (Fig. 19b) but the time lag is clear. The transport through Taiwan Strait decreases after July while the sea level difference between the Tsushima Strait and Tsugaru Strait decreases after August. On the other hand, the Kuroshio onshore flux across 200-m isobath is generally out of phase with the sea level difference between the Tsushima Strait and Tsugaru Strait. The former decreases from January to June and increases from June to November while the latter increases from February to August and decreases from August to November.

The above comparison suggests that the sea level difference between the Tsushima Strait and Tsugaru Strait is difficult to be the primary cause for the seasonal variation of the volume transport through the Taiwan Strait and that of the Kuroshio onshore flux across the 200-m isobath in the ECS. It also suggests that some local processes in the ECS, which were not considered by Minato and Kimura (1980) and Ohshima (1994), have modified the dependence of the TWC on the sea level difference between the Tsushima Strait and Tsugaru Strait. One candidate for the local processes is the seasonal variation of winds over the ECS. The monthly Ekman transport across the 200-m isobath is shown in Fig. 19a, which produces 1.3 Sv of onshore transport in January, 0.5 Sv of offshore transport in June, and 1.5 Sv of onshore transport in November. The 1.5 Sv of onshore transport in November apparently contributes to the TWC.

b. Dynamical interpretation on the seasonality of total Kuroshio onshore flux in the ECS

The Ekman transport across the 200-m isobath is a part of total Kuroshio onshore flux in the ECS and its seasonal variation is generally in phase with the Kuroshio onshore flux (Fig. 19a). The difference between them is minimum in March, increases gradually from March to September, becomes maximum in October, and decreases from November to next March (Fig. 19a). Among the total Kuroshio onshore flux, the Ekman transport has an annual variation range of 2 Sv, and the residual part has the same order of annual variation range. Therefore, in addition to the local winds, other unknown factors are also important to the total Kuroshio onshore flux.

Mertz and Wright (1992) gave an equation to calculate the transport normal to f/H contours from specified wind and density fields [see (19) in Mertz and Wright (1992)], where f is the Coriolis parameter and H is water depth. The equation separates the contribution of local winds to the transport normal to f/H contours from that of density field; the latter is expressed by the so-called joint effect of baroclinicity and relief (JEBAR) term. Because f changes little in the ECS, the 200-m isobath along the shelf break corresponds roughly to a contour of f/H. Therefore, by following the idea in Mertz and Wright (1992), we can examine the different role of local winds and density field in the seasonal variation of Kuroshio onshore flux across the shelf break in the ECS.

It must be noted that the equation involving the JEBAR term is only a diagnostic tool of specified flow and density fields. In fact, JEBAR was initially used to interpret the results of a diagnostic model that calculates the current field from a given density field (Sarkisyan and Ivanov 1971; Holland and Hirschman 1972). Because the density field is fixed in the diagnostic model, this concept is useful to consider the relation between the calculated current field and the given density field. However, in a prognostic model like the model we used, the density field is not fixed and can be changed by many factors. Among these factors, some changes the density field directly, while some changes the flow field directly and as a result of the change in the flow field, the density field is changed. The equation with the JEBAR term reflects the combined effects of these factors and cannot clarify the causal relationship between the flow field and the density field.

Our numerical calculation, however, is not designed to clarify the causal relationship between the Kuroshio onshore flow and density field. This will be the second step. As the first step, we want to confirm whether the change in density field is important to the Kuroshio onshore flux, by comparing the JEBAR term with the contribution from local winds.

After vertically averaging the primitive momentum equations and then cross differentiating to eliminate the unnecessary terms, the following vorticity equation can be obtained [see Mertz and Wright (1992) or Mellor (1996, chapter 8) for details]:

View Expanded

In (1), two operators are defined as J(A, B) = ∂A/∂x∂B/∂y − ∂A/∂y∂B/∂x and curl_z(C) = ∂C_y/∂x − ∂C_x/∂y; M = ∫⁰_−H(ui + υj) dz is a volume transport vector with u and υ being the eastward and northward component of water velocity; J(χ, H⁻¹) is the JEBAR term with χ = ∫⁰_−Hzgρ/ρ₀ dz being the potential energy; τ_a is the wind stress; and τ_b is the bottom stress. The wind stress term can be further separated into two terms: (ρ₀H)⁻¹ curl_z(τ_a), the vorticity directly from wind stress, and ∇(ρ₀H)⁻¹ × τ_a, the vorticity induced by the surface Ekman transport across isobaths. The bottom stress term can also be similarly separated into two terms, and one of them is from the bottom Ekman transport. Two other vectors, A = A_xi + A_yj and D = D_xi + D_yj, are the nonlinear advection term and the vertically integrated horizontal diffusion term, respectively.

In a quasi steady state such as monthly mean or annual mean state, the first term in the left-hand side of (1) is negligible and the second term M·∇( fH⁻¹) is balanced by the five terms in the right-hand side of (1). A positive M·∇( fH⁻¹) [hereinafter referred to as APV (advection of the geostrophic potential vorticity)] corresponds to an onshore flux in the shelf break of ECS. Among the five terms in the right-hand side of (1), the JEBAR term is the only term related to the density field.

The monthly APV as well as the five terms in the right-hand side of (1) are integrated along the 200-m isobath in the ECS and shown in Fig. 20a. As expected, the APV corresponds well with the total onshore flux across the 200-m isobath (Fig. 19a). Both of them have a clear seasonal variation showing a minimum in June and a maximum in November. Most of the seasonal variation of the total onshore flux across the 200-m isobath occurs in the surface layer (0–50 m) (Fig. 20b). The seasonal variations in the two middle layers (50–100 and 100–150 m) and in the bottom layer (150 m– bottom) are small (Fig. 20b) but have an apparent increasing from September to November.

The annual averaged APV—that is, the annual averaged Kuroshio onshore flux—is primarily balanced by the JEBAR term (Fig. 20a). In Fig. 20a, the annual mean of the APV is 0.77 m² s⁻², while the JEBAR term is 0.50 m² s⁻². This, however, just indicates that the Kuroshio onshore flow across the 200-m isobath in the ECS is in a basically geostrophic state. The bottom stress and the wind stress produce an annual mean of 0.21 and 0.17 m² s⁻² in Fig. 20a, respectively, and become the secondary and third factors to balance the annual averaged APV. The contribution from residual two terms, the horizontal diffusion term (−0.07 m² s⁻²) and the nonlinear advection term (−0.09 m² s⁻²), are both small.

On the other hand, the seasonality of the Kuroshio onshore flux is primarily balanced by the wind stress term and the JEBAR term is secondary. Among the five terms in the right-hand side of (1), the wind stress term has almost the same seasonal variation as the APV (Fig. 20a). They both have a minimum in June and increases from June to November. After November, the APV decreases until next June, while the wind stress term keeps increasing to December and then also decreases until next June. This result is consistent with the comparison of the Kuroshio onshore flux and the surface Ekman transport in Fig. 19a. It is worthy of noting that nearly 95% of the wind stress term shown in Fig. 20a is from the surface Ekman transport across the 200-m isobath and the residual is from wind stress curl.

The change in density field—that is, the JEBAR term—and the nonlinear advection term in Fig. 20a can be related to the difference between total Kuroshio onshore flux and the Ekman transport across the 200-m isobath shown in Fig. 19a. The JEBAR term shows a minimum in March, increases from March to August, keeps a maximum from August to November, and decreases to the minimum in next March; the nonlinear advection term keeps almost constant through a year except for a decrease from July to August and an increase from September to October (Fig. 20a). The combination of these two terms explains well the maximum in the difference between total Kuroshio onshore flux and the Ekman transport across the 200-m isobath in autumn (Fig. 19a).

As depicted in Fig. 19, the dependence of the TWC on the sea level difference between the Tsushima Strait and Tsugaru Strait is not held from September to December. According to Fig. 20a, the wind-induced surface Ekman transport across the shelf break in the ECS and the change in the density field in the ECS are probably the most possible explanation on the discrepancy.

c. Dynamical interpretation on the locality of Kuroshio onshore flux along the shelf break of the ECS and its seasonality

The locality of the Kuroshio onshore flux along the 200-m isobath and its seasonal variation has been shown in Fig. 13. To know the major factor controlling the seasonal variation of the onshore flux at a given location, we show the distribution of the monthly anomaly of APV, the JEBAR term, and the wind stress term along the 200-m isobath in Fig. 21.

The magnitude of the terms shown in Fig. 21 suggests that the change in the density field affects much more than the wind stress on the seasonal variation of the onshore flux at a given location. Differing from the wind, whose surface Ekman transport has the same sign almost all the way along the shelf break, the JEBAR term changes sign along the shelf break. Therefore, although the monthly anomaly of the JEBAR term at a given point is larger than that of the wind stress term by one order, the total JEBAR term contributes less to the total onshore flux across the shelf break than the total wind stress term.

Figure 21 can be linked to the observational results northeast of Taiwan. The abrupt intrusion of the Kuroshio northeast of Taiwan in mid-October has been captured by a buoy-mounted ADCP (Tang and Yang 1993) and by moored current meters (Chuang and Liang 1994), and in satellite images (Chen et al. 1996). The observations in other months suggest seasonal variations of the intrusion there. Hsueh et al. (1992) reported the Kuroshio intrusion in spring based on hydrographic data in April 1989. In a subsequent paper, Hsueh et al. (1993) reported a blocking of the Kuroshio there in August 1991. Numerical models (Chao 1990; Chen et al. 1996) also show the same seasonal variation of the Kuroshio onshore intrusion northeast of Taiwan. The local wind effect suggested by numerical model results (Chao 1990; Chen et al. 1996) is not obvious in observed current data (Tang and Yang 1993; Chuang and Liang 1994). Instead, Tang and Yang (1993) suggested that nonlocal factors induced the abrupt intrusion of Kuroshio in mid-October. Chuang and Liang (1994) suggested that cooling should be the major cause for triggering the massive intrusion event in mid-October.

Figure 21 suggests that the local wind really contributes to the Kuroshio intrusion northeast of Taiwan but it is not the major factor. The major factor is in the change of density field. The cooling suggested by Chuang and Liang (1994) could be one possible cause changing the local density field northeast of Taiwan. On the other hand, a seasonal change in the basin-scale atmospheric forcing can alter the density and current structures of the Kuroshio and then affect the intensity of impinging of the Kuroshio on the shelf break northeast of Taiwan, which can alter the local density field northeast of Taiwan too. Therefore, to clarify the real physical process beneath the JEBAR term, more numerical experiments are necessary.