Annual Variation of the Kuroshio Transport in a Two-Layer Numerical Model with a Ridge

Transcription

1 994 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 Annual Variation of the Kuroshio Transport in a Two-Layer Numerical Model with a Ridge ATSUHIKO ISOBE Department of Earth System Science and Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, Japan SHIRO IMAWAKI Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan (Manuscript received 28 September 2000, in final form 3 August 2001) ABSTRACT A two-layer numerical model driven by the wind stress is used to explain the observed annual variation of the Kuroshio transport south of Japan. Special attention is given to the effect of a ridge, representing the Izu Ogasawara Ridge, on the generation of the baroclinic activity through the coupling of the barotropic and baroclinic modes of motion. For annual variation, lower-layer motion is found in areas surrounding the ridge because isostasy (a state of no motion in the lower layer) is not achieved within such a short timescale. Thus, the lowerlayer flow impinges on the bottom slope. This impinging process generates anomalies of the upper-layer thickness especially on the eastern side of the ridge. Thereafter, anomalies move westward with characteristic velocities composed of the vertically averaged flow and westward propagation of the long baroclinic Rossby wave forced above the ridge. As anomalies of the upper-layer thickness move westward above the ridge, isostasy is accomplished with respect to these anomalies. As a result, the positive (negative) anomaly of the upper-layer thickness carries the information about the positive (negative) anomaly of the volume transport as it reaches the western edge of the ridge. Thereafter, anomalies of the volume transport are released to the west of the ridge. This experiment shows that the annual range of the volume transport east of the ridge is around 40 Sv, which is nearly equal to the zonal integration of the Sverdrup transport there. The annual range west of the ridge, however, reduces to around 10 Sv, which is mostly caused by the baroclinic activity generated above the ridge. Results are compared with the observed Kuroshio transport across the ASUKA line south of Japan. The annual range west of the ridge is consistent with that estimated from the observation. 1. Introduction The annual cycle is the most energetic component of the wind stress driving the general ocean circulation. Therefore, it is reasonable to anticipate a prominent annual cycle in the Sverdrup transport. Moreover, it is anticipated that the zonal integration of the Sverdrup transport well describes the annual transport variation of the western boundary current as the compensation flow of the interior transport, because the barotropic adjustment is achieved instantaneously compared to the annual timescale. In the case of the Gulf Stream, however, the annual range of the volume transport variation is less than 10 Sv (1 Sv 10 6 m 3 s 1 ) in the Florida Strait (Niiler and Richardson 1973), which is much smaller than that of the Sverdrup transport there ( 30 Corresponding author address: Dr. Atsuhiko Isobe, Department of Earth System Science and Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1, Kasuga- Koen, Kasuga, Fukuoka , Japan. isobe@esst.kyushu-u.ac.jp Sv; Anderson and Corry 1985). Such an annual cycle of the Gulf Stream has been confirmed by Molinari et al. (1985) and Schott and Zantopp (1985) for the Florida Strait, and by Sato and Rossby (1995) for the east of Cape Hatteras, although the transport variation due to interactions between the stream and surrounding eddy field makes it difficult to determine an accurate annual cycle. In the case of the Kuroshio, the western boundary current of the North Pacific subtropical gyre, recent observations by the Affiliated Surveys of the Kuroshio off Cape Ashizuri (ASUKA) Group provided a time series of volume transport for seven years (Imawaki et al. 1997, 2001; H. Uchida and S. Imawaki 2001, personal communication, hereafter UI). They carried out moored current-meter measurements and repeated hydrographic surveys along a line shown in Fig. 1 (ASUKA line), and estimated the absolute geostrophic transport of the Kuroshio across the ASUKA line. In addition, they found an empirical formula converting the altimetry data to the volume transport of the Kuroshio. As a result, 2002 American Meteorological Society

2 MARCH 2002 ISOBE AND IMAWAKI 995 FIG. 1. Study area of the western North Pacific and results of the ASUKA observations. Thick solid lines represent the ASUKA and PN lines. A thick broken line shows the path of the Kuroshio schematically. Also shown are isobaths in kilometers. The solid curve in the lower-right panel shows the annual variation of the Kuroshio volume transport (after UI. The broken line is the annual variation of the negative value of the Sverdrup transport integrated over the North Pacific at 30 N, evaluated from ECMWF wind data (K. Kutsuwada 1999, personal communication). they are now monitoring the Kuroshio volume transport every 10 days using the satellite altimetry data. According to the climatological mean of the geopotential anomaly field depicted by Hasunuma and Yoshida (1978), a stable anticyclonic eddy exists south of Shikoku Island. This eddy might prevent an accurate estimate of the Kuroshio volume transport. However, the ASUKA line from Cape Ashizuri to 25 N extends to the south beyond the local eddy. Hence, the contribution of the eddy is cancelled effectively in their estimate of the Kuroshio volume transport. This means that the annual cycle in the observed Kuroshio volume transport originates from the annual variability of gyre-scale motion. Nevertheless, as shown in Fig. 1, the averaged annual range of the volume transport variation is estimated to be about 10 Sv, which is much smaller than that of zonally integrated Sverdrup transport (40 50 Sv) at 30 N over the North Pacific (K. Kutsuwada 1999, personal communication); this transport is estimated from wind data of the European Center for Medium- Range Weather Forecasts (ECMWF) with the drag coefficient of Large and Pond (1981). The actual ocean has a complicated bottom topography, so the classical (i.e., nontopographic) Sverdrup relation is only applicable to phenomena with a timescale longer than the time for baroclinic Rossby waves to cross the ocean and compensate for the effect of the bottom topography (Anderson and Killworth 1977). For the midlatitude Atlantic and Pacific, it takes years or decades for compensation by baroclinic Rossby waves to occur. Therefore, for shorter period (annual or less), the stratification is unlikely to filter out the effect of topography. Thus, one may consider that the volume transport variation for shorter period is explained by the Sverdrup relation for a homogeneous ocean with topography, that is, the topographic Sverdrup relation described by Gill and Niiler [1973, see their Eq. (5.9) and discussion] and Thompson et al. (1986). This means

3 996 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 2. Two-layer model adopted in this study. The upper panel shows the plane view of the model ocean. Thin lines in the panel represent the grid spacing; it is shown only in the central part of the domain for the y direction. Meridional distribution of the wind stress is depicted schematically on the right-hand side of this panel. The lower panel shows the vertical view of the model. A ridge and the shelf slope are depicted in the panel. that a one-layer numerical model (i.e., barotropic model) with realistic topography can reproduce the annual transport variation. In fact, the phase of the annual transport variation is well reproduced by the one-layer models by Anderson and Corry (1985) and Greatbatch and Goulding (1989) for the Gulf Stream, and by Greatbatch and Goulding (1990) and Kubota et al. (1995) for the Kuroshio. However, they all underestimate the annual ranges compared to the observed variation. Namely, the observed annual ranges of the volume transport of the Gulf Stream and Kuroshio are smaller than those of the nontopographic Sverdrup transport, but larger than those of the topographic Sverdrup transport. Anderson and Corry (1985) adopted a two-layer numerical model with realistic topography as well as the one-layer model, and found that the annual range of the volume transport variation of the Gulf Stream is amplified by baroclinic activity associated with a baroclinic Kelvin wave. The Kelvin wave is generated by winds to the north of the Florida Straits, passing south over varying bottom topography. However, they still underestimate the annual range. In the present study, we also use a two-layer numerical model to identify the baroclinic activity inducing the observed annual range of the Kuroshio volume transport. As shown later, the annual range in the present model is consistent with the observed value on the ASUKA line. As shown in Fig. 1, the ASUKA line is located west of the Izu Ogasawara Ridge which extends meridionally over the whole region of the North Pacific subtropical gyre. In the present study, special attention is given to the effect of the ridge on the generation of a baroclinic Rossby wave through the coupling of the barotropic and baroclinic modes of motion (e.g., Barnier 1988; Gerdes and Wübber 1991). As shown later, the annual range of the modeled Kuroshio volume transport variation is larger than that of the topographic Sverdrup transport because of baroclinic motion excited above the ridge. The two-layer numerical model in the present study is described in section 2. In section 3, we show results in which the baroclinic activity above the ridge controls the annual variation of the Kuroshio volume transport. A physical interpretation and the comparison with the ASUKA observation are provided in section 4. Section 5 gives the conclusions. 2. Model descriptions To provide a simple interpretation for the annual variation of the Kuroshio volume transport, a rectangular ocean ( km 2000 km) with a simplified bottom topography is adopted in this model. We use Cartesian coordinates where directions of x and y axes (with origin at the southwestern corner) are eastward and northward, respectively. As shown in Fig. 2, the model ocean is flat except for a meridional ridge in the western part (1550 km x 2050 km) and the shelf slope at the western boundary. The ridge represents the Izu Ogasawara Ridge in the western North Pacific (see appendix A for its applicability to the real ocean). In the present study, the depth H of the ridge is modeled as Hr 2 H(l) H0 1 sin l, 2 W 2 where H 0 is the depth in the flat-bottom region, H r the maximum height of the ridge, W the width of the ridge, and l the eastward distance from the western edge of

4 MARCH 2002 ISOBE AND IMAWAKI 997 TABLE 1. Parameters used in the present study. Reduced gravity Planetary Coriolis parameter at southern sidewall Horizontal viscosity coefficient Amplitude of the wind stress Depth in the flat-bottom region Maximum height of the ridge Width of the ridge Undisturbed upper-layer thickness g : 2.0 cm s 2 : cm 1 s 1 f (y 0): s 1 A h : cm 2 s 1 a: dyn cm 2 H 0 : 3000 m H r : 1500 m W: 500 km H 1 : 600 m the ridge. In order to avoid computational instability, a shelf slope of 100 km width is imposed along the western boundary, prohibiting the width of the western boundary layer from being too thin. The model ocean is divided into two active layers. In the present study, the Kuroshio transport is defined as the volume transport between the western boundary and western edge of the ridge. This modeled transport corresponds to the observed Kuroshio transport across the whole ASUKA line (i.e., the transport of the Kuroshio Throughflow in Imawaki et al. 2001; UI). The governing equations are the same as those in Sekine and Kutsuwada (1994) except that momentum advection is not included in the present model. We neglect momentum advection because our attention is not focused on the current structure in the western boundary region where momentum advection cannot be neglected. More attention is given to processes around the ridge in the interior region far from the western boundary. Nonlinearity remains in the continuity equation because a large displacement of the interface is expected. Friction at both the bottom and layer interface is neglected. The lateral boundaries are nonslip sidewalls, as well as prohibiting the flow across them. The ridge intersects the northern and southern sidewalls, so sidewall boundary layers are produced artificially at both ends of the ridge. In addition, discontinuities in the f/h contours at both ends of the ridge might be artificial sources of vorticity (Barnier 1988). However, processes of importance to the present study occur apart from sidewalls, as shown in section 4. The governing equations with hydrostatic, rigid-lid, and Boussinesq approximations are f h2 J, g J, h1 t H H y H 2 Ah, (1) û h1 2 f ˆ g Ah û, (2) t x h 1 ˆ h 1 2 fû g Ah ˆ, t y (3) h1 u1h1 1h1 0, t x y (4) where is the vorticity of the vertically averaged flow, the (volume transport) streamfunction, f the Coriolis parameter on the plane, g the reduced gravity, h 1 and h 2 the layer thickness of the upper and lower layers respectively, the wind stress, û( u 1 u 2 ) and ˆ ( 1 2 ) the difference of the upper-layer velocity (u 1, 1 ) and lower-layer velocity (u 2, 2 )inx and y directions respectively, and J(A, B) the Jacobian ( A x B y A y B x ); otherwise notation is standard. The vorticity and streamfunction are defined as 1, (5) H uh 1 1 uh 2 2 y. (6) h h x The model is driven only by the zonal wind stress. The amplitude of the wind stress varies sinusoidally in the y direction. The wind stress is composed of mean and time-dependent parts as follows: a 2 cos y a cos t, (7) L 2 T where T is the period of the fluctuating wind stress ( 360 days in the present study), and L the total length of the model domain in the y direction. In this model, the wind stress is maximum on day 0 and day 360 (defined as midwinter), and the minimum on day 180 (midsummer). The parameter a in (7) is a constant determining the magnitude of wind forcing; its value is chosen so that the annual mean and range of wind stress curl integrated zonally take the same values as those estimated from ECMWF wind data [about 40 Sv for the annual mean and Sv for the annual range (Sv 10 6 m 3 s 1 )]. Parameters used in the present study are listed in Table 1. Equations (1) (4) are numerically integrated using the leapfrog scheme with the Matsuno scheme every 25 time steps. Equation (5) is solved using the successive over-relaxation method. The grid spacing in the x direction varies zonally (see Fig. 2); it is 20 km wide above the ridge and shelf slope at the western boundary, km wide west of the ridge, and km wide east of the ridge. The grid spacing in the y direction is fixed at 20 km. Initially, distributions of the streamfunction and upper-layer thickness are determined using linearized solutions of a flat-bottom case in the steady state, x f g H y x 1 (x, y) dx, (8) y x e h (x, y) h dx, (9) 1 0 x e 1

5 998 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 3. The streamfunction (upper panel) and upper-layer thickness (lower panel) in the twolayer model with the ridge, driven by the annually averaged wind stress. Broken lines represent the location of eastern and western edges of the ridge. Contour intervals for the streamfunction and upper-layer thickness are 5 Sv and 50 m. Contours within the western boundary layer are omitted because of over crowding. where the location x e denotes the eastern sidewall, H 1 is the undisturbed upper-layer thickness, and h 0 is a constant such that the spatially averaged upper-layer thickness is equal to the undisturbed value H 1. The wind stress is the annually averaged value in above equations. Time integration is continued until the end of the tenth year when the year-to-year variability disappears. Results taken from the final tenth year are discussed in the following sections. 3. Results a. Annual mean Before looking at the annual variation, the effect of the ridge on the annually averaged field is described. As expected, distributions of the streamfunction and upper-layer thickness represent the wind-driven ocean circulation in a textbook way when we use a two-layer model without a ridge, driven by the annual mean wind stress. In addition, as shown in Fig. 3, the solutions do not change, even though we use a two-layer model with the ridge, driven by the annual mean wind stress. This is because lower-layer motion vanishes in the annual mean case. We here refer to a state of no motion in the lower layer as isostasy. The achievement of isostasy in the steady state can be explained by the steady-state vorticity equation in the lower layer (Rooth et al. 1978; Rhines and Young 1982): f 2 f 2 0. (10) y h x x h y 2 2 Here viscous terms are neglected so that the above equation is valid in the Sverdrup interior region. Equation (10) means that the streamfunction of the lower layer, 2, is advected by characteristic velocities whose streamfunction is the geostrophic contour, f/h 2. Figure 4 shows the horizontal distribution of f/h 2 of the solution in Fig. 3. In the flat-bottom region east of the ridge, all geostrophic contours originate from the eastern sidewall along which the lower-layer streamfunction is defined to be zero. Hence, isostasy is achieved east of the ridge. The geostrophic contours from the eastern sidewall turn southward in the eastern half of the ridge due to large topographic on the ridge (see lower-left panel of Fig. 4 for the geostrophic contour f/h 2 and lowerright panel for f/h). Other geostrophic contours on the ridge originate from the northern and southern sidewalls of the ridge. In addition, the contours in the flat-bottom region west of the ridge originate from the southern sidewall of the ridge. Therefore, isostasy on the ridge and in the flat-bottom region west of the ridge results from the condition of no motion required along the sidewalls on the ridge. Two areas of closed geostrophic contours are revealed in the northwestern corner of the flat-bottom region west of the ridge and on the northern part of the ridge. In these areas, lower-layer motion is permitted even in the steady state because the areas are isolated from sidewalls. However, the present model does not directly force motion of the lower layer [e.g., by interfacial drag as in Rhines and Young, (1982) and Jarvis and Veronis (1994)]. Therefore, in the steady state, lower-layer isos-

6 MARCH 2002 ISOBE AND IMAWAKI 999 FIG. 4. Geostrophic contours of the lower layer ( f/h 2 ) over the flat bottom (upper panel) and those over the ridge (lower-left panel) in the case of the flow field in Fig. 3. Also shown is the horizontal distribution of contour lines of f/h (lower-right panel) over the ridge. Unit is in cm 1 s 1. Contour intervals are cm 1 s 1 for f/h 2 and cm 1 s 1 for f/h. tasy is accomplished through the whole domain of the present model. In the above experiment, the modeled ocean is driven by the annual mean wind stress. We here adopt the twolayer numerical model with the ridge, driven by the fluctuating wind stress expressed by Eq. (7). Annually averaged distributions (not shown) of the streamfunction and upper-layer thickness are identical to those in Fig. 3. It is interpreted that the steady-state solution accomplishing isostasy is superimposed on the timedependent part of the solution. Thus, the ridge has almost no effect on the annually averaged circulation. b. Annual variation Figure 5 shows the streamfunction every 60 days in the experiment with the ridge and wind stress varying in time. The volume transport has a large variation east of the ridge with an annual range of more than 40 Sv [see panels of day 180 (midsummer) and day 360 (midwinter)]. However, west of the ridge, a gyre with the volume transport of more than 40 Sv is maintained throughout the year. Figure 6 shows the time series of the streamfunction at the eastern and western edges of the ridge. Positive streamfunction represents net northward volume transport between the western boundary and each point. Also shown is the negative value of the nontopographic Sverdrup transport zonally integrated between the eastern sidewall and each point. This value is estimated by Eq. (8) using the time-varying wind stress. The annual means of the calculated volume transport on the eastern and western sides of the ridge are 40 Sv and 42 Sv, respectively. Annual ranges on the two sides are 45 Sv and 13 Sv, respectively. The annual range of the calculated volume transport is nearly the same as that of the nontopographic Sverdrup transport

7 1000 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 5. Horizontal distributions of the streamfunction every 60 days in the two-layer model with the ridge, driven by the wind stress varying annually. Broken lines represent the location of eastern and western edges of the ridge. Contour interval is 5 Sv. The streamfunction within the western boundary layer is omitted because of over crowding.

8 MARCH 2002 ISOBE AND IMAWAKI 1001 FIG. 6. Time series of the streamfunction (solid line) at eastern and western edges of the ridge, whose locations are shown in the upper panel. The broken line shows the time series of the nontopographic Sverdrup transport at corresponding point. east of the ridge, because the flat-bottom region extends east of the ridge. In addition, the phase of the calculated volume transport variation is nearly the same as that of the Sverdrup transport because the barotropic adjustment is achieved rapidly. However, the annual range decreases drastically west of the ridge in comparison with that of the nontopographic Sverdrup transport at the same point. On the other hand, the annual mean is nearly the same as that of the nontopographic Sverdrup transport. The cause of the reduction of the annual range west of the ridge is readily understood, considering the steady-state solution mentioned previously. The steadystate solution is equal to the annually averaged part of the solution in the time-dependent experiment. Isostasy is achieved in the steady-state solution, so that the effect of the ridge disappears. Therefore, the steady-state solution is permitted in the whole domain including west of the ridge. In contrast, isostasy is not achieved in the time-dependent part of the solution because the annual period is too short for the long baroclinic Rossby wave to cross the ocean. Thus, lower-layer motion remains only in the time-dependent part of the solution. Motion propagates westward because of the planetary effect, but the signal of the time-dependent part of the volume transport is prohibited from crossing the ridge due to the topographic effect. As a result, the annually averaged part of the solution (steady-state solution) is dominant in the western portion of the ridge. Although the annual range of the volume transport variation west of the ridge is much smaller than that of the nontopographic Sverdrup transport there, the volume transport varies in time slightly. Figure 7 shows the time series of the streamfunction at the western edge of the ridge, which is compared with the time series of the volume transport calculated by a one-layer numerical model with the ridge, driven by the same time-varying wind stress. As mentioned previously, the result in the one-layer model is described by the topographic Sverdrup relation. Above the ridge imposed in this model, almost all f/h contours entering from the east of the ridge turn to the south and encounter the southern sidewall (see the lower-right panel of Fig. 4). Thus, in the one-layer model, variability with an annual range west of the ridge is restricted to about 3 Sv. On the other hand, the annual range of the volume transport west of the ridge is about 10 Sv in the two-layer model. That is, the annual range of the volume transport in the twolayer model is smaller than the range of the nontopographic Sverdrup transport, but larger than that of the topographic Sverdrup transport. This means that the baroclinic activity amplifies the annual range of the volume transport. In the flat-bottom ocean without bottom friction, the baroclinic activity does not affect the volume transport but affects the vertical structure of the current. Therefore, the amplification of the volume transport variability in the two-layer model, as shown in Fig. 7, is

9 1002 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 7. Time series of the streamfunction (solid line) at the western edge of the ridge. Note that the scale of the ordinate is enlarged compared to that in Fig. 6. Broken line indicates the time series of the streamfunction at the same point in the one-layer model; the annual mean transport of the one-layer model (3 Sv) is shifted to that of the two-layer model (42 Sv). induced by the baroclinic activity generated above the ridge. As shown in Fig. 7, the phase of the volume transport in the one-layer model is nearly the same as that of the nontopographic Sverdrup transport at the same point (see lower-left panel of Fig. 6). The maximum volume transport appears on day 0 or day 360 (midwinter), while the minimum value appears on day 180 (midsummer). However, the phase in the two-layer model is delayed about one month. Figure 8 shows the y t (distance from the southern sidewall time) plot of the streamfunction along the western edge of the ridge. Thick broken lines represent times when the maximum and minimum values appear at each latitude. The annual variation is remarkable between 500 and 1500 km from the southern sidewall, so these two lines are depicted within this area. It is found that the phase is delayed northward. In the one-layer model, the phase delay is minimal because barotropic adjustment is achieved instantaneously compared to the annual timescale at all latitudes. Thus, the phase delay in the two-layer model is due to the baroclinic activity generated on the ridge. The baroclinic activity, which determines the annual range and phase of the volume transport west of the ridge, is discussed in detail in the next section. FIG. 8. Temporal variation of the streamfunction along the western edge of the ridge. The ordinate represents the northward distance (y) from the southern sidewall. Two broken lines indicate the times at which the maximum and the minimum values appear at each latitude. Contour interval is 5 Sv. 4. Discussion a. Anomaly fields We look at anomaly fields from annually averaged values because the baroclinic activity affects only the time-dependent part of the solution. Figure 9 displays anomalies of the upper-layer thickness (left panels) and streamfunction (right panels) every 60 days. The anomaly fields in the western part (0 x 3200 km) of the model domain are shown in order to emphasize the process around the ridge. As shown in the anomaly field of the upper-layer thickness on day 360, the negative anomaly is generated in the southeastern part of the ridge (labeled a ). This anomaly moves westward (see a on day 60, 120, and 180). Thereafter, the negative anomaly leaves the ridge and enters the flat-bottom region west of the ridge. Similarly, the negative anomaly of the upper-layer thickness is generated on day 180 in the northeastern part of the ridge (labeled b ). Although this anomaly also moves westward (see b on day 240, 300, and 360), its speed seems to be slow compared to that of a. In addition, an anomaly generated in the north vanishes on the western side of the ridge. It is also found that positive anomalies are generated on the eastern side of the ridge and move westward. The anomaly fields of the streamfunction show that FIG. 9. Horizontal distributions of the anomaly of the upper-layer thickness (left) and streamfunction (right) displayed every 60 days. Distribution only in the western part of the domain (0 x 3200 km) is depicted. Two long-broken lines in the central part of the domain indicate the location of the ridge. Contour intervals for the left and right panels are 20 m and 5 Sv, respectively. The short-broken lines are used for the negative anomalies. See the text for the explanations of letters a and b.

10 MARCH 2002 ISOBE AND IMAWAKI 1003

11 1004 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 10. Horizontal distributions of the magnitude of the impinging term above the ridge displayed every 60 days. Positive (negative) values indicate downwelling (upwelling). Contour interval is cm s 1 as shown in the lower portion of these panels. A broken line is used for the negative value. Contours near the sidewalls are omitted. an annual variation with a range of 40 Sv appears east of the ridge. On the contrary, the annual range of the volume transport is small west of the ridge. It is interesting to note that the negative (positive) anomaly of the streamfunction is released from the ridge to the west when the negative (positive) anomaly of the upper-layer thickness reaches the western edge of the ridge from the east (see, e.g., a and b both in the right and left panels). This implies that the anomaly of the upperlayer thickness above the ridge carries the information of the volume transport variation to the west of the ridge. In the next subsection, we show a physical interpretation for the generation and behavior of the anomaly of the upper-layer thickness, and show why such baroclinic activity is related to the anomaly of the volume transport. b. Physical interpretation In order to interpret the behavior of the upper-layer thickness, we further simplify the governing equations. As shown in Fig. 9, the anomaly of the upper-layer thickness is mostly generated apart from the sidewall (see a on day 360 or b on day 180), and presumably not generated by the process in the sidewall boundary layer. Except in the sidewall boundary layer, the Coriolis and pressure gradient terms are dominant in Eqs. (2) and (3) throughout the year (not shown). Thus, as a consequence of the geostrophy, Eq. (4) can be rewritten as follows (see appendix B for details): h1 h1 h1 h1 dh ũ u 2, (11) t x y H dx where characteristic velocities, ũ and, are defined as ũ R. (12) H y H x As shown in Eq. (11), two processes govern the temporal variation of the upper-layer thickness. One is expressed by the second and third terms on the left-hand side of Eq. (11), which are the advection of the upperlayer thickness due to the combination of the vertically averaged flow and westward propagation of the long baroclinic Rossby wave [see Eq. (12)]. The advection due to the vertically averaged flow occurs when nonlinearity remains in Eq. (4). The right-hand side of Eq. (11) expresses another process that generates the anom-

12 MARCH 2002 ISOBE AND IMAWAKI 1005 FIG. 11. Horizontal distributions of the characteristic velocity above the ridge displayed every 60 days. The speed is indicated by gradation and the direction is indicated by arrows. Contours near the sidewalls are omitted. aly of the upper-layer thickness when the lower-layer flow impinges on the bottom slope. When the lowerlayer flow is heading toward the shallow (deep) portion, upwelling (downwelling) occurs through this term. Hereafter, we call this the impinging process as described by Isobe (2000). The ridge extends meridionally in this model, so that the impinging process is induced only by the zonal flow in the lower layer. Next, we show how these two processes work around the ridge. Figure 10 shows the distribution of the impinging term above the ridge (1550 km x 2050 km) every 60 days. As mentioned previously, the lower-layer flow remains throughout the annual cycle because isostasy is not accomplished for such short period variation. This means that the stratification acts as a high-pass filter on motion in the lower layer. The ridge prohibits motion from propagating westward due to the topographic effect so that the lower-layer flow impinging on the bottom slope is restricted to the eastern side of the ridge. Therefore, the impinging process works mainly on the eastern side of the ridge as shown in Fig. 10. Hence, the anomaly of the upper-layer thickness is generated on the eastern side of the ridge. Figure 11 shows the distribution of the characteristic velocities above the ridge every 60 days, representing the advection process of the upper-layer thickness. In general, the anomaly of the upper-layer thickness generated on the eastern side of the ridge is carried westward above the ridge. In the northern part, it is found that magnitudes of the characteristic velocities are small, and directions change both in time and space. This is because directions of two components of the characteristic velocity (i.e., the vertically averaged flow and westward propagation of the long baroclinic Rossby wave) are opposite in the northern part of the ridge. Namely, the propagation speed of the anomaly of the upper-layer thickness varies meridionally. The anomaly generated in the southern part of the ridge quickly moves westward, while the anomaly in the northern part is likely to move slowly. Thereafter, the anomaly of the upper-layer thickness reaches the western half of the ridge. Figure 12 shows the speed of the lower-layer flow above the ridge every 60 days. The lower-layer flow almost vanishes above the western half of the ridge because the topographic effect prohibits lower-layer motion from crossing the ridge and because the steady-state solution with isostasy dominates the western half of the ridge. As shown in Fig. 12, large lower-layer flow is found along geostrophic contours of the lower layer east of the ridge (see lower-left panel of Fig. 4). Figure 13 shows the space time plot of the speed of the lower-layer flow along line A B parallel to the geostrophic contours. The speed of the lower-layer flow is large both in summer

13 1006 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 FIG. 12. Horizontal distributions of the speed of the lower-layer flow above the ridge displayed every 60 days. Contour interval is 2 cm s 1. Also shown is the contour of 1 cm s 1 by the broken line. FIG. 13. Space time plot of the speed of the lower-layer flow along the line A B over the ridge, whose location is shown in the right panel with horizontal distribution of the speed on day 360. Contour interval is 2 cm s 1. Stippling has been chosen to emphasize speed greater than 6 cm s 1. and winter because the anomaly of the volume transport is large in these seasons. It is found that lower-layer motion generated around A propagates toward the southern sidewall with a timescale of about 50 days. In addition, lower-layer motion can be seen over the western half of the ridge although its speed is considerably weak. This motion also propagates toward the northern sidewall with a similar timescale (not shown). Thus, lower-layer motion generating the anomaly of the upperlayer thickness quickly propagates toward the sidewall, and decays afterwards. Consequently, the anomaly of the upper-layer thickness, generated by lower-layer motion east of the ridge, is not accompanied with lower-layer motion when it reaches the western edge of the ridge. Namely, isostasy is accomplished with respect to each anomaly of the upper-layer thickness moving over the bottom topography. As a result, the positive (negative) anomaly of the upper-layer thickness carries the information of the positive (negative) anomaly of the volume transport when it reaches the western edge of the ridge. This experiment shows that the annual range of the volume transport variation is about 10 Sv west of the ridge. The variation is caused mostly by the baroclinic activity generated on the ridge. As mentioned previously, the time when the anomaly reaches the western edge of the ridge varies meridionally because of the difference of the characteristic velocities. Hence, the

14 MARCH 2002 ISOBE AND IMAWAKI 1007 phase of the annual variation of the volume transport is delayed northward as shown in Fig. 8. c. Comparison with the ASUKA observations As mentioned previously, the Kuroshio transport in the present study is defined as the volume transport between the western boundary and western edge of the ridge, corresponding to that of the Kuroshio throughflow across the whole ASUKA line. We here compare the present model results with observed values in Fig. 1, although rigorous comparison should be done using a more realistic ocean general circulation model. As shown in Fig. 1, the observed Kuroshio transport across the ASUKA line has an annual range of about 10 Sv, which is one-fourth or one-fifth of the Sverdrup transport estimated from ECMWF wind data. In our model, the annual range of the wind stress curl integrated zonally is adjusted to be the same as that estimated by the observed wind. The resultant annual range of the volume transport west of the ridge is about 10 Sv in the model (see Fig. 6), which is nearly the same as the observed value despite the simplified topography of the model. Considering that a one-layer model with realistic topography is unlikely to reproduce the annual range of the Kuroshio volume transport (e.g., Kubota et al. 1995), it is suggested that the annual range of the Kuroshio volume transport is mostly determined by the baroclinic activity generated above the ridge. In the present model, the phase of the annual variation of the Kuroshio transport is delayed about one month in comparison with that of the Sverdrup transport. However, such a delay is not clear in the observed transport in Fig. 1. We wish to emphasize that the phase of the annual variation of the volume transport varies in latitude as shown in Fig. 8. This means that the phase of the annual variation of the observed Kuroshio transport cannot be reproduced by a model with a simplified topography and wind field. d. Kuroshio transport across the PN-line In the present study, our concern is mostly focused on the annual variation in the volume transport of the Kuroshio throughflow across the ASUKA line. However, previous observational and numerical studies often focus on the eastward Kuroshio transport southwest of Japan, especially across the PN line in the East China Sea (see Fig. 1 for its location). For instance, based on the geostrophic calculation referred to the observed surface current velocity, Ichikawa and Chaen (2000) show that the Kuroshio transport across the PN line is maximum in summer and minimum in winter with an annual range of 14 Sv. We here consider how the annual range of the Kuroshio transport is determined for the PN line. Besides the annual variation controlled around the Izu Ogasawara Ridge, annual variation of the Kuroshio transport across the PN line may contain the variation of the closed circulation in the Philippine Basin. It is reasonable to consider that the annual variation of the Sverdrup transport integrated over the Philippine Basin is compensated by the eastward Kuroshio transport southwest of Japan. However, according to the numerical modeling by Sekine and Kutsuwada (1994), such a variation is blocked by the shelf slope east of Ryukyu Islands, and cannot propagate into the East China Sea. Rather, local downstream wind stress is responsible for the annual variation of the Kuroshio transport across the PN line (Ichikawa and Beardsley 1993). Besides the local wind forcing, the baroclinic activity may enhance the annual range of the Kuroshio transport across the PN line. Using a realistic ocean general circulation model, Kagimoto and Yamagata (1997) reproduce the annual variation of the Kuroshio transport across the PN line. They show the large contribution of an anticyclonic eddy to the Kuroshio transport variation. Their study suggests that the annual variation of the Kuroshio transport is controlled by baroclinic activity around the Ryukyu Islands. e. Variation with other timescales It is of interest to discuss the response of the simplified ocean model with the ridge to winds with various periods although this was not the main subject of this study. Even if the wind varies on very short timescales (less than annual), the impinging process occurs above the ridge because the lower-layer flow is still found at higher frequencies. However, the anomaly of the upperlayer thickness does not become large because upwelling and downwelling stop at once as the wind varies rapidly. Thus, the baroclinic activity does not work effectively. As a result, the meridional ridge acts as a barrier to the westward propagation of the volume transport variation. If the timescale of the wind variation is much longer than the time taken for the long baroclinic Rossby wave to cross the ocean, the baroclinic activity again does not work effectively above the ridge because isostasy is accomplished even east of the ridge. The baroclinic activity on the ridge, modifying the amplitude and phase of the volume transport variation, occurs for timescales up to several years. In fact, decadal variation of the sea level in the Gulf Stream region, although not the volume transport, is well reproduced by simple numerical models in which baroclinic Rossby waves are forced by the observed wind (Sturges and Hong 1995; Sturges et al. 1998; Hong et al. 2000). 5. Conclusions In the present study, we identify the baroclinic activity inducing the annual variation of the Kuroshio volume transport observed on the ASUKA line. The scenario is summarized as follows. For annual variation, lower-layer motion is found in areas surrounding the ridge because isostasy is not

15 1008 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 achieved within such a short timescale. Thus, the flow impinges on the bottom slope. Anomalies of the upperlayer thickness are generated on the eastern side of the ridge through the impinging process expressed by the term on the right-hand side of Eq. (11). Thereafter, anomalies move westward with characteristic velocities composed of the vertically averaged flow and westward propagation of the long baroclinic Rossby wave. As anomalies of the upper-layer thickness move westward above the ridge, isostasy is accomplished with respect to these anomalies. As a result, the positive (negative) anomaly of the upper-layer thickness carries information about the positive (negative) anomaly of the volume transport as it reaches the western edge of the ridge. Thereafter, anomalies of the volume transport are released to the west of the ridge. When modeling the annual variation of the Kuroshio volume transport, it is important to reproduce the baroclinic activity as well as the circulation induced by the local wind forcing. Particularly, the accurate expression of the impinging process. [see Eq. (11)] is crucial because this process is a source of the baroclinic activity controlling the annual cycle of the Kuroshio volume transport. Acknowledgments. Authors express their sincere thanks to Drs. Yukio Masumoto and Hiroshi Uchida for their fruitful discussions. Thanks are also extended to Mr. Rolando S. Balotro for his critical reading of the manuscript. Detailed comments made by the editors and two anonymous reviewers helped to clarify many parts of an early version of the manuscript. This study has been supported by the Core Research for Evolutional Science and Technology (CREST) of Japan Science and Technology Corporation (JST). APPENDIX A Applicability of the Model Topography to the Real Ocean In the present study, we emphasize the impinging process as a source of the baroclinic activity above the ridge. As shown on the right-hand side of Eq. (11), the magnitude F of this process is measured by h1 H F u 2, H x where h 1, H, and u 2 are the upper-layer thickness, depth, and lower-layer velocity, respectively. Applying idealized topography in the present study [h m, H 3000 m, H/ x 1500 m/(500 km/2)], F above the ridge is estimated to be u 2. As shown in Fig. 1, the real Izu Ogasawara Ridge is narrower and steeper than the modeled ridge (W 200 km; the ridge with height 2000 m in a flat-bottom region with depth 5000 m). A narrow ridge requires fine resolution of the model, so we adopted a relatively gentle slope. In addition, the lower-layer flow would be weakened in the flat-bottom region with increased depth of 5000 m. As shown in the text, the lower-layer flow is the time-dependent part of the barotropic flow (i.e., vertically homogeneous flow). Even though the deeper flatbottom region is adopted in the model, time-dependent part of the volume transport does not change because it is determined by the wind stress. Therefore, multiplying the ratio of the model to real depths, the real lower-layer flow u 2 is evaluated to be 0.6u 2. Thus, a plausible value for F for realistic topography [h m, H 5000 m, H/ x 2000 m/(200 km/2), and u 2 ] is estimated to be u 2. This value is nearly the same as that for the modeled topography. The values of F are nearly the same even if H is replaced with the mean depth on the slope. Therefore, the modeled modification of the topography likely has little effect on the impinging process. APPENDIX B Simplification of the Governing Equations Assuming geostrophy, Eqs. (2) and (3) can be written as h f ( ) g x h f (u u ) g (B1) y Using Eqs. (6) and (B1), the velocities in the upper layer are obtained as 1 g h2 h1 u1 H y fh y 1 g h2 h1 1. (B2) H x fh x Substituting the above velocities into Eq. (4) yields h1 1 h1 1 h 2 1 R t H y x H x y h1 1 g h1 h1 dh, (B3) H H y fh y dx where R 2 is the internal Rossby deformation radius squared ( g h 1 h 2 / f 2 H). Using Eqs. (6) and (B1), the lower-layer velocity in the x direction (u 2 ) is expressed as 1 g h1 h1 u2. (B4) H y fh y Substituting Eq. (B4) into the parenthesis on the righthand side of Eq. (B3), we have Eq. (11). REFERENCES Anderson, D. L. T., and P. Killworth, 1977: Spin-up of a stratified ocean, with topography. Deep-Sea Res., 24,

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