## Abstract

The effects of mesoscale eddies on the subduction and distribution of the North Pacific Subtropical Mode Water (STMW) are investigated using an eddy-resolving ocean general circulation model (OGCM). First, the subduction rate is calculated and the contribution of eddies to the subduction of STMW is estimated. It is found that eddy subduction significantly contributes to the total subduction of STMW. Second, eddy thickness transport and diapycnal flux are directly diagnosed to investigate the large-scale eddy-induced transport process of STMW. The large southward eddy thickness transport in the STMW core density is consistent with eddy subduction. The eddy transport on the isopycnal surface of STMW is directed down the thickness gradient and traverses the mean flow. The meridional eddy transport streamfunction indicates two eddy circulation cells south of 30°N, associated with the circulation of STMW. These cells flatten density surfaces, similar to the effect of the Gent and McWilliams (GM) scheme. The subducted STMW is gradually dissipated to lower or higher densities in the main thermocline, basically by vertical diffusion. Finally, local processes of eddy subduction and transport of STMW are explored using an anticyclonic eddy. Results imply two possible local processes of the eddy subduction of STMW. One is the destruction of a potential vorticity (PV) gradient by eddy mixing, where the PV gradient is due to winter deep mixed layer formation. The other is the southward translation of anticyclonic eddies that accompany low PV.

## 1. Introduction

North Pacific Subtropical Mode Water (STMW; Masuzawa 1969), which is located in the west of the subtropical gyre, is one of the important mode waters in the North Pacific. Many studies (e.g., Suga and Hanawa 1990; Suga and Hanawa 1995; Suga et al. 2004) have investigated the climatological features of its distribution, formation, and circulation based on hydrographic climatologies. STMW originates from late winter deep mixed layer (ML) water, and the subduction process (e.g., Stommel 1979; Marshall et al. 1993) of the deep ML water to the main thermocline is essential to the maintenance of STMW. The climatological features of subduction in the North Pacific have been estimated in several studies (e.g., Huang and Qiu 1994; Qiu and Huang 1995; Suga et al. 2008). From a theoretical viewpoint, subduction of STMW can be interpreted as subduction of low potential vorticity (PV) water across the mixed layer depth (MLD) front on outcrop lines (Kubokawa and Inui 1999; Nishikawa and Kubokawa 2007).

Because of the recent increase of observational data provided by the Argo profiling floats and satellite altimetry, detailed structures of the North Pacific STMW, which could not be obtained from climatologies or limited observations, have been revealed by observational studies. These studies demonstrate that the formation and circulation of STMW is highly variable in time and space and is strongly affected by mesoscale eddies and recirculation gyres in the Kuroshio Extension region (e.g., Uehara et al. 2003; Qiu et al. 2006, 2007; Oka 2009). Uehara et al. (2003) investigated the role of mesoscale eddies in the formation and transport of North Pacific STMW using hydrographic data by Argo profiling floats. They pointed out that a deep ML is accompanied by anticyclonic eddies, which contribute substantially to the STMW transportation. As indicated from these recent observations, small-scale disturbances (eddies) play a significant role in the formation and circulation of STMW, because its formation region (the Kuroshio Extension) is rich in eddies.

High-resolution ocean general circulation models (OGCMs) are important tools to determine how small-scale disturbances affect the formation and circulation of STMW. For the past decade, subduction of mode waters in the subtropical gyre has been investigated in many studies using high-resolution OGCMs. For example, the high-resolution OGCMs of Qu et al. (2002) and Tsujino and Yasuda (2004) realistically reproduced STMW and Central Mode Water (CMW) in the North Pacific with the associated frontal structures, and they estimated the corresponding subduction rate. Some of those studies have pointed out an important role of mesoscale eddies in the subduction of STMW. Hazeleger and Drijfhout (2000) investigated the role of eddies in the subduction of mode waters using an idealized high-resolution isopycnic model of the North Atlantic subtropical gyre. They estimated the eddy contribution to the total subduction rate and demonstrated the important contribution of the eddy subduction rate to the total subduction rate. In their calculation, the eddy contribution is lower than the mean flow by a factor of 2–3. Qu et al. (2002) estimated the annual subduction rate and the eddy contributions to that rate in the North Pacific using the output of a global high-resolution OGCM. They found that mesoscale eddies enhance the annual subduction rate in the formation region of the mode waters. In their estimates, the contribution of mesoscale eddies accounts for 34% of the total subduction.

Although these high-resolution OGCMs represent eddies and fronts related to mode waters to some extent, their resolution may not be sufficient to capture the fine structures of mode waters revealed in recent observations. These eddy-permitting OGCMs, with horizontal resolution ranging from 20 to 40 km, do not fully resolve mesoscale eddies (e.g., Tsujino and Fujii 2007). Therefore, the eddy effect in the previously mentioned studies might be partial and underestimated. Furthermore, eddy-permitting OGCMs tend to have difficulty representing the Kuroshio Extension, including its separation from the coast (e.g., Nakano et al. 2008). This leads to somewhat unrealistic representations of MLD and mode waters in the North Pacific. A promising approach to avoid these difficulties is to use an eddy-resolving OGCM whose horizontal resolution exceeds 10 km. Recently, Rainville et al. (2007) studied the formation of the North Pacific STMW using a high-resolution OGCM whose horizontal resolution is . Their analysis revealed the highly variable nature of STMW, and they demonstrated that eddies have a dominant role in the transport and distribution of STMW. However, their analysis was limited to a relatively localized region, and the length of their model outputs for analysis was 3 yr at most.

In this study, we use an eddy-resolving OGCM of the western North Pacific to investigate the role of eddies in the subduction and distribution of STMW. The model used in this study has several advantages. The horizontal resolution is high enough to resolve the fine structures of mesoscale eddies. This enables us to analyze the local subduction of STMW by eddies, which would be difficult in eddy-permitting models. The region of the present model covers almost the entire subtropical North Pacific, enabling us to explore the basin-scale circulation of STMW induced by eddies, which was not obtained by Rainville et al. (2007) because of the limitation of their analyzed region. The use of sufficiently long-term (12 yr) model outputs enables us to obtain clearly the decomposition of the model fields into mean and eddy components in eddy analysis. This length of the model outputs is much longer than that in the previous studies mentioned earlier. Making use of these advantages in the present eddy-resolving model, we aim to establish the basin-scale circulation of STMW in a fully eddying regime. This would improve the present understanding of the basin-scale circulation of STMW in the noneddying regime mentioned earlier.

This study has three specific objectives. First, subduction of STMW and the contribution of eddies to the subduction are quantified by calculating the kinematic subduction rates. Second, the effects of mesoscale eddies on the basin-scale transport and dissipation of STMW are examined by directly calculating eddy thickness flux and diapycnal flux, based on isopycnal analysis. Third, local processes that contribute to the eddy subduction and transport of STMW are explored using a local subduction event by an anticyclonic eddy.

The rest of this paper is organized as follows: Section 2 briefly describes the model and experiment configuration. Section 3 introduces general features of the simulated fields in relation to STMW. Section 4 examines subduction, eddy transport, and dissipation of STMW. Section 5 examines the local process. Section 6 discusses the eddy-induced circulation of STMW and compares with a noneddying model. Section 7 offers conclusions.

## 2. Model

The OGCM used is the Meteorological Research Institute Community Ocean Model (MRI.COM; Ishikawa et al. 2005). MRI.COM is a *z*-coordinate multilevel OGCM that solves the primitive equations under hydrostatic and Boussinesq approximations. It adopts an Arakawa B-grid arrangement, and coastlines are created by connecting tracer points instead of velocity points. The vertical coordinate near the surface follows the surface topography like the sigma coordinate models (Hasumi 2006).

Two simulations, an eddy-permitting simulation and an eddy-resolving simulation, are performed. The model domain of the eddy-permitting model is the Pacific Ocean north of 15°S, spanning from 100°E to 75°W (Fig. 1). At the southern edge of the domain, temperature and salinity are restored to the climatology of the *World Ocean Atlas 2001* (*WOA01*; Conkright et al. 2002) from top to bottom, with a restoring time of 30 days. The horizontal resolution is ¼° in the zonal direction and ⅙° in the meridional direction. Because the meridional resolution corresponds to 18 km, we refer to the eddy-permitting model as the 18-km model. The model domain of the eddy-resolving model is the western North Pacific, spanning from 15° to 65°N and from 117°E to 125°W (Fig. 1). The horizontal resolution is in the zonal direction and in the meridional direction. Because the meridional resolution corresponds to 6 km, we refer to the eddy-resolving model as the 6-km model. Both models have 50 levels in the vertical direction, with thickness increasing from 4 m at the surface to 600 m at the maximum depth (6300 m). The 6-km model is nested within the 18-km model using a one-way nesting method. Details of the nesting method are presented in Tsujino et al. (2006).

For both models, a biharmonic operator is used for horizontal turbulent mixing of tracers with a diffusivity coefficient of 1.0 × 10^{8} m^{4} s^{−1} for the 18-km model and 1.0 × 10^{7} m^{4} s^{−1} for the 6-km model. A biharmonic friction with a Smagorinsky-like viscosity (Griffies and Hallberg 2000) is used for momentum with a scaling constant *C* = 2.5 in their notation. The quadratic upstream interpolation for convective kinematics with estimated streaming terms (QUICKEST; Leonard 1979) and the uniformly third-order polynomial interpolation algorithm (UTOPIA; Leonard et al. 1993) are used as the vertical and horizontal tracer advection schemes. Vertical viscosity and diffusivity are determined by the turbulence closure level 2.5 scheme (Mellor and Yamada 1982; Mellor and Blumberg 2004). The parameterization of St. Laurent et al. (2002) for tidally driven mixing over rough topography is used as background diffusion.

The models are driven by the idealized repeating normal year forcing of the Coordinated Ocean-Ice Reference Experiments (COREs; Griffies et al. 2009). Therefore, there is no interannual variability in the forcing. Latent and sensible heat fluxes are calculated using the bulk formulae of Large and Yeager (2004). Though the model is driven by freshwater fluxes based on COREs, there is also a restoring term for sea surface salinity toward the monthly climatology from *WOA01* with a piston velocity of 4 m per 4 days. The 18-km model is integrated for 45 yr from a state of rest with an initial stratification derived from *WOA01*. Using the results from the 11th to the 45th year of the 18-km model as the side boundary condition, the 6-km model is integrated for 35 yr from the state of rest, with an initial stratification derived from the end of the 10th year of the 18-km model. A series of 5-day mean outputs for the last 12 yr (from the 24th to 35th years) of the 6-km model is used for analysis. Based on our experience, the 5-day mean outputs are sufficient for evaluating the effects of mesoscale eddies.

For comparison, a noneddying simulation with a horizontal resolution of 1° (called the 1° model) is also performed. Neutral physics with an isopycnal diffusion of tracers (Redi 1982) and the Gent and McWilliams (GM) parameterization for an eddy-induced tracer transport (Gent and McWilliams 1990; Gent et al. 1995) are used with isopycnal and thickness diffusion coefficients of 1.0 × 10^{3} m^{2} s^{−1}. A Laplacian friction with a Smagorinsky-like viscosity is used for momentum with a scaling constant *C* = 3.5. The other aspects of the 1° model, including the integration period, are identical to those of the 18-km model. The results of the 1° model will be used in the discussion in section 6.

## 3. General features of the simulation related to STMW

In this section, the 12-yr mean fields of the 6-km model results are compared with observational climatologies. Also, the general features of the simulated fields are briefly introduced in relation to STMW.

Figures 2a,b present sea surface heights of the model and the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) altimetry data (AVISO 2008). The model effectively reproduces the separation of the Kuroshio and the structure of the Kuroshio Extension. Figure 3 presents potential density *σ _{θ}* distributions along 160°E from the model and

*WOA01*. The model reproduces the upper-ocean stratification including STMW relatively well, except for a slightly lighter (warmer) bias. The core density of STMW in the 6-km model is 25.0

*σ*, which will be confirmed by calculating subduction rates in section 4. In this study, we define the STMW density range as

_{θ}*σ*= 24.8–25.3.

_{θ}Figures 2c,d depict eddy kinetic energy (EKE) distributions of the model and the AVISO altimetry data. EKE is defined by ()/2, where *u* and *υ* are zonal and meridional velocities, *u*′ = *u* − *u*, *υ*′ = *υ* − *υ*, and the bar denotes time mean. The model’s EKE distribution in the Kuroshio Extension region is similar to that from the AVISO data, though the model’s EKE is a little larger. Thus, the model’s variability and eddy activity in the Kuroshio Extension region are comparable to those of the observations. A region of large EKE off the southern coast of Japan appears in the model, but is not seen in AVISO. This feature is often found in high-resolution models in which a biharmonic operator is used for viscosity and the viscosity coefficient is small. Its effect on STMW subduction is considered to be small because its location is far from the STMW subduction region.

Figure 4 depicts PV distributions on isopycnal surfaces from the model and *WOA01*. PV *q* at an original model grid point is calculated by

Here, *ρ* is potential density, *f* is the Coriolis parameter, *ζ* = (∂*υ*/∂*x*) − (∂*u*/∂*y*) is relative vorticity, and *ρ*_{0} is a reference density; then, *q* is casted in isopycnal layers. The Montgomery potential (*M* = *p* + *ρgz*) is superimposed on the figures, where *p* is pressure, *z* is depth, and *g* is gravitational acceleration. This gives a streamfunction on isopycnal surfaces. Figure 4a indicates that the streamlines are approximately along the contours of PV in the model. Low PV (less than 2.0 × 10^{−10} m^{−1} s^{−1}) in Fig. 4a corresponds to STMW in the model, and low PV (less than 1.5 × 10^{−10} m^{−1} s^{−1}) in Fig. 4b corresponds to STMW in *WOA01*. Although the core density is lighter, the model reproduces the low PV distribution of STMW relatively well.

## 4. Large-scale effects of eddies on STMW

This section examines the effects of eddies on the large-scale circulation of STMW. Section 4a investigates the subduction process, which is important in considering the budget of STMW in the main thermocline. The remaining subsections discuss isopycnal analysis and calculation of eddy thickness flux (section 4b), eddy transport streamfunction (section 4c), and diapycnal flux (section 4d).

### a. Subduction rate

The subduction rate is useful in examining the transport of mode waters to the main thermocline and may be calculated in several ways. This study adopts kinematic approaches. Two simple methods of calculating subduction rate are often used in model studies with high resolution (e.g., de Miranda et al. 1999; Hazeleger and Drijfhout 2000; Tsujino and Yasuda 2004; Valdivieso da Costa et al. 2005), though each has advantages and disadvantages. One is based on a maximum climatological ML, and the other follows a varying ML. In this section, we calculate the subduction rates using these two methods and discuss the subduction of STMW by comparing them. Both methods can be used to quantify the eddy effects on the subduction of STMW by introducing eddy subduction rates, although they may not be direct assessments for eddy effects, as discussed later.

With the first method, which is similar to that of Marshall et al. (1993), the subduction rate is calculated as the flux across a maximum climatological ML base. Figure 5 presents the maximum MLD distribution used in this analysis. This subduction rate is based on the fact that there is no interannual variability in the forcing (e.g., Hazeleger and Drijfhout 2000) and basically avoids the effect of reentrainment. It gives a net annual volume flux at the maximum ML base into/out of the main thermocline. Although the model forcing has no interannual variability, the model field does have an interannual variation that is caused mainly by the internal dynamic variation of the Kuroshio Extension (e.g., Qiu and Chen 2005). As discussed later, the contribution of the interannual variation is relatively small compared to that of the mesoscale eddy variation.

In this definition, the local and instantaneous subduction rate *s* is given by

where *h _{b}* is the maximum ML thickness,

**u**is the horizontal velocity,

*w*is the vertical velocity, and

**∇**is the horizontal gradient operator. The annual subduction rate

*S*of a density range (

*σ*<

_{a}*σ*<

*σ*) is calculated by regionally and temporally integrating

_{b}*s*,

Here, (*i*, *j*) is the horizontal grid index, Δ*A* is the area of a grid, *t* is time, and *T* is the averaging period. The integration region is depicted in Fig. 5. We introduce three subduction rates.

Total subduction rate

*S*_{total}:This is calculated from the 5-day mean outputs for 12 yr.

Mean subduction rate

*S*_{mean}:This is calculated from the monthly 12-yr mean fields.

Eddy subduction rate

*S*_{eddy}:This is defined by the difference between the total and mean (i.e.,

*S*_{eddy}=*S*_{total}−*S*_{mean}).

Adopting the average period of 12 yr presumably excludes the mesoscale eddy effect from the monthly 12-yr mean fields. We estimated the contribution of the interannual variation to the eddy subduction rate *S*_{eddy} of STMW and obtained 20%–30%, using a series of annually averaged data. Thus, *S*_{eddy} is basically dominated by the direct mesoscale eddy variation.

The second method is based on varying ML, and the subduction rate is calculated by following it (e.g., Tsujino and Yasuda 2004; Valdivieso da Costa et al. 2005). This subduction rate gives a net detrainment/entrainment from/into the ML. It explicitly evaluates reentrainment and can be used to examine reemergence. With this definition, local and instantaneous subduction rate *d* is given by

where *h _{m}* is the varying ML thickness. The annual subduction rate

*D*of a density range (

*σ*<

_{a}*σ*<

*σ*) is calculated by regionally and temporally integrating

_{b}*d*,

The integration region is common to Eq. (3). The definition and calculation of the three subduction rates (*D*_{total}, *D*_{mean}, and *D*_{eddy}) are the same as those used with the first method (*S*_{total}, *S*_{mean}, and *S*_{eddy}).

Figures 6a–c depict the three subduction rates (*S*_{total}, *S*_{mean}, and *S*_{eddy}) at 0.1 *σ _{θ}* interval. The total subduction

*S*

_{total}(Fig. 6a) has a peak at

*σ*= 25.0–25.1. This corresponds to the STMW core density. The relatively high values at

_{θ}*σ*= 26.0–26.5 correspond to those of CMW. The peak of the mean subduction

_{θ}*S*

_{mean}for each mode water is less remarkable, though it is found at

*σ*= 25.0–25.2 and

_{θ}*σ*= 26.0–26.1 (Fig. 6b). The eddy subduction

_{θ}*S*

_{eddy}(Fig. 6c) has a remarkable peak at

*σ*= 25.0–25.1, which corresponds to the STMW core density. We can formally calculate the total subduction rate for STMW (

_{θ}*σ*= 24.8–25.3) as 4.93 Sv (1 Sv ≡ 10

_{θ}^{6}m

^{3}s

^{−1}), comprised of 2.41 Sv from the mean subduction and 2.52 Sv from the eddy subduction. Thus, eddy subduction plays an important role in the STMW subduction. The eddy subduction rate indicates narrow positive subduction in the STMW density range and broad negative subduction in the lighter density range (

*σ*= 22.8–24.8). This result implies a vertical eddy-induced circulation, which will be discussed in the following subsections. Integration of the eddy subduction over an entire density range becomes almost zero, implying that the eddy-induced circulation is almost closed in the integration region.

_{θ}To examine the role of the mean subduction *S*_{mean} in the STMW subduction, the subduction rates calculated between 130°E and 160°W (Figs. 6a–c) are divided zonally into those between 130° and 144°E (Figs. 6d–f) and those between 144°E and 160°W (Figs. 6g–i; see also Fig. 5). The mean subduction *S*_{mean} (Fig. 6b) consists of the eastern mean subduction (Fig. 6h) and the western mean obduction (negative subduction; Fig. 6e). This is an effect of the large-scale mean flow across the MLD gradients, because the maximum ML becomes shallow along the mean flow in the eastern mean subduction region and becomes deep along the mean flow in the western mean obduction region (white dotted lines and MLD in Fig. 5). Because of the cancellation of the STMW peak of the eastern mean subduction by the western mean obduction, the STMW peak in the mean subduction *S*_{mean} in Fig. 6b is less remarkable. The eastern mean subduction rate in Fig. 6h may correspond to the subduction rates by Qiu and Huang (1995) and Suga et al. (2008), because their subduction rates may have missed the effect of the western mean obduction caused by the Kuroshio. In fact, the mean subduction (Fig. 6h) is qualitatively comparable to the subduction rate by Suga et al. (2008, their Figs. 5b, 6b), which is the updated calculation of the subduction rate in the North Pacific based on state-of-the-art climatological data.

Figure 7 presents the three subduction rates (*D*_{total}, *D*_{mean}, and *D*_{eddy}) at 0.1*σ _{θ}* interval. The total subduction

*D*

_{total}(Fig. 7a) has two remarkable peaks of mode waters (STMW and CMW) and negative values in lower densities. Here,

*D*

_{total}is dominated by the MLD change term (∂

*h*/∂

_{m}*t*) (not shown). These features are basically consistent with the subduction rate calculated in Tsujino and Yasuda (2004) if the difference of the calculation region is considered. With the exception of the negative values in lower densities, which are partly due to the southern limitation (17°N) of the calculation region,

*D*

_{total}is qualitatively similar to

*S*

_{total}(Fig. 6a). The mean and eddy subduction rates,

*D*

_{mean}and

*D*

_{eddy}, are also qualitatively similar to

*S*

_{mean}and

*S*

_{eddy}in mode water densities. Again, we can formally calculate the total subduction rate for STMW (

*σ*= 24.8–25.3) as 11.16 Sv, comprised of 5.08 Sv from the mean subduction and 6.08 Sv from the eddy subduction, again suggesting the importance of the eddy subduction in the subduction of STMW. An important implication from this result is that the STMW peak of the eddy subduction is related to the rapid shoaling of the deep ML accompanied by anticyclonic eddies (see section 5). The flux of

_{θ}*D*

_{total}is generally larger than that of

*S*

_{total}in the mode water densities. This is related to the difference between the depths where these subduction rates are calculated and implies that the detrained water in

*D*

_{total}is strongly dissipated before reaching the maximum ML base. This issue is discussed further in section 4d.

As stated earlier, reentrainment and reemergence can be assessed using the second method. Figure 8 depicts the isopycnal distribution of the total subduction rate *D*_{total} on the STMW core density (*σ _{θ}* = 25.05). The effect of the MLD change dominates in the strong detrainment (subduction) region near March outcrop. However, a broad entrainment region exists north of the March outcrop, where reentrainment occurs. The entrainment region north of the March outcrop corresponds to the region where the remote reemergence of STMW occurs (Sugimoto and Hanawa 2005), because the eastward mean flow dominates there (Fig. 8). Many patches with high entrainment rates are found in this region, implying that reemergence events are related to the excursion of eddies.

The effects of eddies on the subduction of STMW are formally estimated by introducing the eddy subduction rates (*S*_{eddy} and *D*_{eddy}), which indicate large contributions of eddy subduction. However, these are not direct evaluations of the eddy effects by definition. For direct assessment, analysis in isopycnal coordinates is useful (e.g., de Szoeke and Bennett 1993), because the motion of seawater approximately conserves density. In the following sections, the effects of eddies are directly evaluated using thickness fluxes in isopycnal coordinates.

### b. Eddy thickness flux

In this section, we calculate eddy thickness flux based on isopycnal analysis, which more comprehensively evaluates eddy effects on the STMW transport. Detailed formulation of the eddy flux is presented in Tsujino et al. (2010).

We introduce the total thickness flux (*h***u**) in isopycnal coordinates, where *h* is the thickness defined by *h* = −Δ*ρ*(∂*z*/∂*ρ*) = *z*(*σ _{a}*) −

*z*(

*σ*),

_{b}*z*is the depth of the isopycnal, Δ

*ρ*=

*σ*−

_{b}*σ*,

_{a}**u**= (

*u*,

*υ*) is the horizontal velocity on the isopycnal, and the bar denotes isopycnal time mean. We can divide

*h*and

**u**into the isopycnal time mean and the difference,

*h*=

*h*+

*h*′ and

**u**=

**u**+

**u**′, where the prime denotes the difference from the isopycnal time mean. The total thickness flux is then decomposed as follows:

Here, *h***u** is the mean thickness flux and *h*′**u**′ is the eddy thickness flux. The period of the time mean is 12 yr.

Figures 9a,b present the total and eddy meridional thickness fluxes (*hυ* and *h*′*υ*′), which are zonally integrated from 144°E to 180°. The total meridional thickness flux (Fig. 9a) has a peak of southward transport at 28°–33°N on *σ _{θ}* = 25.0. This corresponds to the subduction of STMW and is consistent with the total subduction rates (Figs. 6a, 7a). The eddy meridional thickness flux (Fig. 9b) also has a peak of southward transport at 28°–30°N on

*σ*= 25.0, corresponding to the subduction of STMW. We calculated the total and eddy southward transports across 29°N in the STMW density range (

_{θ}*σ*= 24.8–25.3) and obtained 8.20 and 2.70 Sv. This implies that the eddy thickness flux significantly affects the STMW subduction and transport.

_{θ}Figure 9c depicts the distribution of the eddy thickness flux vector divided by the mean thickness (*h*′**u**′/*h*) known as the bolus velocity, on the isopycnal surface of the STMW core density (*σ _{θ}* = 25.05). The PV (shading), Montgomery potential (white solid contours), and MLD front (white dotted line) are superimposed. The eddy thickness flux is in the southward to southeastward direction across the MLD front, down the mean thickness gradient, and across the mean flow. Figure 9c implies that the southward eddy thickness flux causes the southward spreading of STMW (Fig. 4a).

### c. Eddy transport streamfunction

Calculation of meridional transport streamfunction facilitates determining the large-scale circulation of STMW and the eddy effects. We introduce the total transport streamfunction *ψ*_{total} in isopycnal coordinates by integrating the total meridional thickness flux (*hυ*) zonally and vertically:

Here, *ρ*_{max} is the bottom density, and we introduce the following eddy transport streamfunction based on McDougall and McIntosh (2001) and Lee et al. (2007): Using the Eulerian time-mean meridional velocity in depth coordinates (*υ*_{em}), we define the following mean transport streamfunction,

where mean thickness (*h*) is derived from a temporal average of depths of isopycnals. Because , the mean streamfunction [Eq. (8)] is closed at the surface. The eddy transport streamfunction is defined by the difference between the total and Eulerian mean streamfunctions,

The mean streamfunction [Eq. (8)] is calculated from the monthly 12-yr mean quantities (*h* and *υ*_{em}). The effect of seasonal variation is included in *ψ*_{em}, not in *ψ*_{eddy}.

Figure 10 presents the total and eddy transport streamfunctions (*ψ*_{total} and *ψ*_{eddy}). The output of the 18-km model is used to calculate the total transport streamfunction outside of the nesting region. The total transport streamfunction (Fig. 10a) is similar to that of Tsujino and Yasuda (2004, their Fig. 12b). The clockwise circulation in the subtropics is dominated by subduction. For example, a large southward transport at 28°–30°N on *σ _{θ}* = 25.0 reflects the total subduction of STMW. The eddy transport streamfunction (Fig. 10b) also has a large southward transport at 28°–30°N on

*σ*= 25.0, which reflects the subduction of STMW. Its structure is relatively consistent with the eddy subduction rates in Figs. 6c and 7c. South of 30°N are two eddy circulation cells related to the circulation of STMW: a clockwise cell at density lighter than

_{θ}*σ*= 25.0 and a counterclockwise cell below that. These eddy circulation cells flatten isopycnals, like the GM scheme (Gent and McWilliams 1990; Gent et al. 1995). The effect of these cells and their relation to the GM effect will be discussed further in section 6.

_{θ}The transport streamfunctions (Fig. 10) indicate that the subducted STMW is adiabatically transported along isopycnals. However, they also indicate that the subducted STMW gradually shifts to lower or higher densities, implying the dissipation of STMW. This tendency is relatively remarkable in the eddy streamfunction (Fig. 10b), and the effect of eddies may be implied. In the next section, we examine the diapycnal flux.

### d. Diapycnal flux

The transport streamfunctions discussed in the previous section imply the existence of STMW dissipation in the main thermocline region. In addition, the fact that the flux of *D*_{total} is larger than that of *S*_{total} in mode water densities (section 4a) implies the effect of strong dissipation in the seasonal thermocline region. To examine the dissipation of STMW, we calculate diapycnal flux (flux across isopycnals). Qiu et al. (2006) estimated the erosion of STMW in the recirculation gyre region where the seasonal thermocline dominates, and Rainville et al. (2007) evaluated the regionally averaged property of STMW erosion. In this study, we focus on the main thermocline region south of 30°N and investigate the horizontal and vertical structure of the STMW dissipation there. The causes of the diapycnal flux (diffusion terms) are also addressed.

The diapycnal flux *e* is defined by

where *z* is the depth of the isopycnal (e.g., de Szoeke and Bennett 1993). Figure 11 presents the 12-yr mean of the diapycnal flux on two isopycnals. The isopycnal *σ _{θ}* = 24.8 corresponds to the upper part of STMW. The diapycnal flux on this surface is upward in the main thermocline region (south of 29°N). The isopycnal

*σ*= 25.3 corresponds to the lower part of STMW. The diapycnal flux on this surface is downward in the main thermocline region (south of 31°N). These results indicate that the subducted STMW gradually shifts to the adjacent density and that the STMW itself becomes thin after subduction. This structure of diapycnal flux is also implied from the total transport streamfunction (Fig. 10a), which indicates upward flux at

_{θ}*σ*= 24.8 and slight downward flux at

_{θ}*σ*= 25.3 between 20° and 30°N.

_{θ}Figure 11a indicates a large positive diapycnal flux region near the March outcrop (white line), which means a large dissipation region. This region corresponds to the seasonal thermocline region where the variability of isopycnals and MLD is large. In Figs. 8 and 11a, the large diapycnal flux region corresponds to the high subduction rate (*D*_{total}) region (Fig. 8). This result implies that subduction there (*D*_{total}) is strongly affected by dissipation and that the detrained water tends to shift to lower densities by dissipation before it reaches the maximum ML base. Therefore, the subduction rate based on the maximum ML base *S*_{total} becomes smaller than that based on the varying ML base *D*_{total} in mode water densities (Figs. 6a, 7a).

The diapycnal flux *e* is due to explicit and implicit diffusions, because it corresponds to the source term of the density equation (e.g., de Szoeke and Bennett 1993). Although its general tendency is similar to that of the flux caused by the explicit vertical diffusion term, the diapycnal flux is several times larger (Fig. 12a). This discrepancy is assumed to be caused by numerical diffusion, because the horizontal diffusion is very small and the advection scheme in the present model (UTOPIA/QUICKEST) includes numerical diffusion. To confirm this assumption, we conducted another model experiment in which the second-order moment (SOM) scheme (Prather 1986) is used for the advection scheme instead of UTOPIA/QUICKEST. The numerical diffusion is very small in the model using the SOM scheme (e.g., Hofmann and Morales Maqueda 2006). Figure 12b presents the result. The flux caused by the explicit vertical diffusion term is enhanced, and the diapycnal flux is comparable. These results indicate that the general tendency of the diapycnal flux is essentially determined by the explicit vertical diffusion, although it is enhanced by the numerical diffusion in the present model. The result using the SOM scheme is not used for the present analysis, because this run is conducted for only 5 yr because of computational limitations and it was decided that 5 yr is not long enough for a faithful representation of the data, as indicated in Fig. 12b.

For comparison, the vertical diffusivity at 25°N, 160°E on *σ _{θ}* = 24.8 is roughly estimated by

*e*= ∂

*κ*(∂

*ρ*/∂

*z*)/∂

*ρ*(Hu 1996; Rainville et al. 2007), and

*κ*= 0.2 − 1.0 × 10

^{−4}m

^{2}s

^{−1}is obtained. This result is comparable to the estimation by Rainville et al. (2007).

## 5. Local processes

In the previous section, the significant contribution of mesoscale eddies in the subduction and transport of STMW was demonstrated by calculating the subduction rates and eddy thickness flux. In this section, we discuss two processes that may dominantly contribute to the eddy subduction and transport, using a local subduction event caused by an anticyclonic eddy.

Before examining the local processes, we confirm the relationship between anticyclonic eddies and the winter deep ML that is the source of mode waters. Figure 13 presents the 5-day mean fields of MLD and sea surface height on 7–11 March in the 30th year. The ML becomes deepest during this time every year. Results indicate that a deep ML occurs selectively at the anticyclonic eddies and recirculation gyres. ML is relatively shallow at the cyclonic eddies and troughs of the Kuroshio meander jet. This correspondence of anticyclonic eddies and deep ML is consistent with the observational results by Uehara et al. (2003), implying that anticyclonic eddies play an important role in the local dynamics of eddy subduction.

To determine how thick water is locally subducted and transported to the main thermocline by eddies, we consider the anticyclonic eddy whose trajectory is depicted in Fig. 14. The trajectory starts on 11 May and ends on 17 December in the 26th year. The anticyclonic eddy is first located in the north of the MLD front (Fig. 5) and stays there until mid-June. From mid-June to July, the eddy rapidly translates southward across the MLD front. After that, the eddy translates westward along the streamline of the mean flow.

Figure 15 presents the isopycnal PV distributions of *σ _{θ}* = 25.05 for four terms in the trajectory. The center of each figure corresponds to the center of the anticyclonic eddy. Figures 15a,b imply that the anticyclonic eddy brings low PV water from the north to the south on the eastern side of the eddy and brings high PV water from the south to the north on the western side of the eddy. This eddy mixing of PV causes the southward transport of thickness. Figures 15c,d, along with Fig. 14, imply that the anticyclonic eddy traps low PV water and translates southward. This also causes the southward transport of thickness by the eddy.

To generalize these findings, we make PV composites on anticyclonic eddies near the MLD front (27°–31°N) for 12 yr. The composites are made among anticyclonic eddies on the same days from the 24th to the 35th years. Figure 16 presents the results of 22–26 March and 3–7 September. Figure 16a (22–26 March) indicates that there is a PV gradient where low PV is in the north, and the anticyclonic eddy destructs the PV gradient by transporting low PV southward on the eastern side and transporting high PV northward on the western side. Figure 16b (3–7 September) indicates that low PV water is trapped in the anticyclonic eddy. From these results, we can consider the following two processes that cause the southward eddy thickness flux in the STMW subduction region.

Eddy mixing of PV, which destructs the PV gradient. The PV gradient is due to the late winter deep ML formation and is formed in spring.

Southward translation of anticyclonic eddies that accompany low PV.

It is assumed that the former process works in Figs. 15a,b and that the latter process works in Figs. 15c,d.

We roughly estimate the southward eddy thickness flux in the previous event and its contribution to the annual eddy flux. The southward eddy flux between 156° and 160°E at 29°N (Fig. 14) averaged from 16 May to 29 June (45 days) is 1.24 Sv. The annual number of anticyclonic eddies in the area 28°–30°N, 145°E–180° is also estimated, and an average of 2.7 is obtained. The annual existence of two or three anticyclonic eddies is enough to contribute to the annual eddy thickness flux of 2.70 Sv (section 4b). Thus, the local processes of the anticyclonic eddy discussed earlier may cause eddy subduction.

## 6. Discussion

In this section, based on the results of sections 4 and 5, we suggest a series of the eddy-induced transport processes of STMW as an eddy-induced circulation of STMW. Furthermore, we compare the present results in the eddy-resolving (6 km) model with those of the noneddying (1°) model to examine the role of mesoscale eddies in STMW circulation.

Based on the analyses in sections 4 and 5, the eddy-induced transport process of STMW is outlined as follows:

(i) Eddy subduction:

A deep ML is formed at the anticyclonic eddies and recirculation gyres (Fig. 13), producing low PV water. The low PV water is transported southward by the eddy mixing of PV and the southward translation of the anticyclonic eddy itself (e.g., Figs. 14, 15). It is subducted to the main thermocline across the MLD front.

(ii) Isopycnal eddy transport:

The subducted water is advected southward to southeastward, down the mean thickness gradient (the mean negative PV gradient), and across the mean flow (Fig. 9c).

(iii) Diapycnal transport:

After subduction, the water gradually shifts to the adjacent density by vertical diffusion (Fig. 11).

As compensation for these processes, water is obducted or transported northward, mainly at lighter density (Figs. 6c, 10b). A series of these processes might compose an eddy-induced circulation of STMW. The (traditional) mean circulation of STMW, in which low PV water is subducted across the MLD front by mean flow and advected southwestward along the mean streamline (e.g., Fig. 17a), also occurs. In reality, the STMW circulation should occur as a mixture of the eddy-induced transport process and the mean circulation and could not be divided.

It is worthwhile to compare the present results with the noneddying model and discuss the effects of eddies. Figure 17a, which depicts the PV distribution on the STMW density surface from the 1° model, is compared with Fig. 4a. The STMW distribution of the 6-km model is relatively broad in the zonal direction, and the eddy flux causes the southward spreading of STMW across the mean flow (Fig. 4a). In contrast, STMW of the 1° model (Fig. 17a) is relatively concentrated at the intersection of the MLD front and the outcrop (e.g., Kubokawa and Inui 1999; Xie et al. 2000; Nishikawa and Kubokawa 2007) and spreads southward to southwestward along the mean flow. These results indicate that eddy flux in the eddying regime significantly affects the subduction and transport structure of STMW and gives rise to a substantial difference between the STMW distribution of the eddying regime and that of the noneddying regime. The traditional image of STMW subduction (e.g., Luyten et al. 1983) should be modified in the eddying regime (Cox 1985).

Figure 17b depicts the GM transport streamfunction [*ψ*_{GM} = ∫(*κρ _{y}*/

*ρ*)

_{z}*dx*] estimated in the 1° model. The clockwise GM circulation cell in the lower density (above

*σ*= 25.0) south of 30°N is similar to the clockwise eddy circulation cell in Fig. 10b but somewhat weaker. Although the eddy circulation cell qualitatively coincides with the GM circulation cell, the local processes of the eddy transport discussed in section 5 may differ somewhat from the process related to the GM effect (e.g., baroclinic instability). These results imply that, although the reason might be incorrect, the GM parameterization has an effect similar to that of the eddy circulation cells obtained in the present model and is partly effective in improving the representation of STMW in low-resolution models.

_{θ}## 7. Concluding remarks

In this study, we use long-term outputs of an eddy-resolving OGCM of the western North Pacific under idealized repeating normal year forcings to investigate the effects of mesoscale eddies on subduction and distribution of STMW. We focus primarily on the main thermocline region.

Subduction of STMW and the effect of mesoscale eddies are quantified by calculating the kinematic subduction rates in two ways. Both methods confirm the large contribution (about half) of the eddy subduction to the total subduction in the STMW density, although these eddy subduction rates are formal estimates of the eddy effect. This effect is also indicated from the calculation of the total and eddy thickness fluxes, which provides a direct assessment of the eddy effect.

The effects of mesoscale eddies on the large-scale circulation and distribution of STMW are examined by directly calculating the eddy thickness flux and diapycnal flux based on isopycnal analysis. There is a large eddy thickness flux where the mean thickness (PV) gradient is large and subduction of STMW occurs. The direction of the eddy thickness flux is down the mean thickness gradient (up the mean PV gradient). The eddy transport streamfunction (Fig. 10b) indicates vertical eddy circulation cells south of 30°N, which include the subduction and dissipation of STMW. The subducted STMW is advected on isopycnal surfaces and is gradually dissipated to the lower or higher densities. This diapycnal transport of the subducted STMW is basically due to vertical diffusion, although numerical diffusion also exists in the present model.

Local processes of the eddy transport and subduction of STMW are explored using a local subduction event by an anticyclonic eddy. Deep ML or low PV occurs in anticyclonic eddies and recirculation gyres south of the Kuroshio Extension front. Two possible local processes are suggested. One is the eddy mixing of PV by eddy flow in the presence of a large PV gradient, which leads to the southward transport of thickness (low PV). The other is the southward translation of the anticyclonic eddy itself, which accompanies large thickness (low PV). Brief estimation indicates that the annual persistent existence of two or three anticyclonic eddies accompanying low PV accounts for the zonally integrated eddy thickness transport of STMW at 29°N. This result appears to be reasonable and consistent with the estimate of Uehara et al. (2003).

Based on these results, we suggest a series of eddy-induced transport processes of STMW on a basin scale, which consists of eddy subduction, isopycnal eddy transport, and diapycnal flux (see section 6). These eddy-induced transport processes of STMW revealed by the eddy-resolving model would play an important role in determining the mean STMW transport and distribution in the real ocean. Finally, we briefly discuss several issues to be clarified in the future.

The southward translation of anticyclonic eddies may be a key process in the eddy subduction and transport of STMW. Theoretical or simple model studies of isolated eddies confirm that anticyclonic (cyclonic) eddies move southwestward (northwestward) in the presence of the beta effect. Recent studies using satellite altimetry data indicate the same tendencies (e.g., Morrow et al. 2004; Chelton et al. 2007). The tendency of anticyclonic eddies to move southwestward is also found in the present eddy-resolving model. Some theoretical or simple model studies have discussed the mechanisms of the southward translation of anticyclonic eddies (e.g., Chassignet and Cushman-Roisin 1991; Morel and McWilliams 1997; Ito and Kubokawa 2003). Those mechanisms may be related to the cause of the eddy subduction. Furthermore, eddy–eddy interaction and properties of geostrophic turbulence (e.g., Theiss 2004) may be important in the southward translation of anticyclonic eddies. Clarifying these points will be an interesting subject of future study.

The effects of interannual variation and reemergence are briefly discussed in relation to STMW subduction (section 4a) and are important in discussion of the surface climate and comparison with observations. However, the effects in this study are partial, because the present model uses idealized repeating normal year forcing in which there is no interannual variability. To evaluate these effects more thoroughly, it will be necessary to use a hindcast run that is driven by interannually varying forcing. This is one of our future tasks.

Although the representation of STMW is highly improved by using eddy-resolving OGCMs whose horizontal resolution is higher than 10 km, there is still room for improvement. The representation of MLD distribution may be improved. Recent studies imply that submesoscale processes play an important role in representing MLD (e.g., Boccaletti et al. 2007). It may be worthwhile to use higher-resolution (submesoscale eddy-resolving) OGCMs to investigate the effect of submesoscale processes in STMW formation and subduction. Although the diapycnal fluxes were estimated in this study, the detailed process of the STMW dissipation and its relation to eddies remain unclear. Clarifying this point will also be important.

## Acknowledgments

Discussion with Prof. A. Kubokawa was useful to improve the analysis of this study. Comments from anonymous reviewers greatly help improve the manuscript. The numerical experiments were performed on the Earth Simulator at the Japan Agency for Marine Science and Technology (JAMSTEC). We thank Dr. Y. Tanaka for offering the computer resource and Ms. M. Ikeda for kind help in performing the numerical experiments. This study is conducted under the research project “KAKUSHIN” funded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT). We thank the project leader, Prof. H. Hasumi, for general support. This study is partially supported by the Japan Society for the Promotion of Science [Grant-in-Aid for Scientific Research (B) 21340133].

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## Footnotes

*Corresponding author address:* Shiro Nishikawa, Oceanographic Research Department, Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan. Email: snishika@mri-jma.go.jp