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  • View in gallery

    The meridional profiles of the specific temperature and the surface wind stress: (a) specific temperature Ta and (b) surface wind stress τ.

  • View in gallery

    Horizontal flow fields: (a) barotropic streamfunction (Sv ≡ 106 m3 s−1), horizontal current vectors at (b) z = −36 m, (c) z = −109 m, and (d) z = −199 m. In the shaded regions in (b)–(c), the current vectors are directed between ±22.5° with respect to the east, and their magnitudes are larger than 2 cm s−1. The current vector is plotted at each 2° × 2° grid, although the model resolution is 1° × 1°. The meridional boundaries of the model basin are located at 1° and 72° longitude.

  • View in gallery

    Horizontal distribution of the density σθ at (a) z = −2 m, (b) z = −54 m, (c) z = −148 m, and (d) z = −341 m.

  • View in gallery

    Distributions of the zonal flow, density, and potential vorticity in a meridional section in the western region: (a) zonal velocity (cm s−1), (b) potential density σθ, and (c) potential vorticity (× 10−10 m−1 s−1). The longitudes are 21.0° for (a) and 20.5° for (b) and (c). The region with eastward current in (a) and the region with potential vorticity lower than 1.5 × 10−10 m−1 s−1 in (c) are shaded.

  • View in gallery

    Horizontal distributions of isopycnal potential vorticity (× 10−10 m−1 s−1) at (a) σθ = 25.4, (b) σθ = 25.6, (c) σθ = 25.8, and (d) σθ = 26.1. Symbols +, ○, ×, and □ denote the grid points having minimum potential vorticity at given latitudes. The region with potential vorticity lower than 1.5 × 10−10 m−1 s−1 is shaded.

  • View in gallery

    Mixed layer depth distribution, defined as the depth where the density is 0.1σθ heavier than that on the sea surface. The contour interval is 20 m.

  • View in gallery

    Trajectories of low potential vorticity fluids on four isopycnal surfaces: symbols +, ○, ×, and □ denote the positions of local minima for given latitudes on the isopycnal surface of σθ = 25.4, σθ = 25.6, σθ = 25.8, and σθ = 26.1, respectively. The region with potential vorticity lower than 10−10 m−1 s−1 is shaded.

  • View in gallery

    Results of the case with KH = 2 × 107 cm2 s−1: (a) horizontal current vector at z = −36 m, (b) mixed layer depth distribution, and (c) the potential vorticity on an isopycnal surface of σθ = 25.6.

  • View in gallery

    As in Fig. 4 but for the case with KH = 2 × 107 cm2 s−1.

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Subtropical Countercurrent in an Idealized Ocean GCM

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  • 1 Graduate School of Environmental Earth Science, Hokkaido University, Sapporo, Japan
  • | 2 Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan
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Abstract

In the North Pacific, there is a shallow eastward current called the subtropical countercurrent, which flows across the central subtropical gyre. The present article studies the generation mechanism of the subtropical countercurrent reproduced in an ocean general circulation model (GCM) with a simple geometry, driven by surface wind stress and surface buoyancy forcing.

In the ocean GCM, the deep mixed layer occurs in the northern part of subtropical gyre and shoals abruptly in the central subtropical gyre. The mixed layer front, the narrow transition zone of the mixed layer depth, slants from the western central subtropical gyre to the northeast, and the low potential vorticity fluid is formed at the intersection of the mixed layer front and the outcrop line. Since the surface density is almost zonally uniform and the mixed layer front slants northeastward, the minimum potential vorticity fluids on denser isopycnals are formed in the northeastern region, while those on lighter isopycnals are formed in the western region. Subducted and advected southwestward, the low potential vorticity fluid in each isopycnal overlaps that on another isopycnal and makes a thick low potential vorticity pool in the western central subtropical gyre. It is found that the model subtropical countercurrent occurs along the southern edge of this pool.

Corresponding author address: Dr. Atsushi Kubokawa, Graduate School of Environmental Earth Science, Hokkaido University, Sapporo 060, Japan.

Email: kubok@ees.hokudai.ac.jp

Abstract

In the North Pacific, there is a shallow eastward current called the subtropical countercurrent, which flows across the central subtropical gyre. The present article studies the generation mechanism of the subtropical countercurrent reproduced in an ocean general circulation model (GCM) with a simple geometry, driven by surface wind stress and surface buoyancy forcing.

In the ocean GCM, the deep mixed layer occurs in the northern part of subtropical gyre and shoals abruptly in the central subtropical gyre. The mixed layer front, the narrow transition zone of the mixed layer depth, slants from the western central subtropical gyre to the northeast, and the low potential vorticity fluid is formed at the intersection of the mixed layer front and the outcrop line. Since the surface density is almost zonally uniform and the mixed layer front slants northeastward, the minimum potential vorticity fluids on denser isopycnals are formed in the northeastern region, while those on lighter isopycnals are formed in the western region. Subducted and advected southwestward, the low potential vorticity fluid in each isopycnal overlaps that on another isopycnal and makes a thick low potential vorticity pool in the western central subtropical gyre. It is found that the model subtropical countercurrent occurs along the southern edge of this pool.

Corresponding author address: Dr. Atsushi Kubokawa, Graduate School of Environmental Earth Science, Hokkaido University, Sapporo 060, Japan.

Email: kubok@ees.hokudai.ac.jp

1. Introduction

In the central subtropical gyre of the North Pacific Ocean, there is a shallow upper current flowing eastward, which originates from the western North Pacific around 20°–25°N and tilts slightly northward as it flows eastward. The classic Sverdrup theory suggests that the current should be southwestward in this region. This eastward current is called the subtropical countercurrent and is accompanied by a density front called the Subtropical Front. This front and countercurrent were documented by Uda and Hasunuma (1969), Roden (1972, 1975, 1980), and Hasunuma and Yoshida (1978), and the map of annual mean dynamic height of the sea surface (e.g., Wyrtki 1974) also shows the eastward flow near this latitude in the western North Pacific. Takeuchi (1984a, 1986) succeeded in reproducing this countercurrent in an ocean general circulation model with a rectangular basin driven by wind stress and buoyancy forcing.

Before Takeuchi’s (1984a) numerical experiment, it was thought that this current could be caused by a local wind structure. Yoshida and Kidokoro (1967a,b) found that the wind stress curl in the spring season has a trough that produces eastward Sverdrup transport in the central subtropical gyre. The importance of Ekman convergence induced by the westerlies and trade winds was suggested by Roden (1975), Welander (1981), and Cushman-Roisin (1981). However, Takeuchi (1984a) showed that wind stress curl without a trough can also produce the countercurrent and he also showed that the countercurrent can occur even if the model is driven by meridional wind stress. Therefore, the local wind stress distribution is not essential, although it may enhance the frontal structure.

The possibility of geostrophic current convergence causing this front and countercurrent was discussed by Cushman-Roisin (1984), Takeuchi (1984b), Dewar (1992), and Kubokawa (1995, 1997). Cushman-Roisin showed that, if the vertical density structure has a similarity form that is assumed only as a function of surface density and latitude, the wind stress and north–south differential heating can produce a subtropical frontlike structure. On the other hand, Takeuchi (1984b) discussed the density distribution under north–south differential heating and the Sverdrup-like barotropic flow, using a simple two-level model on an f plane, and showed that, if the density at the eastern boundary is vertically uniform at the same value of the surface density that is a function of the latitude, a density front similar to the Subtropical Front can occur. For generation of the front in these models, the eastern boundary ventilation (see, e.g., Pedlosky 1983) is essential.

Theoretical models excluding the eastern boundary ventilation were presented by Dewar (1992) and Kubokawa (1995, 1997). In those studies, the frontgenesis is caused by remotely forced nonlinear stationary Rossby waves. Dewar (1992) showed that a two-layer ventilated thermocline model can yield a front similar to the subtropical one if the outcrop line slants northeastward. Kubokawa (1995, 1997) discussed the possibility of generating the subtropical front caused by the density distortion at the northwestern region of the subtropical gyre where the vertically uniform water called the subtropical mode water is formed (see, e.g., Suga et al. 1989).

The above theories show that, if some specific density structure is imposed on a boundary, that is, surface boundary (Dewar 1992), eastern boundary (Takeuchi 1984b), or western boundary (Kubokawa 1995, 1997), the subtropical frontlike structure is possible to occur. However, those theories have not been confirmed by comparing them with any numerical experiment or observational data, and the generation mechanism is still unclear. It should also be noted that numerical experiments have seldom been carried out on this current except those of Takeuchi (1984a, 1986). This might suggest that there is some difficulty in reproducing the subtropical countercurrent in ocean GCMs. In the present study, we reproduce a subtropical countercurrent in an ocean GCM with a simple geometry and investigate its generation mechanism.

After describing the model configuration in section 2, section 3 describes the experimental results, and the summary and discussion are given in section 4. The numerical result in section 3 shows that low potential vorticity fluid is formed at the southern edge of the deep mixed layer appearing in the northern half of the subtropical gyre. The low potential vorticity fluid on denser isopycnal is subducted in the east, while that on lighter isopycnal is subducted in the west, because the southern edge of the deep mixed layer slants northeastward. When flowing southwestward, the low potential vorticity fluids on the different isopycnals converge on the horizontal plane and overlap. As a result, a thick low potential vorticity pool appears in the western central subtropical gyre, and the model countercurrent flows along the southeastern edge of this pool. None of the previous theoretical works mentioned above explain the present experimental result satisfactorily, and a theory consistent with this experiment will be presented by Kubokawa (1999).

2. Model description

The model used in the experiment is a primitive equation model, the GFDL Modular Ocean Model (MOM version 1.1). The equations of motion are the Navier–Stokes equations, simplified by the Boussinesq and hydrostatic approximations and, when the density stratification is unstable, the convective adjustment scheme is applied to the density field. A spherical coordinate system is used. The model basin is 71° wide in longitude, meridionally extends from 1° to 46°N, and has a constant depth of 3000 m. The horizontal resolution is 1° × 1°, and the vertical structure is resolved for 24 levels. The arrangement of grid points in the vertical section is the same as that in Inui and Hanawa (1997).

The viscosity and the diffusion terms have a Laplacian form with constant coefficients. Their values are

  1. horizontal eddy viscosity coefficient: AH = 108 cm2 s−1

  2. vertical eddy viscosity coefficient: AV = 10 cm2 s−1

  3. horizontal eddy diffusion coefficient: KH = 5 × 106 cm2 s−1

  4. vertical eddy diffusion coefficient: KV = 0.3 cm2 s−1.

Although we discuss mainly the results obtained by the above parameters, we have carried out two additional experiments in which KH = 1 × 107 cm2 s−1 and KH = 2 × 107 cm2 s−1, respectively, but the other parameters are held the same as in the above case. In the above standard case and the case of KH = 1 × 107 cm2 s−1, the countercurrent occurred, while in the case of KH = 2 × 107 cm2 s−1 the countercurrent was not clear. The value of KH in the standard case seems somewhat smaller than that widely used in this type of model, for example, KH = 107 in Cox and Bryan (1984), 2 × 107 in Inui and Hanawa (1997), etc. The smaller the value of KH, the clearer the countercurrent is; however, we have adopted the above value. The dependence on KH will be discussed in section 3c.

The model ocean is driven by both the surface zonal wind stress and Haney-type heat flux (Haney 1971). The boundary conditions at the ocean surface (z = 0) are
i1520-0485-29-6-1303-e2-1
where u, υ, and w are eastward, northward, and vertical velocity components, respectively; T is the temperature;τ the zonal wind stress; ρ0 the density; z the vertical coordinate; and θ is the latitude. Here τ and Ta are given functions of θ, their distributions are shown in Fig. 1, and γ is set to be 90 cm day−1. At the bottom boundary no flux conditions are applied, and no-slip and no buoyancy flux conditions are used at the lateral wall boundary.

The model ocean is initially at rest. The initial density field is the same as that used by Inui and Hanawa (1997), which is based on the zonally averaged climatological mean temperature (Levitus 1982) and constant salinity of 34.9 psu. The time step is 1 h. We analyze the results after 40 years of integration starting from the initial condition. Although only a few lower baroclinic modes can transverse the model basin within 40 years, the 40-yr integration is long enough for free baroclinic modes to decay. The quasi steadiness was checked by comparing data of the 40-yr integration and those of a 50-yr integration.

3. Results

a. Subtropical countercurrent in the model

Figure 2a shows the barotropic streamfunction field, which resembles well the classical Munk solution. This means that the Sverdrup balance holds, except near the western boundary. However, the upper-layer velocity field shown in Fig. 2b is significantly different from the barotropic field. In Figs. 2b–d, the significant eastward current regions are shaded. The shaded region from 30° to 40°N corresponds to the eastward current around the subtropical–subpolar gyre boundary. In addition to this region, we can find another eastward current region in Fig. 2b, around 15°N in the west to 20°N in the east, where the barotropic flow is southwestward. This eastward current in the southern half of the subtropical gyre is the model subtropical countercurrent. This countercurrent is confined in a thin upper layer. At z = −109 m (Fig. 2c) it almost vanishes, and at z = −199 m (Fig. 2d) the current direction reverses and the current there is westward. It was reported that the countercurrent in the western North Pacific flows between 20° and 25°N (see, e.g., Uda and Hasunuma 1969). This difference possibly arises from the difference in the wind stress distribution; the southern edge of the subtropical gyre in the Sverdrup transport lies along 10°N in the present model, while that in the real North Pacific lies along 15°N (see, e.g., Qiu and Joyce 1992).

Figure 3 shows the horizontal density fields. In the surface layer (Fig. 2a), the density is almost zonally uniform in the subtropical gyre. In the subsurface layers, the density fields are distorted by the countercurrent. At z = −341 m (Fig. 2d), the density field is very different from those in the upper layers. This difference between the horizontal density distribution in upper ocean and that in the deeper ocean is similar to that of Kubokawa (1997). However, this does not necessarily mean that the mechanism presented by Kubokawa (1997) works in this model. Also, since the outcrop line is almost zonal in this model, the direct application of Dewar’s (1992) theory is impossible.

Figure 4 shows the distributions of zonal flow, density, and potential vorticity in a meridional section in the western region. The potential vorticity in this paper is defined by
i1520-0485-29-6-1303-eq1
where f is the Coriolis frequency. Although the eastward current dominates the surface layer, even in the southern half of the subtropical gyre in this section, the two eastward current cores are clearly seen in Fig. 4a, separated by a weak eastward or westward current region around 24°N. The southern core corresponds to the subtropical countercurrent, whose maximum velocity is greater than 6 cm s−1 near 15°N at 15-m depth in this section, and the eastward current extends to more than 100-m depth. On the other hand, in the region deeper than 150 m, the eastward current is confined in the northern half of the gyre as suggested by the classical Sverdrup theory.

The isopycnals in the countercurrent region rise on its north side, where the surface layer is strongly stratified (Fig. 4b), suggesting that the countercurrent satisfies the thermal wind balance. On the other hand, the isopycnal surfaces outcropping in the northern half of the subtropical gyre show an interesting structure; the σθ = 25.4 isopycnal surface shoals near 20° and the σθ = 25.6 surface near 18°N. This suggests the existence of low potential vorticity fluid at this latitude. It should also be noted that the weak current region separating the shallow eastward current into the two cores lies over the northern slope of this, unexpected, rise of the isopycnals, where the density decreases northward so that the shallow eastward current weakens. In the lower thermocline where σθ is greater than 26.0, such an unexpected rise of isopycnal surface is not seen.

Corresponding to the density structure, high potential vorticity regions occur in the low-latitude shallow thermocline and in the midlatitude deeper thermocline (Fig. 4c). These two high potential vorticity regions are obliquely split by the low potential vorticity region (less than 2.0 × 10−10 m−1 s−1) extending from the sea surface between 28° and 38°N. This low potential vorticity fluid probably corresponds to the subtropical mode water (e.g., Suga et al. 1989). Since the potential vorticity is a nearly conservative property for fluid particles, the low potential vorticity fluid in the subsurface should be formed somewhere and advected to this region. On the other hand, the density stratification near the surface must be maintained by the sea surface buoyancy forcing and local Ekman pumping, while that in the lower thermocline must be determined by the initial stratification. If the thick low potential vorticity fluid intrudes between them, the vertical density gradient will be enhanced in the surface layer, and the isopycnals in the lower thermocline will be pushed downward. If the low potential vorticity fluid is confined meridionally, the horizontal density gradient in the shallow layer will also be enhanced around the southern edge of the low potential vorticity region, while it will be weakened around its northern edge. This gives an interpretation of the occurrence of the countercurrent and weak current region to the north of the countercurrent since the horizontal density gradient tends to intensify the upper-layer eastward current as expected from the thermal wind balance. Therefore, detecting the formation region and the trajectory of this low potential vorticity fluid would provide a key to understanding the generation mechanism of the countercurrent.

b. Potential vorticity field and mixed layer

The horizontal distributions of the potential vorticity on several isopycnals are shown in Fig. 5. For denser isopycnals low potential vorticity (PV) fluid appears in the east, whereas for lighter isopycnals low PV fluid appears in the west. For example, the minimum potential vorticity fluid on σθ = 25.4 is formed at latitude 28°, longitude 20°, while that on σθ = 25.8 is formed at latitude 32°, longitude 40°, and they are advected southward, diffusing and increasing their values. The marks plotted on each panel denote the grid points of minimum potential vorticity at given latitudes. That is, these marks are tracers representing the trajectory of the low potential vorticity fluid formed at the outcrop latitude.

Since the surface density is almost zonally uniform (Fig. 3a), the localized low potential vorticity of subducted fluid must be related to the vertical density structure at the outcrop latitude. Figure 6 shows the horizontal distribution of mixed layer (vertically homogeneous layer) depth. The mixed layer is shallow in the southeastern region, and its depth changes rapidly from less than 40 m to more than 200 m within a short distance. We refer this narrow transition zone of the mixed layer depth to as the mixed layer front. It may be an interesting problem why the mixed layer depth changes over so short a distance, but we focus our attention only on the result from this structure.

From Figs. 3a, 5, and 6, we can easily find that the source of the low potential vorticity fluid on each isopycnal surface is the southern edge of this deep mixed layer. The relation between the potential vorticity of subducted fluid and the mixed layer depth gradient was theoretically discussed by Williams (1991), and the formation regions of low potential vorticity fluids in this model coincide with those expected by the theory.

Figure 5 shows that the low potential vorticity fluid is advected southwestward, and the tendency of the westward migration is stronger for deeper isopycnal surface. This tendency can be explained by the β spiral (see Stommel and Schott 1977), implying clockwise rotation of the horizontal current vector with depth. In Fig. 7, we plot the trajectories of the minimum potential vorticity for several isopycnals, in which the tendency mentioned above is clearly seen. Since the low potential vorticity on the deeper isopycnal surface is formed in the east and migrates westward faster than those on the shallower isopycnals, the trajectories of the minimum potential vorticity on each isopycnal surface converge on the horizontal plane. This means that the low potential vorticity fluids accumulate vertically and produce a thick layer with a density between 25.4 and 26.1 in the central western subtropical gyre, as seen in the meridional section (see Fig. 4c). The trajectories of the minimum potential vorticity seems to converge along the trajectory on the σθ = 26.1 isopycnal, and the subducted low potential vorticity fluids are confined to its north. As a result, the contrast in the layer thickness between the low potential vorticity region and its south are enhanced here. Comparing Fig. 7 with Fig. 2b, we can find that the location of the subtropical countercurrent coincides with this convergence zone.

c. Dependence on the horizontal diffusion coefficient

As mentioned in section 2, we carried out two additional experiments, changing the horizontal diffusion coefficient to KH = 1 × 107 cm2 s−1 and KH = 2 × 107 cm2 s−1. We found that in the case of KH = 1 × 107 cm2 s−1, the subtropical countercurrent is similar to that in the standard case (KH = 0.5 × 107 cm2 s−1), but is weaker (not shown). In the case of KH = 2 × 107 cm2 s−1, however, the subtropical countercurrent is not observed, at least at z = −36 m as shown in Fig. 8a. Although the eastward current exists in the southern half of the subtropical gyre, it is weak and broad and is not separated from the eastward current in the northern half of the gyre. The horizontal distribution of the current is rather similar to the surface current in a ventilated thermocline model without the surface mixed layer (see, e.g., Huang 1988). The weak, broad eastward current dominating the upper layer can be attributed to the northward gradient in surface density. In this section, we briefly discuss what causes this difference by examining the results of the case with KH = 2 × 107 cm2 s−1.

As shown in Fig. 8b, even in the case with KH = 2 × 107 cm2 s−1, the mixed layer front occurs at almost the same position as in the standard case, and the low potential vorticity fluid is formed around the intersection of the mixed layer front and the outcrop line (see Fig. 8c). The potential vorticity contour of 2 × 10−10 m−1 s−1, however, does not extend westward, and comparison with Fig. 5b shows the potential vorticity minimum in the case of KH = 2 × 107 cm2 s−1 diffuses much faster than that in the standard case. As expected from the generation mechanism inferred above, this difference results in the density structure in a meridional section shown in Fig. 9. Comparing Fig. 9c with Fig. 4c, we can find that the low potential vorticity region extending from the sea surface in the northern half of the subtropical gyre is reduced, and subsurface potential vorticity increases between 15° and 25°N. Corresponding to this change in potential vorticity distribution, the shallow isopycnals lighter than 25.0 σθ become deeper between 15° and 20°N, and the deeper isopycnals heavier than 26.0 σθ become shallower (compare Fig. 9b with Fig. 4b). As a result, the baroclinic structure is weaken and the countercurrent-like flow only occurs in the vicinity of the sea surface (Fig. 9a).

All of the above results suggest the importance of the contrast in distribution of the isopycnal potential vorticity for generation of the subtropical countercurrent. When the horizontal diffusion is strong, the potential vorticity minimum formed near the intersection of the mixed layer front and the outcrop line diffuses rapidly and cannot form the subsurface thick low potential vorticity pool. In such a case, the upper-layer current distribution is similar to that in a ventilated thermocline model without a mixed layer. On the other hand, in the case of weak horizontal diffusion (standard case), the subsurface thick low potential vorticity pool intensifies the eastward surface current in the southern region, while it weakens that in the central region so that the subtropical countercurrent, which is defined as the upper-layer eastward current maximum in the southern half of the subtropical gyre, occurs. If we want to reproduce the subtropical countercurrent in numerical models, we need to use a small horizontal diffusion coefficient.

4. Summary and discussion

The present numerical experiments suggest the following scenario for generation of the subtropical countercurrent.

  1. In the ocean GCM, the deep mixed layer occurs in the northern subtropical gyre, and it shoals abruptly in the central subtropical gyre. This mixed layer front, the narrow transition zone of the mixed layer depth, slants from the western central subtropical gyre to northeastern subtropical gyre.

  2. The low potential vorticity fluid is formed at the intersection of the mixed layer front and the outcrop line. Since the surface density is almost zonally uniform while the mixed layer front slants northeastward, the minimum potential vorticity fluid on a dense isopycnal is formed in the northeastern region, while that for a lighter density isopycnal is formed in the western region.

  3. Advected southwestward, the low potential vorticity fluids on different isopycnals converge in the horizontal plane and vertically accumulate, forming a thick low potential vorticity pool in the central western subtropical gyre.

  4. Because of the thick low potential vorticity pool in the western central gyre, the isopycnal surfaces in the surface layer shoal in this region, relative to those in the south where the low potential vorticity fluid is not advected. As a result, the horizontal density gradient in the surface layer is enhanced around the southern edge of this low potential vorticity pool. This density structure drives the surface eastward geostrophic current, which is the subtropical countercurrent in the model.

The existence of the mixed layer front is crucial for the above mechanism to work. Huang and Qiu (1994), who discussed thermocline structure of North Pacific by analyzing the Levitus data (1982), shows that the mixed layer in winter is deep in the northwestern subtropical gyre and shoals in a narrow region around 30°N. This suggests that the mixed layer front exists in the real ocean. Recently, Suga et al. (1997) also calculated the wintertime mixed layer depth in the North Pacific based on temperature data, and their Fig. 10a shows that the mixed layer front slants northeastward from 30°N at 150°E to 40°N at 160°W. The width of the mixed layer front in both studies is about 5°. However, this width is probably overestimated because of the temporal average. On the other hand, the mixed layer depths in the north of the mixed layer front are shallower than 200 m in those studies, except for that in northeastern region in Suga et al. (1997). This may also be affected by the averaging technique or vertical resolution since Suga and Hanawa (1990) and Bingham (1992) reported that the maximum mixed layer depth in the western North Pacific subtropical gyre is deeper than 300 m in winter. Therefore, the mixed layer depth distribution in the present model seems reasonable, although it includes some unrealistic features. For example, in the present model, the maximum mixed layer depth occurs near the northeastern corner of the basin. Such a deep mixed layer in the east is not observed in the real North Pacific, although the role of this unrealistically deep mixed layer in the east is expected to be minor as far as the mechanism inferred in the present study is concerned.

The mechanism inferred in the present study suggests that a subtropical countercurrent will occur in a ventilated thermocline or an ideal-fluid thermocline model if we give an appropriate mixed layer depth distribution. Williams (1991) and Pedlosky and Robbins (1991) discussed the effect of the mixed layer on the thermocline structure, and Huang and Russell (1994) investigated the thermocline structure in the North Pacific using an ideal-fluid thermocline with the same mixed layer depth distribution as that calculated by Huang and Qiu (1994). However, in those papers, there is no subtropical countercurrent. This is probably because the mixed layer distributions used by them are too smooth for the countercurrent to occur. The countercurrent in a ventilated thermocline model is discussed in the accompanying paper, Kubokawa (1999), in detail.

The present study suggests that one of the most important keys in simulating the upper-ocean circulation in numerical models is how well the mixed layer is realistically reproduced. In the present model, the mixed layer deepening is caused by a convective adjustment. Even in such a simple case, it is not very clear why the mixed layer depth distributes as shown in Fig. 6 since the mixed layer depth is determined by the combination of the surface density and the subsurface density structure. The subsurface density field will be dominated by the horizontal advection, which may be affected by the surface density and mixed layer depth distributions as partly demonstrated here. Therefore, the problem seems complicated, and we should make efforts to clarify the dynamics governing the global distributions of mixed layer depth.

Acknowledgments

This work was financially supported by the Japanese Ministry of Education, Science and Culture. The authors would like to thank Prof. Kensuke Takeuchi for fruitful discussions and two anonymous reviewers for helpful comments. The GFD-DENNOU Library was used for drawing the figures.

REFERENCES

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Fig. 1.
Fig. 1.

The meridional profiles of the specific temperature and the surface wind stress: (a) specific temperature Ta and (b) surface wind stress τ.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 2.
Fig. 2.

Horizontal flow fields: (a) barotropic streamfunction (Sv ≡ 106 m3 s−1), horizontal current vectors at (b) z = −36 m, (c) z = −109 m, and (d) z = −199 m. In the shaded regions in (b)–(c), the current vectors are directed between ±22.5° with respect to the east, and their magnitudes are larger than 2 cm s−1. The current vector is plotted at each 2° × 2° grid, although the model resolution is 1° × 1°. The meridional boundaries of the model basin are located at 1° and 72° longitude.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 3.
Fig. 3.

Horizontal distribution of the density σθ at (a) z = −2 m, (b) z = −54 m, (c) z = −148 m, and (d) z = −341 m.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 4.
Fig. 4.

Distributions of the zonal flow, density, and potential vorticity in a meridional section in the western region: (a) zonal velocity (cm s−1), (b) potential density σθ, and (c) potential vorticity (× 10−10 m−1 s−1). The longitudes are 21.0° for (a) and 20.5° for (b) and (c). The region with eastward current in (a) and the region with potential vorticity lower than 1.5 × 10−10 m−1 s−1 in (c) are shaded.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 5.
Fig. 5.

Horizontal distributions of isopycnal potential vorticity (× 10−10 m−1 s−1) at (a) σθ = 25.4, (b) σθ = 25.6, (c) σθ = 25.8, and (d) σθ = 26.1. Symbols +, ○, ×, and □ denote the grid points having minimum potential vorticity at given latitudes. The region with potential vorticity lower than 1.5 × 10−10 m−1 s−1 is shaded.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 6.
Fig. 6.

Mixed layer depth distribution, defined as the depth where the density is 0.1σθ heavier than that on the sea surface. The contour interval is 20 m.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 7.
Fig. 7.

Trajectories of low potential vorticity fluids on four isopycnal surfaces: symbols +, ○, ×, and □ denote the positions of local minima for given latitudes on the isopycnal surface of σθ = 25.4, σθ = 25.6, σθ = 25.8, and σθ = 26.1, respectively. The region with potential vorticity lower than 10−10 m−1 s−1 is shaded.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 8.
Fig. 8.

Results of the case with KH = 2 × 107 cm2 s−1: (a) horizontal current vector at z = −36 m, (b) mixed layer depth distribution, and (c) the potential vorticity on an isopycnal surface of σθ = 25.6.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 4 but for the case with KH = 2 × 107 cm2 s−1.

Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1303:SCIAIO>2.0.CO;2

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