Mixed Layer Depth Front and Subduction of Low Potential Vorticity Water in an Idealized Ocean GCM

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1 Journal of Oceanography, Vol. 63, pp. 125 to 134, 2007 Mixed Layer Depth Front and Subduction of Low Potential Vorticity Water in an Idealized Ocean GCM SHIRO NISHIKAWA* and ATSUSHI KUBOKAWA Graduate School of Environmental Earth Science, Hokkaido University, Sapporo , Japan (Received 13 December 2005; in revised form 15 September 2006; accepted 20 September 2006) It is known that there is a front-like structure at the mixed layer depth (MLD) distribution in the subtropical gyre, which is called the MLD front, and is associated with the formation region of mode water. In the present article, the generation mechanism of the MLD front is studied using an idealized ocean general circulation model with no seasonal forcing. First, it is shown that the MLD front occurs along a curve where u g T s = 0 is satisfied (u g is the upper ocean geostrophic velocity vector, T s is the sea surface temperature and is the horizontal gradient operator). In other words, the front is the boundary between the subduction region (u g T s > 0) and the region where subduction does not occur (u g T s < 0). Second, we have investigated subduction of low potential vorticity water at the MLD front, which has been pointed out by past studies. Since u g T s = 0 at the MLD front, the water particles do not cross the outcrop at the MLD front. The water that is subducted at the MLD front has come from the deep mixed layer region where the sea surface temperature is higher than that at the MLD front. The temperature of the water in the deep mixed layer region decreases as it is advected eastward, attains its minimum at the MLD front where u g T s = 0, and then subducts under the warmer surface layer. Since the deep mixed layer water subducts beneath a thin stratified surface layer, maintaining its thickness, the mixed layer depth changes abruptly at the subduction location. Keywords: Mixed layer depth front, subduction, low potential vorticity water, subtropical gyre, idealized ocean GCM. 1. Introduction In the subtropical gyre region, water is transfered from the surface mixed layer into the thermocline below by downward Ekman pumping. This process is called subduction. The subducted water flows along an isopycnal surface, isolated from the direct effect of wind stress, and is advected by Sverdrup flow, conserving its potential vorticity. The thermocline structure in the subtropical gyre region is mainly determined by this process. This view of the wind-driven circulation in the subtropical gyre was first given by Luyten et al. (1983) and is called the ventilated thermocline theory. The ventilated thermocline theory implies that the lateral distribution of the mixed layer depth (MLD) is important in the determination of thermocline structure. Williams (1989, 1991) formulated the effect of the mixed layer depth distribution on the subducted fluid and combined it into the ventilated thermocline model. He expressed the potential vorticity (PV) of the ventilated fluid, q, in terms of the mixed layer depth, density, and the ve- * Corresponding author. nishiro@ees.hokudai.ac.jp Copyright The Oceanographic Society of Japan/TERRAPUB/Springer locities at the base of the mixed layer: f ub σ q = θ, 1 ρ w + u h b where f is the planetary vorticity, ρ is a reference density, u b and w b are the horizontal and vertical velocities at the base of the mixed layer, σ θ is the potential density of the mixed layer, h is the mixed layer depth, and is the horizontal differential operator. Williams formula indicates a low PV of subducted water where the gradient of MLD, h, is large. Recent studies based on the ventilated thermocline theory, including Williams study, have shown that the subtropical ocean interior structure is affected by the MLD distribution. Among these studies, Kubokawa and Inui (1999) studied the MLD distribution in an ocean general circulation model (GCM) and its effects on the upper ocean structure, and Kubokawa (1999) gave a theoretical discussion of the ventilated thermocline, strongly affected by the mixed layer distribution. They showed that there is a front-like structure in the MLD distribution (where h is large) and low PV water is formed around the inter- b () 125

2 section of the outcrop and this front-like structure in each isopycnal layer. They referred to this front-like structure as the mixed layer front. The low PV waters formed at each isopycnal layer are advected southwestward along the subtropical gyre, converge in the horizontal plane and accumulate vertically, as a result forming thick low PV pool (mode water) in the central western subtropical gyre. Furthermore, they explained that the isopycnal surfaces in the upper layer are raised by the formation of the mode water and this structure drives a surface eastward current (subtropical countercurrent) along the southern edge of the mode water. Several studies indicate that the mechanism presented by Kubokawa and Inui (1999) and Kubokawa (1999) is important for the formation of some mode waters observed in the real ocean. It is known that there are three mode waters in the North Pacific: subtropical mode water (STMW), central mode water (CMW), and eastern subtropical mode water (ESTMW). Xie et al. (2000) reproduced these three mode waters in their realistic GCM simulation. They showed that low PV water is formed at the intersection of the MLD front (mixed layer front) and the outcrop of each isopycnal surface in their model. They suggested that such low PV waters are the sources of STMW and CMW. The role of the MLD front in determining the thermocline structure presented by Kubokawa and Inui (1999) and Kubokawa (1999) has been applied to other problems. One example is the problem of oceanic thermocline response to an intensification of the Westerlies. It is known that a sudden change in the atmospheric circulation over the North Pacific during the mid-1970s caused a cooling of the subsurface ocean interior. Inui et al. (1999) investigated the cooling mechanism using an idealized ocean GCM. They showed that when westerly intensification occurred, the MLD front shifts northward by the anomalous change of the MLD distribution, the location of the mode water shifts westward, and as a result, isopycnals of the subsurface rise, which causes the cold anomaly. On the other hand, Kubokawa and Xie (2002) presented a somewhat different mechanism for the problem. They argued that the westerly intensification strengthens the Sverdrup flow in that region and this causes the westward shift of the low PV water (mode water) without the anomalous change of the MLD distribution. As mentioned above, the effect of the MLD front on the ocean interior structure has been investigated in several studies. However, the structure and determination of the MLD front itself have not been studied so far. Since the MLD distribution is one of the boundary conditions of the ventilated thermocline model, an exact understanding of the MLD distribution in an idealized situation is important for theoretical studies. In addition, since past studies have considered the MLD front as a source region of low PV water (mode water), the subduction process at the MLD front is also important. The purpose of this paper is to investigate the MLD front in an idealized situation. We focus on the following two points: what determines the location of the MLD front? And how is the low PV water subducted at the MLD front, in the absence of seasonal forcing? The location of the MLD front, the subduction of the low PV water and the generation of the sharp MLD front are three aspects of the same phenomenon. Investigation of the subduction process will lead us to an interpretation of why the MLD front is so sharp. In this study, for simplicity we use an idealized ocean GCM with no seasonal variation, similar to models used by Kubokawa and Inui (1999), Inui et al. (1999), etc. We adopt Stommel s mixed layer demon concept (Stommel, 1979), that is, the surface density condition is fixed in late winter where the mixed layer is deepest and the annual mean wind forcing is used. Although seasonality is important for the subduction process in the real ocean (e.g., Woods, 1985; Williams et al., 1995), such a simple model would be helpful in understanding the essence of the mechanism of MLD front generation and its relation to the subduction of low PV water. The rest of this paper is organized as follows. Section 2 describes the configuration of the model. Section 3 briefly discusses the model s upper ocean structure. In Section 4 we discuss the determination of the location of the MLD front, while in Section 5 we discuss the subduction at the MLD front. Finally, a summary and discussion are given in Section Model Description The model used in this study is the Center for Climate System Research (CCSR) Ocean Component Model (COCO, described by Hasumi, 2000) ver. 3.3 developed at University of Tokyo. COCO is a Bryan-Cox type ocean GCM (e.g., Bryan, 1969; Cox and Bryan, 1984). This model solves the three dimensional primitive equations under hydrostatic and Boussinesq approximations. Spherical coordinates are used horizontally and geopotential height coordinate is used vertically. The free surface is explicitly treated by a method similar to that introduced by Killworth et al. (1991). COCO uses UTOPIA (Leonard et al., 1993) as a tracer advection scheme, and isopycnal diffusion with weak background horizontal diffusion. When the density stratification is unstable, the convective adjustment scheme is applied to the density field. The model domain is a rectangular basin with no bottom topography, which is 60 wide in longitude, extends meridionally from the equator to 60 N, and has a constant depth of 3000 m. The horizontal resolution is There are 30 vertical levels. The vertical reso- 126 S. Nishikawa and A. Kubokawa

3 Fig. 1. Meridional profiles of τ x (left) and T a (right). Unit of τ x is dyne cm 2 and unit of T a is C. lution is high in the upper ocean and low near the bottom. For example, the thickness of the uppermost layer is 10 m and that of the lowest layer is 400 m. The viscosity and diffusivity coefficients are constant spatially and temporally. The horizontal and vertical viscosity coefficients are A H = cm 2 s 1 and A V = 1.0 cm 2 s 1, respectively. The isopycnal diffusion coefficient and vertical diffusion coefficient are K HI = cm 2 s 1 and K V = 0.3 cm 2 s 1, respectively. The model ocean is driven by surface wind stress and surface temperature flux. The surface wind stress, (τ x, τ y ), is τ x = π τ ϕ ϕ cos 065. ( 0< 15) 15 π π τ ϕ + 0 cos ( 15 < ϕ 60), 30 2 ( 2) τ y = 0, () 3 where ϕ is latitude, and τ 0 = 0.7 dyne cm 2. Its functional form is based on Hellerman and Rosenstein s (1983) annual and zonal mean data. The surface temperature flux is ( ) ( ) Q= γ T T, 4 where T a is a reference temperature and T s is the sea surface temperature of the model ocean (Haney, 1971). T a in this study is < ϕ 15 T a = ϕ + ( 15 ϕ < 60), 45 3 a s ( ) ( 5) and γ = 100 cm day 1. The functional forms of (τ x, τ y ) and T a are the same as those used in Sumata and Kubokawa (2001). The meridional profiles of τ x and T a are shown in Fig. 1. Initially, the model ocean is at rest and has a temperature stratification. The initial temperature stratification is zonally uniform, given by the zonal average of northern hemisphere winter climatology of World Ocean Atlas 94 (Levitus and Boyer, 1994). The salinity in this model is constant at 34.9 psu. The reference temperature, T a, in (5) mimics a zonal mean of the winter sea surface temperature, while the wind stress, τ x, in (2) mimics the annual mean τ x. This is based on the idea of Stommel s mixed layer demon (Stommel, 1979; Williams et al., 1995). Although the mixed layer depth has seasonal variability, Stommel (1979) argued that only the water leaving the mixed layer in wintertime irreversibly enters the permanent thermocline. This means that the properties of the main thermocline are controlled by the winter mixed layer rather than by the annual-mean state. The model is integrated for 80 years. The time step is 1 hour. After 80 years, the wind-driven circulation fully spins up and the model ocean reaches a quasi-steady state. We analyze the 1-month averaged data after 80 years integration. 3. Model s Upper Ocean Structure Before discussing the location and the formation mechanism of the MLD front, let us fist survey the model results. Figure 2 shows the barotropic stream function. The barotropic ocean current system consists of three gyres. The region from 15 N to 44 N is an anticyclonic subtropical gyre region. To the north is a cyclonic subpolar gyre region and to the south is also a cyclonic gyre region. These are the result of the applied wind stress (see the left panel of Fig. 1). Mixed Layer Depth Front in an Idealized Ocean GCM 127

4 Fig. 2. Barotropic stream function. Unit is Sv = 10 6 m 3 s 1. Dotted contours denote negative. Fig. 4. Sea surface density σ θ field (at z = 5 m). Fig. 3. Horizontal velocity field at z = 40 m. Fig. 5. Mixed layer depth (MLD) distribution. MLD is defined as a depth where the density is 0.01σ θ heavier than that on the sea surface. Contour interval is 20 m. Contours deeper than 500 m are omitted and shaded. It should be noted that there is no wind-induced mixed layer in this model. Figure 3 shows the velocity field at z = 40 m. Except for the uppermost layer in which Ekman flow is dominant, the upper layers (shallower than about 200 m) have a similar horizontal flow structure vertically in the northern part of the subtropical gyre (not shown). Figure 4 shows the sea surface density field. Since salinity is constant in this model, the density distribution corresponds to the temperature distribution. Figure 5 shows the mixed layer depth (MLD) distribution. The MLD in this study is defined as a depth at which the density difference from that of the sea surface is 0.01σ θ to resolve the thin surface stratified layer. If we use 0.1σ θ, as many studies have (e.g., Kubokawa and Inui, 1999), the location of the MLD front cannot be obtained correctly. The mixed layer is very shallow in the south and deep in the north. Between 30 N and 40 N, there is a front-like region where the MLD varies sharply. This is the MLD front. Figure 6 shows the potential vorticity (PV) distribution on isopycnal surfaces, σ θ = 25.6, 25.8, 26.0, The potential vorticity in this study is given by f σ q = θ. 6 ρ z ( ) 128 S. Nishikawa and A. Kubokawa

5 Fig. 6. Potential vorticity (PV) distribution on isopycnal surfaces, (a) 25.6σ θ, (b) 25.8σ θ, (c) 26.0σ θ, and (d) 26.2σ θ (thin solid contours), with Bernoulli function (thick dotted contours) and the location of the MLD front denoted by diamonds ( ). Outcrops are denoted by dashed lines. Unit of PV is m 1 s 1 and the region lower than m 1 s 1 is shaded. Contour interval of the Bernoulli function is kg m 1 s 2. The streamlines are superimposed on these isopycnal surfaces. They are given by the Bernoulli function, B = p + ρgz, where p is the pressure, ρ is the potential density, g is the gravitational acceleration and z is the vertical coordinate. Low PV water is formed at the intersection of the MLD front and the outcrop of each isopycnal surface. The low PV water formed at the intersection is advected along the streamline. This result is consistent with that of Kubokawa and Inui (1999) and Inui et al. (1999). 4. Location of the MLD Front In the steady state the occurrence of subduction and convection depends on the upper ocean geostrophic velocity distribution (Fig. 3) and the sea surface temperature distribution (Fig. 4). Using them, we here discuss the location of the MLD front. We can divide the subtropical gyre region into two regions according to the relation between the direction of the upper ocean geostrophic velocity, u g, and that of the horizontal gradient of the sea surface temperature, T s. In the northwestern region of the subtropical gyre, u g T s is negative (Fig. 7). In this region, southern warm water is advected northward by the western boundary current and the subsurface (the depth of m where Ekman flow is small enough) is warmed, while there is a surface cooling; therefore convection tends to occur and the deep mixed layer is developed and maintained in this region. On the other hand, in the rest of the subtropical gyre, u g T s is positive (Fig. 7). Marshall and Nurser (1992) and Marshall et al. (2001) showed that the vertical component of potential vorticity (PV) flux in ocean surface mixed layer can be written as J z = fu g σ θ in the steady state. In the region where u g T s is positive, the PV flux is negative. This means that water particles with Mixed Layer Depth Front in an Idealized Ocean GCM 129

6 Fig. 7. Distribution of u g T s, where u g is given by the horizontal velocity at z = 40 m and T s is the sea surface temperature. Shaded region denotes negative. Contour interval is K s 1. Location of the MLD front is denoted by diamonds ( ). some PV enter into thermocline through the surface outcrops, that is, subduction occurs. In this region, colder (denser) water is subducted below warmer (lighter) water along the isopycnal surface. Thus, the surface stratification is developed, convection cannot occur and a mixed layer is not formed. The relation u g T s > 0 can be considered to be a condition of subduction. The boundary, u g T s = 0, between the subduction region and the region where subduction does not occur coincides with the MLD front (Fig. 7). The location of the zero surface temperature flux (Q = 0) differs slightly from that of u g T s = 0, because Ekman advection is important for the surface temperature flux (e.g., Nurser and Marshall, 1991; Marshall et al., 1993) and the line of Q = 0 does not coincide with the location of the MLD front (Fig. 8). Whether or not the convection occurs is determined by the relation between the upper most layer temperature (T s ) and temperature in the adjacent subsurface layer (T g ). The uppermost layer temperature is determined by the surface temperature flux Q, temperature flux to subsurface and the horizontal advection including the Ekman flow, while the subsurface temperature is determined by the convection and the geostrophic advection u g T g. On the northern side of the MLD front where the mixed layer is deep, the subsurface temperature is equal to the surface temperature (T g = T s ). Therefore, the subsurface geostrophic advection is given by u g T s. In this region, since u g T s < 0, the geostrophic advection tends to warm the subsurface layer and destabilize the stratification, leading to convection. The Fig. 8. Distribution of surface temperature flux. Shaded region denotes negative. Contour interval is 10 5 K m s 1. Location of the MLD front is denoted by diamonds ( ). boundary where u g T s = 0 is satisfied is the southern boundary of the convective region with a deep mixed layer. This boundary corresponds to the MLD front. Since there is cooling by the Ekman advection, Q = 0 lies a little north of the MLD front (Fig. 8). It should be noted that the Ekman flow effect does not enter the subsurface temperature balance; instead, Ekman flow indirectly affects the MLD front through the surface temperature balance. The above discussion allows us to describe the MLD distribution and the location of the MLD front as follows: 1) In the region of u g σ θ > 0, the stratification tends to be unstable and a deep mixed layer develops. 2) In the region of u g σ θ < 0, the ordinary ventilation occurs, and the stratification tends to be stabilized. 3) At the boundary between these two regions, which satisfies u g σ θ = 0, the mixed layer depth abruptly changes: This is the mixed layer depth front. 5. Subduction at the MLD Front As shown in Section 3, low potential vorticity (PV) water is formed and subducted at the intersection of the MLD front and the outcrop of each isopycnal surface. Here a problem arises. How is the low PV water subducted at the MLD front where the horizontal velocities are parallel to the outcrop lines, i.e., u g T s = 0? In this section we examine the subduction process at the MLD front using a trajectory of a water particle. It will also be shown that the subduction process is closely related to the reason why the MLD front is so sharp. Figure 9(a) shows an example of a water particle trajectory starting from the deep mixed layer region and Figs. 130 S. Nishikawa and A. Kubokawa

7 Fig. 9. (a) Example of the trajectory of a water particle (thick solid line) which is subducted at the MLD front, with the MLD distribution (dotted contours). Symbol denotes the starting point of the trajectory and dashed line denotes the outcrop of the isopycnal into which the particle is subducted. (b) Vertical potential density distribution along the trajectory (solid contours). Dash-dotted line denotes the depth of the particle and the arrow denotes the position of the MLD front. (c) Value of u p T s along the trajectory, where u p is the horizontal velocity of the particle and T s is the sea surface temperature (SST). Unit is 10 8 K s 1. (d) Temperature of the particle (dash-dotted line) and SST along the trajectory (dotted line). 9(b) (d) show the particle s depth, u p T s, and temperature along the trajectory, where u p is the horizontal velocity of the particle. The particle tracing method is the same as that presented in Masuda (2003). At about 1150 km from the starting point the particle is considered to be subducted at the MLD front (Fig. 9(b)) and u p T s changes from negative to positive (Fig. 9(c)). From this result, we can describe the subduction process along the water particle as follows: 1) Before the particle reaches the MLD front, u p T s < 0: The particle is in the deep mixed layer. It flows from warmer to colder and is approaching the outcrop. The temperature at the position of the particle decreases and the MLD gradually becomes deeper. 2) At the MLD front, u p T s = 0: The particle reaches the outcrop and the velocity direction is parallel to the outcrop. Here, the temperature of the water particle coincides with that of the outcrop and the MLD abruptly becomes shallower. 3) After the particle passes the MLD front, u p T s > 0: The particle flows toward the higher sea surface temperature (SST) region and is subducted beneath a shallow stratified layer. Figure 9(a) indicates that the trajectory (thick solid line) does not cross the outcrop (dashed line), but just contacts it tangentially, as already suggested above. Be- Mixed Layer Depth Front in an Idealized Ocean GCM 131

8 front. Since water is subducted along the outcrop, the vertically homogeneous water, which has the thickness of MLD, is subducted under the thin surface stratified layer, maintaining its thickness as implied by Williams formula (1). This forms the abrupt change in the MLD distribution. If the water is not subducted at the location of u g T s = 0, the mixed layer gradually deepens and does not form the MLD front. Such a case will be discussed in Section 6. Fig. 10. Diagram showing the relation between the outcrops (solid contours) and the water particle trajectories (dotted contours) in the subduction process at the MLD front (diamonds). fore getting to the tangent point, water temperature is decreasing because of the surface cooling. At the tangent point, the temperature attains its minimum. Since the temperature of the water particle is unchanged while the SST along the trajectory increases, the subduction occurs (Fig. 9(d)). In the present model, one tangential point exists for each outcrop. This is because the surface temperature decreases eastward and becomes zonally uniform while the current is anticyclonic. Figure 10 schematically illustrates this relation among the streamlines, SST and the MLD front. The potential vorticity of the water subducted at the MLD front is zero from Williams equation (1), as the numerator u b σ θ = 0 gives q = 0 in his formulation. On the other hand, Marshall and Nurser (1992) and Marshall et al. (2001) show that the subduction rate in the steady state is given by J fu z g σθ S = =. 7 ρq ρq If this formula and Williams PV formula (1) are both valid, these two give the subduction rate, S = w b u b h (e.g., Marshall et al., 1993). Estimation of the subduction rate at the MLD front will be possible using this equation. The subduction rate is extremely high at the MLD front because the lateral induction term (u b h) is extremely large there. Lateral induction is dominant and vertical pumping (w b ) will be negligible at the MLD front. The subduction process when u g T s = 0 is satisfied is closely related to the generation mechanism of the MLD ( ) 6. Summary and Discussion In this paper we have studied the mixed layer depth (MLD) front and its relation to subduction using an idealized ocean GCM. The MLD front is a remarkable structure in the MLD distribution in the subtropical gyre region. Its importance was pointed out by past studies, such as Kubokawa and Inui (1999) and Kubokawa (1999). They showed that low PV water is formed at the intersection of the MLD front and the outcrop of each isopycnal surface. However, the structure and determination of the MLD front itself has not been studied hitherto. We first investigated the relation of the MLD front to subducting and non-subducting regions, and second, we investigated the subduction of the low PV water at the MLD front. The occurrence of the subduction and convection depends on how the upper ocean geostrophic velocity vector u g crosses the contour of the sea surface temperature field T s. Using this, we discussed the location of the MLD front. In the northwestern region of the subtropical gyre where u g T s < 0, convection tends to occur and the deep mixed layer is formed and maintained. On the other hand, in the remaining part of the subtropical gyre where u g T s > 0, subduction occurs and the surface stratification is developed. The boundary, u g T s = 0, gives the boundary of subduction. We compared the location of the MLD front with the location of u g T s = 0 and found that they coincide. The above result shows that the MLD front is formed where the upper ocean geostrophic velocities become parallel to the outcrops of the isopycnals. This means that there are no velocity components normal to the outcrops at the MLD front. The question then is how subduction occurs at the MLD front. We investigated this using a water particle that is subducted at the MLD front. Before a particle reaches the outcrop of the ventilated isopycnal, u g T s is negative and it approaches the outcrop from the south through the deep mixed layer region. At the MLD front, u g T s vanishes, that is, the horizontal velocity of the particle becomes parallel to the outcrop. After that, u g T s is positive and it leaves the outcrop and flows southeastward along the isopycnal under thin surface stratification. In this subduction, the trajectory of the water particle does not cross the outcrop; instead, it is subducted parallel to the outcrop at the MLD front (see Fig. 10). 132 S. Nishikawa and A. Kubokawa

9 Fig. 11. Example of surface density made by controlling surface temperature condition (left), and MLD distribution corresponding to that case (right). MLD is defined using the density difference 0.01σ θ. The present experiment allows us to outline how the mixed layer depth is determined, and why the sharp front occurs in the mixed layer depth, as follows: The western boundary current advects a thick warm water northward and the surface is cooled in this region. The mixed layer depth there will be determined by the sea surface temperature (SST) and the stratification; that is, the mixed layer depth is the depth of the isopycnal whose temperature is the same as SST. Therefore, it increases northward in the western boundary region. Since SST tends to be high in the west because of the temperature advection, the water flowing eastward after leaving the western boundary still experiences the decrease of SST and the mixed layer continues to deepen. While flowing eastward, the current direction gradually changes from eastward to southward as the Sverdrup theory predicts, and the development of the mixed layer ceases where the current direction is parallel to the SST contour. After that, since the SST is higher than that of the water flowing from the western boundary region, the water is subducted under a thin stratified surface layer. This causes the abrupt change in MLD. This survey suggests that, if the SST increases eastward, the subduction described above will not occur and the deep mixed layer will lie only in the western boundary region. Figure 11 shows that case, in which T a is increased eastward to control the SST distribution. Although the mixed layer is deep in the subpolar gyre (north of 44 N) and near the western boundary, there is no MLD front in the interior region of the subtropical gyre. It should also be noted that there seems to be an MLD front in the subpolar gyre region but the MLD changes rather gradually. In this region, water particles flow from the southern region where u g T s > 0 to the northern deep mixed layer region where u g T s < 0. The flow direction in this case is opposite to that in the subtropical gyre. Therefore, the surface temperature gradually decreases along the flow trajectories and the mixed layer gradually develops northward to the north side of u g T s = 0. That is, the sharp MLD front such as is seen in the subtropical gyre region is not formed. Here we have defined the MLD as a depth at which the density difference from that of the sea surface is 0.01σ θ. In model studies, 0.1σ θ is often used as the density difference (e.g., Kubokawa and Inui, 1999). When we use 0.1σ θ, the MLD front comes out a little to the south (about 2 3 degrees) compared with that defined by 0.01σ θ. This means that there is thin surface stratification in the area between the MLD front defined by 0.01σ θ and that defined by 0.1σ θ. In other words, the density difference 0.1σ θ is too large to resolve the important surface stratification which is associated with the MLD front. Thus, 0.01σ θ is a better value for this study. In the present study we used an idealized ocean GCM in which the formation of the mixed layer occurs only by convective adjustment, the ocean is driven by steady forcing and meso-scale eddies are not permitted. These simplifications yield a clear result. Qu et al. (2002), using an eddy-permitting GCM, found that meso-scale activities enhance the subduction rate. The relation between the mean location of MLD front and mean upper layer current/sst may also be affected by meso-scale eddies. Time-dependent forcing may have similar effects to the eddies. These points should be clarified in a future study. Acknowledgements The authors would like to thank Prof. L. D. Talley for valuable comments and advice. Dr. H. Hasumi kindly Mixed Layer Depth Front in an Idealized Ocean GCM 133

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