Effects of large-scale wind on the Kuroshio path south of Japan in a 60-year historical OGCM simulation

Abstract

The effects of large-scale wind forcing on the bimodality of the Kuroshio path south of Japan, the large meander (LM) and non-large meander (NLM), were studied by using a historical simulation (1948–2007) with a high-resolution Ocean general circulation models (OGCM). The Kuroshio in this simulation spent much time in the NLM state, and reproduced several aspects of its long-term path variability for the first time in historical OGCM simulation, presumably because the eddy kinetic energy was kept at a moderate level. By using the simulated fields, the relationships between wind forcing (or Kuroshio transport) and path variation proposed by past studies were tested, and specific roles of eddies in those variations were investigated. The long-term variation of the simulated net Kuroshio transport south of Japan was largely explained by the linear baroclinic Rossby wave adjustment to wind forcing. In the simulated LM events, a triggering meander originated from the interaction of a wind-induced positive sea surface height (SSH) anomaly with the upstream Kuroshio and was enlarged by cyclonic eddies from the recirculation gyre. The cyclonic eddy of the trigger meander was followed by a sizable anticyclonic eddy on the upstream side. Subsequently, a weak (strong) Kuroshio favored the LM (NLM). The LM tended to be maintained when the Kuroshio transport off southern Japan was small, and increasing Kuroshio transport promoted decay of an existing LM. The supply of disturbances from upstream, which is related to the wind-induced SSH variability at low latitudes, contributed to the maintenance of an existing LM.

Appendices

Appendix 1: Linear baroclinic vorticity model

To understand the long-term variation of the simulated Kuroshio transport, the result is compared with that of the linearized quasi-geostrophic 1.5-layer reduced gravity model that governs the large-scale, baroclinic ocean response to surface wind stress curl forcing (Qiu 2003). The governing equation is

$$ \frac{\partial \Uppsi_{\rm Sv}}{\partial t}-c_R \frac{\partial \Uppsi_{\rm Sv}} {\partial x} = - \frac{g^{\prime}H} {\rho_0 f^2} \hbox{curl} \tau, $$

(2)

where $\Uppsi_{\rm Sv}$ is the vertically integrated horizontal transport stream function relative to the eastern boundary, c _R is the speed of the long baroclinic Rossby waves, $g^{\prime}$ is the reduced gravity, ρ₀ is the reference density, f is the Coriolis parameter, H is the upper layer thickness, and curl τ is the wind stress curl. Integrating (2) from the eastern boundary (x _e ) along the baroclinic Rossby wave characteristic, we have

$$ \Uppsi_{\rm Sv} (x,y,t) = \frac{g^{\prime}H} {\rho_0 f^2 c_{R} } \int\limits^{x}_{x_e} \hbox{curl} \tau \left(x^{\prime}, y, t + \frac{x-x^{\prime}} {c_R} \right) dx^{\prime}, $$

(3)

where we take $\Uppsi_{\rm Sv} (x_e,y,t) = 0$. The layer thickness H is implicitly adjusted so that Eq. (2) becomes the Sverdrup balance in a steady state, that is,

$$ H = \frac{f^2 c_R} {g^{\prime} \beta}, $$

(4)

yielding

$$ \Uppsi_{\rm Sv} (x,y,t) = \frac{1} {\rho_0 \beta} \int\limits^{x} _{x_e} \hbox{curl} \tau \left(x^{\prime}, y, t + \frac{x-x^{\prime}} {c_R} \right) dx^{\prime}, $$

(5)

where β is the meridional gradient of the Coriolis parameter.

To hindcast $\Uppsi_{\rm Sv}$ using Eq. (5), monthly wind stress data either recalculated during the model run (for REL) or given by the reanalysis (for ABS) is used. The speed of the baroclinic Rossby wave (c _R ) is taken from Qiu (2003) for mid-latitudes and from Killworth and Blundel (2003) for low-latitudes.

Appendix 2: Definition of the Kuroshio path

The simulated Kuroshio paths are classified into four states (LM, NNLM, ONLM, and TSLM; Fig. 1) on the basis of the southward extent of water colder than 15°C at 300 m depth from the southern coast of Japan and the longitude of the main body of the meander defined as the location of the minimum barotropic stream function in this cold water region. Note that Mizuno and White (1983) defined the Kuroshio path in the Kuroshio Extension region by the location at 300 m depth of the 12°C isotherm. Our choice of 15°C is made for two reasons: the region of interest is in the warmer upstream region and the model has a slightly warm bias. We used the following procedures:

• If the maximum southward extent of the cold-water region between 135.5°E and 140.5°E is south (north) of 32.5°N, the Kuroshio is determined to be in the LM (NNLM) state, with the following exceptions:

• The LM is determined to be the TSLM if its southward extent at 135°E is south of 31°N.

• The LM is determined to be the ONLM if the longitude of its main body is east of 139°E and its southward extent at 140.5°E is south of 33°N.

• The NNLM is determined to be the ONLM if its southward extent at 140.5°E is south of 33°N.

Appendix 3: Definition of the net Kuroshio transport

In considering the relation between the Kuroshio path and transport, the Kuroshio in an unperturbed state is treated as the basic state. Thus, the net or throughflow transport past the southern coast of Japan, excluding the contribution by eddies, is dynamically relevant. Here we explain the definition of the throughflow transport for the simulation, the linear model, and the repeat hydrographic observation along 137°E. Admittedly the definitions are simplistic, but the results compare well with each other.

3.1 Simulation

Ideally, the net Kuroshio transport should be defined at the saddle point along the stream function ridge of the subtropical gyre south of Japan (Fig. 19b). But a well-defined ridge structure is often deformed by mesoscale eddies. For the simulated fields, the throughflow transport south of Japan is obtained by the following procedure.

• 1. Evaluate the maximum of the barotropic stream function between the southern coast of Japan and 25°N along each meridional lattice point of the model from 135° to 141°E (values are plotted in Fig. 19a, and locations are on the blue line in Fig. 19b).

• 2. The throughflow transport is defined as the smallest of these values (circle in Fig. 19a).

Fig. 19

Schematic that explains the definitions of throughflow transport used in this study. a The maximum of the barotropic stream function for 1996 (shades in b) between the southern coast of Japan and 25°N as a function of longitude. The circle at the lowest value of these maxima defines the throughflow transport for the simulation. b The barotropic stream function for 1996 of the simulation (shades) and the bathymetry (purple dashed contours; depth in km). The heavy blue line connects the locations of the maximum barotropic stream function between the southern coast of Japan and 25°N along each meridional grid line. Their values are plotted in a. The red line represents the meridian of 137°E along which repeat hydrographic observations are conducted. The green line from 26° to 32°N along 140°E represents the line along which the stream function from the linear model is averaged to assess the throughflow transport. c The barotropic stream function along 137°E (red line of b). The symbol X defines the throughflow transport for the hydrographic observation along 137°E. See "Appendix 3" for details

Note that the zero of the simulated stream function is placed on the main island of Japan.

3.2 Linear baroclinic vorticity model

The throughflow transport south of Japan for the linear baroclinic vorticity model ("Appendix 1") is defined as the mean value of the stream function between 26° and 32°N along 140°E (green line in Fig. 19b). The zero of this stream function is placed at the western boundary of the American continent. As shown in Fig. 4c, the maximum stream function in the subtropical gyre of the linear model appears around 26°–32°N south of Japan. The 140°E meridian is on the Izu Ridge and is the eastern entrance for the southwest-flowing recirculation gyre that eventually leaves the region south of Japan as the Kuroshio and the relatively small Tsushima warm current (∼2.5 Sv).

3.3 Repeat hydrographic section along 137°E

To obtain the throughflow transport across the vertical section along the 137°E meridian, we had to exclude its local enhancement by the anticyclonic eddy off Shikoku. The hydrographic observation analysis team of JMA uses the following procedure (T. Nakano, personal communication).

• 1. The eastward transport stream function is calculated by integrating the vertically integrated geostrophic eastward transport relative to a depth of 1,500 m southward from the southern coast of Japan.

• 2. Searching southward along the section from the southern coast of Japan, the net Kuroshio transport is obtained as the first minimum value after the maximum stream function is found (the symbol X in Fig. 19c).

3.4 Comparison

Figure 5b–d show time series. The simulated fields show considerable intra-annual variability reflecting the nonlinear effect, but there is also clear long-term variability that is largely tracked by the linear model (Fig. 5b). The correlation coefficient for the annual mean time series of the simulation and the linear model shown in Fig. 5c is 0.575 for 1948–2007. The effective degree of freedom based on the formula for red-noise processes (Bartlett 1935; Bretherton et al 1999) is 18 for this correlation, and the correlation coefficient at the 1 % significance level for 18 degrees of freedom is 0.561.

Figure 5d compares the method of “Simulation” section applied to the simulation (green line), the step 2 of “Repeat hydrographic section along 137°E” section applied to the simulation (magenta line), and the whole procedures of “Repeat hydrographic section along 137°E” section applied to the hydrographic observations (137°E) (blue line). The bias between the simulation and the observations arises from the fact that the observations use a level of no motion at 1,500 m. The simulation is expected to be larger by the amount of the missing part of the barotropic component in the observations. By definition, the method of “Simulation” section would yield a larger transport than applying the step 2 of “Repeat hydrographic section along 137°E” section to the simulation. The correlation coefficient for the 5-year running mean between and the simulation (green) and the observations (light blue) is 0.776 for 1969–2005. That for the 5-year running mean between the observations (light blue) and the result of applying the step 2 of “Repeat hydrographic section along 137°E” section to the simulation (magenta) is 0.859 for 1969–2005. The effective degree of freedom for the 5-year running mean data is determined here to be 8 (∼(2007–1967)/5). The correlation coefficient at the 1 % significance level for 8 degree of freedom is 0.765.

Appendix 4: Eddy identification and tracking procedure

Eddies are simply connected regions with large and positive values of a quantity (e.g., Isern-Fontanet et al. 2003)

$$ Q = -\left(\frac{\partial u} {\partial x} \right)^2 -\left(\frac{\partial v} {\partial x} \right) \left(\frac{\partial u} {\partial y} \right), $$

(6)

which measures the relative contribution of deformation and vorticity for an almost divergence free two-dimensional turbulent flow. This quantity corresponds to the Okubo-Weiss parameter (Okubo 1970; Weiss 1991) except for a factor of 4 and a global change of sign. Cyclonic eddies are identified as simply connected regions where Q > 2.0 × 10⁻¹²s⁻² and vorticity is positive.

Using a series of 5-day mean outputs, eddies are identified on the basis of the horizontal velocity fields at 100 m depth. The center of an eddy is defined as the SSH maximum or minimum. Eddies are tracked in the following manner: If an eddy with the same sign of vorticity is found within 1.5° of the eddy’s center in the next time step, it is regarded as the same eddy. If two eddies from the previous time step reach the same eddy, tracking continues for the eddy with the longer life time.