Diapycnal mixing induced by tide–topography interaction, one of the essential factors maintaining the global ocean circulation and hence the global climate, is modulated by the 18.6-yr period oscillation of the lunar orbital inclination, and has therefore been hypothesized to influence bidecadal climate variability. In this study, the spatial distribution of diapycnal diffusivity together with its 18.6-yr oscillation estimated from a global tide model is incorporated into a state-of-the-art numerical coupled climate model to investigate its effects on climate variability over the North Pacific and to understand the underlying physical mechanism. It is shown that a significant sea surface temperature (SST) anomaly with a period of 18.6 years appears in the Kuroshio–Oyashio Extension region; a positive (negative) SST anomaly tends to occur during strong (weak) tidal mixing. This is first induced by anomalous horizontal circulation localized around the Kuril Straits, where enhanced modulation of tidal mixing exists, and then amplified through a positive feedback due to midlatitude air–sea interactions. The resulting SST and sea level pressure variability patterns are reminiscent of those associated with one of the most prominent modes of climate variability in the North Pacific known as the Pacific decadal oscillation, suggesting the potential for improving climate predictability by taking into account the 18.6-yr modulation of tidal mixing.
It is well known that the climate in the North Pacific Ocean has significant variability on bidecadal time scales, in contrast to the equatorial Pacific where interannual variability is dominant (Minobe 1999, 2000; Biondi et al. 2001). The bidecadal climate variability over the North Pacific has been explained by the midlatitude air–sea interaction including oceanic Rossby waves and the associated western boundary current fluctuations (e.g., Latif and Barnett 1996; Schneider et al. 2002) and/or by the atmospheric teleconnections from the anomalous sea surface temperature (SST) pattern in the equatorial Pacific induced by El Niño–Southern Oscillation (ENSO)-like decadal variability (e.g., Lau 1997; Kleeman et al. 1999; Deser et al. 2004; Schneider and Cornuelle 2005). However, both explanations paid little attention to the ultimate forcing mechanism of the bidecadal time scale and therefore it remains uncertain whether the bidecadal climate variability in the North Pacific is completely the resonant response to stochastic atmospheric events or if it is forced continuously by some specific mechanism.
Strong tidal currents flowing over prominent topographic features generate large-amplitude internal waves that break, causing vigorous diapycnal mixing. The induced diapycnal mixing is one of the essential factors maintaining the global ocean circulation as well as the associated water mass formation and transportation, and hence the global climate (e.g., Munk and Wunsch 1998). It is widely accepted that tidal mixing is modulated by the oscillation of the lunar orbital inclination; the inclination of the moon’s orbital plane to the earth’s equatorial plane, which is 23.4° on long-term average, oscillates with an amplitude of 5.2° and a period of 18.6 yr, which induces the 18.6-yr oscillation of tidal forcing and presumably of diapycnal mixing. Tidal forcing of the two major diurnal constituents, K1 and O1, in particular, are modulated strongly, by up to 11% and 19%, respectively (Doodson 1921; Loder and Garrett 1978; Ray 2007). The 18.6-yr period nodal tidal cycle has therefore been hypothesized to possibly influence bidecadal variability not only in local water mass characteristics but also in basin-scale climate through the variation of diapycnal mixing (Loder and Garrett 1978; Cerveny and Shaffer 2001; Yasuda et al. 2006; McKinnell and Crawford 2007).
The Kuril Straits separating the Okhotsk Sea from the North Pacific are known as a representative region of strong diurnal tidal mixing caused by breaking coastal trapped waves and/or lee waves, as demonstrated by both numerical and observational studies (Nakamura et al. 2000; Tanaka et al. 2010b; Itoh et al. 2010; Yagi and Yasuda 2012). In addition, intermediate water mass characteristics in the Okhotsk Sea and in the northwestern North Pacific have been observed to show bidecadal variations synchronized with the 18.6-yr period nodal tidal cycle (Osafune and Yasuda 2006). The Kuril Straits are therefore thought to be one of the key locations for bidecadal climate variability over the North Pacific, such as the Pacific decadal oscillation (PDO) (Yasuda et al. 2006), which is one of the most prominent modes of climate variability whose spatial pattern is centered around the midlatitude North Pacific and whose time scale exhibits bidecadal periods as well as pentadecadal periods (Trenberth and Hurrell 1994; Mantua et al. 1997; Minobe 1997; Mantua and Hare 2002). In fact, by analyzing proxy data reconstructed from tree-ring chronologies, Yasuda (2009) showed that negative (positive) PDO tends to occur in the period of strong (weak) diurnal tides, although the underlying physical mechanism was not clarified.
Hasumi et al. (2008) assumed diapycnal diffusivity in the entire Kuril Straits to be uniformly 200 × 10−4 m2 s−1 and varied it with a period of 18.6 yr and amplitude of 30 × 10−4 m2 s−1 in a numerical climate model to examine its effects on climate variability over the North Pacific. They showed that the 18.6-yr modulation of strong tidal mixing localized in the Kuril Straits induces 18.6-yr periodicity in ENSO-like climate variability via a density anomaly first propagating southward along the western rim of the North Pacific as coastal Kelvin waves and then advected eastward by the Equatorial Undercurrent. However, the diapycnal diffusivity in the Kuril Straits assumed by Hasumi et al. (2008) is considerably different from the more realistic one estimated from model-predicted tidal energy dissipation rate (Tanaka et al. 2007, 2010b); specifically, it is not only one order of magnitude too large on the area average but also completely uniform in both the horizontal and vertical directions, both of which could lead to substantial differences in basin-scale ocean circulation and the associated water mass distribution (Tanaka et al. 2010a; Kawasaki and Hasumi 2010). In addition, the effects of 18.6-yr modulation of tidal mixing in regions other than the Kuril Straits are not taken into account at all in Hasumi et al. (2008).
In this study, the spatial distribution of diapycnal diffusivity together with its 18.6-yr oscillation estimated based on a global barotropic tide model is incorporated into a state-of-the-art numerical coupled climate model to investigate its effects on climate variability over the North Pacific. Furthermore, based on the calculated results, we try to explain the underlying physical mechanism in terms of a purely oceanic response to the modulation of tidal mixing and a coupled ocean–atmosphere feedback response that can amplify the oceanic response.
2. Numerical experiments
The numerical model used in this study is the same as Hasumi et al. (2008), that is, the medium resolution version of Center for Climate System Research (CCSR)–National Institute for Environmental Studies (NIES)–Frontier Research Center for Global Change (FRCGC) Model for Interdisciplinary Research on Climate (MIROC) 3.2, which calculates states and interactions of various elements of the climate system (atmosphere, ocean, land, and cryosphere) by specifying solar radiation and atmospheric concentration of radiatively active gases. The atmospheric component has 2.8° horizontal resolution and 20 vertical levels, and the oceanic component has 1.4° zonal resolution, 0.56°–1.4° meridional resolution (enhanced around the equator), and 44 vertical levels.
where KV is the vertical eddy diffusivity coefficient, Γ is the mixing efficiency assumed to be 0.2, N is buoyancy frequency reproduced in the climate model, and ɛ is the energy dissipation rate due to breaking internal waves estimated based on a global barotropic tide model (Egbert and Ray 2000) as follows. First, the energy flux divergence of surface tides is estimated based on the model-predicted global distribution of tidal elevation and tidal velocity. Part of this barotropic energy flux divergence is dissipated by bottom friction, which we assume to be a cube of model-predicted tidal velocity multiplied by a constant drag coefficient of 2.5 × 10−3, and the remaining is assumed to be converted to internal tides. The globally integrated energy conversion rates are then estimated to be 800, 191, 174, and 112 GW for the M2, S2, K1, and O1 tidal constituents, respectively, which are roughly consistent with the latest estimates using a high-resolution global baroclinic tide model (Niwa and Hibiya 2011). Next, following previous studies, it is assumed that, in regions where tidal frequency becomes larger (less) than the inertial frequency, 0.3 (1.0) of the generated internal tide energy flux is dissipated near the generation region inducing the locally enhanced mixing, with the remaining 0.7 (0.0) radiating away contributing to the background vertical diffusivity of 1 × 10−5 m2 s−1. The obtained energy dissipation is then area-averaged within each horizontal grid cell of the climate model as shown in Fig. 1a, where locally enhanced dissipation over rough bottom topography is clearly seen, which is again consistent with the estimates by several previous studies, each employing different manners (Egbert and Ray 2000; St. Laurent et al. 2002; Simmons et al. 2004a; Niwa and Hibiya 2011). Finally, the obtained energy dissipation rate is distributed vertically within each water column by assuming that it decays exponentially away from the ocean bottom with a scale height of 500 m, as suggested by observational studies (St. Laurent et al. 2001) and widely employed in recent ocean general circulation models (Simmons et al. 2004b; Saenko and Merryfield 2005; Jayne 2009).
Since the tidal energy dissipation rate is here assumed to be proportional to the product of tidal elevation and tidal velocity, it is expected to be proportional to the square of the tidal forcing. We therefore assume that the energy dissipation of each tidal constituent is modulated from its mean value at each location by the ratio of twice the modulation of the tidal forcing (22%, 38%, and 7% for K1, O1, and M2 tidal constituents, respectively), under the approximation that the modulation amplitude is small enough compared to the mean value. Figure 1b shows the global distribution of the amplitudes of the 18.6-yr oscillation of the energy dissipation rate. Note that the energy dissipation rate of the semidiurnal M2 constituent is modulated exactly out of phase with those of the diurnal K1 and O1 constituents, which is therefore denoted by negative values. Figure 1b shows that large amplitudes are mostly confined to limited areas such as the Aleutian Passes, the Kuril Straits, the Okhotsk Sea, and the Weddell Sea.
The climate model incorporating the steady tidal energy dissipation rate is first integrated for 100 yr from a control climate state obtained after 2900-yr integration under the fixed external forcing at the year 1850 and the horizontally uniform background ocean vertical diffusivity. Employing the obtained climate state as the initial condition, three numerical experiments are performed by changing the vertical diffusivity as follows. The first experiment assumes the steady energy dissipation rate continuously (case CONST), whereas the second experiment assumes one modulated globally with the period of 18.6 yr (case VAR). In the third experiment, the energy dissipation rate is modulated only in the Kuril Straits and the Okhotsk Sea (hatched region in Fig. 2a) where the strongest 18.6-yr modulation exists (see Fig. 1b; case KURIL). Each experiment is integrated for a further 430 years, all of which are used for the analyses below.
a. 18.6-yr variability of SST and SLP
Figures 2a and 2b show differences of the annual mean SST and the winter mean (December–February) sea level pressure (SLP), respectively, between composites within the periods of strong and weak diurnal tidal mixing for the case VAR. The composites are calculated by first dividing the 430 years into four groups based on the phase of each year relative to the 18.6-yr tidal cycle and then taking an average of each group. During strong tidal mixing, a large positive SST anomaly extends not only into the Kuril Straits and the Okhotsk Sea but also along the Kuroshio–Oyashio Extension (KOE) region where tidal mixing is very weak, surrounded by a relatively small negative SST anomaly in the eastern and northern North Pacific as well as in the equatorial Pacific. We also find that the high SLP anomaly is widely distributed around the southeastern part of the Aleutian low (i.e., the Aleutian low is weakened and shifted northwestward) during strong tidal mixing. The obtained anomalous SST and SLP patterns are similar to those associated with the negative phase of the PDO, which is consistent with the findings from observations (Yasuda et al. 2006; Yasuda 2009). Employing the winter mean instead of the annual mean for the SST does not change either the pattern or magnitude of the difference much in the KOE region, whereas employing the annual mean instead of the winter mean for the SLP does not change the pattern but does reduce the magnitude of the difference to less than one-third, in accordance with the Aleutian low appearing only in winter.
To investigate in more detail the anomalous SST and SLP patterns associated with the modulation of tidal mixing, we calculate lagged linear regression of SST and SLP anomalies onto the normalized 18.6-yr tidal cycle as well as lagged correlation between the SST (SLP) anomaly and the 18.6-yr tidal cycle. Figure 3 shows the maximum regression coefficients and the time lags between the SST anomaly and the 18.6-yr tidal cycle, while Fig. 4 shows the maximum correlation coefficients together with the 5% significance level of a t test with effective degrees of freedom equal to the data length divided by the decorrelation time scale of the SST anomaly at each location (Trenberth 1984). Both Figs. 3 and 4 show data for each of the three numerical experiments. Note that since the lagged regression calculated here is onto the trigonometric function, the maximum regression coefficient and the time lag coincide with the amplitude and phase, respectively, of the harmonic component with the corresponding period (18.6 yr in this case) when the time series is much longer than this period as satisfied in the present numerical experiments. Figures 3b and 4b confirm that, for the case VAR, the SST anomaly is statistically significant not only in the Kuril Straits and the Okhotsk Sea but also along the KOE region where the time lags are ~0 yr and the amplitudes reach more than 0.25°C, whereas it can hardly be identified as significant in the other regions. Furthermore, the SST anomaly along the KOE region for the case KURIL is very similar to that for the case VAR except that the amplitudes are slightly smaller (Figs. 3c and 4c), whereas a significant SST anomaly can hardly be found anywhere in the case CONST (Figs. 3a and 4a). This result indicates that it is the 18.6-yr modulation of tidal mixing in the Kuril Straits and the Okhotsk Sea that mainly induces the anomalous SST pattern along the KOE region, while modulation of tidal mixing in the other regions possibly plays a relatively minor role.
Figures 5a and 5b show lagged regressions of the winter mean SLP anomaly onto the normalized 18.6-yr tidal cycle and lagged correlations between the two, respectively, both for the case VAR. Figure 5a shows that the SLP around the southeastern part of the Aleutian low varies with a maximum amplitude of ~1 hPa and is nearly in phase with tidal mixing. A similar anomalous SLP pattern is obtained for the case KURIL while no such a pattern is obtained for the case CONST (not shown), as for the SST anomaly. Although the correlation coefficients are small, such that the maximum value is ~0.15 (Fig. 5b) since the effects of tidal mixing are masked or overwhelmed by intrinsic variability of the atmosphere, it exceeds the 5% significance level, suggesting that the SST anomaly and the associated surface heat flux anomaly in the KOE region possibly affect the Aleutian low. This inference must be viewed with some caution because such small regions exceeding the 5% significance level can appear even in the case CONST; however, the relation between the SST and the SLP anomalies obtained in the present study is similar to that suggested by previous studies concerning an ocean to atmosphere feedback (Latif and Barnett 1994, 1996; Frankignoul et al. 2011). In addition, the power spectrum of the North Pacific index, defined as a time series of the SLP anomaly averaged over the region 30°–65°N, 160°E–140°W and divided by the standard deviation, shows a weak peak at the periods of 18.6 yr for both cases VAR and KURIL (red and blue lines of Fig. 16b), which is not seen in case CONST (green line of Fig. 16b). All these results support the above inference. Finally, it is noted that a significant SLP anomaly also appears right above the inner Okhotsk Sea with a relatively small horizontal scale, which is nearly out of phase with tidal mixing and is probably produced directly by the locally enhanced SST anomaly below (i.e., a positive SST anomaly warms the lower atmosphere to induce an upward flow accompanied by a negative SLP anomaly, and vice versa).
b. Physical processes inducing the 18.6-yr variability
1) Heat budget in the upper ocean
To clarify the generation mechanism of the above 18.6-yr variability, we first analyze the heat budget in the upper ocean using a linearized thermodynamic equation formulated in terms of long-term mean denoted by an overbar and 18.6-yr period fluctuation denoted by a prime as
where t is the time, T is the temperature, ∇H = (∂/∂x, ∂/∂y) is the horizontal gradient operator with (x, y) the zonal and meridional coordinates, u = (u, υ) is the velocity components in the (x, y) directions, w is the velocity component in the z direction with z the vertical coordinate, Fz is the vertical eddy heat flux, and (residual) indicates all the remaining terms such as convective mixing and horizontal diffusion (Osafune and Yasuda 2012). Here, is defined as
where Qsurface is the surface heat flux from the ocean to the atmosphere. In all the analyses below, the long-term mean and the 18.6-yr period fluctuation terms are both calculated from the amplitudes and phases of the lagged regression.
Figure 6a shows the time series of the volume-averaged heat budget in the upper layer of the Kuril Straits and the Okhotsk Sea region (hatched region in Fig. 2a and a depth of 250 m, roughly corresponding to the maximum vertical temperature gradient between the dichothermal and mesothermal structures). We can see that the largest contribution is from the anomalous vertical diffusion of mean temperature (orange dashed line) nearly out of phase with tidal mixing, meaning that the anomalously increased (decreased) vertical diffusivity during strong (weak) tidal mixing induces heat flux convergence (divergence). This is as expected given that there exists a locally enhanced 18.6-yr modulation of tidal mixing as well as a vertical temperature maximum at the subsurface layer in this region (Ueno and Yasuda 2000). The anomalous vertical diffusion of mean temperature is compensated mainly by the vertical diffusion of temperature anomaly (orange solid line) while the tendency of temperature anomaly (purple line) remains relatively small throughout the tidal cycle. As a result, the temperature anomaly in the upper layer of this region varies nearly out of phase with the aforementioned heat flux divergence resulting from the anomalous vertical diffusivity and hence varies nearly in phase with tidal mixing [i.e., becomes positive (negative) during strong (weak) tidal mixing] as a whole. Figure 6a also shows that the anomalous vertical advection of mean temperature (green dashed line) is always small, probably because the modulation period of 18.6 yr is too short for the Pacific thermohaline circulation to fully develop to attain a quasi-steady balance with the anomalous density distribution.
In contrast to this, in the upper layer of the western part of the KOE region (the left box in Fig. 2a and a depth of 325 m, roughly corresponding to the winter mixed layer depth), it is the anomalous horizontal advection of mean temperature that dominates the heat budget (blue dashed line of Fig. 6b). The spatial distribution of this term at the ocean surface is depicted in Fig. 7, which shows the existence of large amplitudes along the western boundary, especially around the latitudinal range of the KOE. This suggests that tidal mixing first modulates the western boundary current, which then generates the large SST anomaly in the western KOE region where meridional gradient of the mean SST is large (see contours of Fig. 2a) and therefore large values of can be effectively created (Kwon and Deser 2007). The anomalous horizontal advection of mean temperature acts to induce heat flux convergence (divergence) during strong (weak) tidal mixing and is compensated mainly by the horizontal advection of temperature anomaly (blue solid line) while the tendency of temperature anomaly remains small again, so that the temperature anomaly varies nearly out of phase with this heat flux divergence and hence varies nearly in phase with tidal mixing.
In the eastern part of the KOE region (the right box in Fig. 2a and a depth of 325 m), the horizontal advection of temperature anomaly in turn becomes the dominant term (blue solid line of Fig. 6c). This implies that the temperature anomaly created in the western KOE region is advected eastward by the mean Kuroshio and the Oyashio Extension to be extended over a broad area of the North Pacific, while anomalous meridional surface Ekman flow (Wu et al. 2003) and anomalous vertical mixing possibly play relatively minor roles in generating the temperature anomaly in this region. Furthermore, Figs. 6b and 6c also show that the surface heat flux anomaly (red line) is generally in phase with the SST anomaly along the KOE region and thus tends to damp it, indicating that the ocean forces the atmosphere rather than vice versa (Tanimoto et al. 2003; Nonaka and Xie 2003). We speculate that this surface heat flux anomaly induces the SLP anomaly in the Aleutian low (Fig. 5) through the variation of storm-track activity and associated eddy transport of heat and momentum (Peng and Whitaker 1999; Kushnir et al. 2002; Nakamura et al. 2008), bearing in mind that much controversy exists over the expectation that the midlatitude SST anomaly and the resultant surface heat flux anomaly will exert significant effects on the overlying atmosphere. It should be noted that product terms between the fluctuations can induce mean plus harmonic (i.e., 9.3-yr period) components, which can reach nearly half of the maximum term in Eq. (2) in the Okhotsk Sea, whose effect must be examined in the future.
2) Variability of the western boundary current
We next confirm the notion that the western boundary current (WBC) is varied by the 18.6-yr modulation of tidal mixing. Figure 8a shows the amplitudes and phases of 18.6-yr variation of the barotropic streamfunction (defined as the streamfunction of the depth-integrated horizontal velocity) and Fig. 8b shows its anomaly when the tidal mixing is strongest. Anticyclonic circulation anomaly as much as ~1 Sv (1 Sv ≡ 106 m3 s−1) can be found in the latitudinal range of ~(30°–50°)N, which represents northward WBC anomaly in the western KOE region during strong tidal mixing, as expected from the SST anomaly. The largest circulation anomaly is confined locally around the center of the Kuril Straits, whereas the overall pattern of the circulation anomaly extends broadly over the basin, suggesting that the modulation of tidal mixing generates the anomalous flow not only directly but also indirectly probably through the basin-scale wind stress anomaly.
The localized velocity anomaly around the Kuril Straits is more clearly seen in the intermediate depth and can be explained in terms of density anomaly induced by the locally enhanced tidal mixing. Since the amplitude of the 18.6-yr modulation of tidal mixing in the center of the Kuril Straits is extremely large, the water column is homogenized (strongly stratified) so that the upper water becomes denser (lighter) and lower water becomes lighter (denser) than the long-term mean during strong (weak) tidal mixing. If we assume that the modulation of tidal mixing simply varies the water mass distribution within each water column and hence there is no pressure variability at the ocean bottom, anticyclonic (cyclonic) geostrophic circulation anomaly then develops around the homogenized (strongly stratified) water column through the thermal wind balance:
where u′ and ρ′ are the horizontal velocity anomaly and the density anomaly associated with the 18.6-yr modulation of tidal mixing, respectively, g is the acceleration due to gravity, ρc is the reference water density, f is the Coriolis frequency, and k is the vertically upward unit vector. Although this assumption is only approximate, these anomalies are actually seen as in Figs. 9a and 9b, which show the density anomaly at a depth of 825 m and the horizontal velocity anomaly at a depth of 1125 m around the Kuril Straits, both for the time of the strongest tidal mixing. These anomalies roughly satisfy Eq. (5) and the velocity anomaly is strongest while the density anomaly changes the sign around the depth of 1125 m. The correlation coefficients between the barotropic streamfunction anomaly and the 18.6-yr tidal cycle and between the density anomaly below the intermediate depth and the 18.6-yr tidal cycle both exceed 0.7 in the center of the Kuril Straits, large enough to judge that tidal mixing is the main cause of their variability.
Figure 10a shows the annual mean wind stress anomaly when the tidal mixing is strongest, where anticyclonic circulation around the SLP anomaly shown in Figs. 2b and 5a can be clearly recognized. Corresponding to this wind stress anomaly, the wind stress curl anomaly is generally negative except a limited area off the east coast of northern Japan, and hence the Sverdrup transport is southward in the broad area of the North Pacific, as shown in Fig. 10b. Here we define wind-induced barotropic WBC anomaly as the opposite of the integral of the Sverdrup transport from the eastern to the western boundary across the basin with no time lag. Figure 11a shows the time series of the calculated wind-induced barotropic WBC anomaly (dashed line), together with that of the maximum barotropic streamfunction anomaly (solid line), both at 39°N, whereas Fig. 11b shows the latitudinal distribution of the amplitudes of these two transport anomalies. The two lines roughly coincide with each other in both panels, indicating that the barotropic streamfunction anomaly and hence the barotropic WBC anomaly in this latitudinal range are mainly induced by the wind stress anomaly with rapid response time, which is probably achieved by barotropic Rossby waves that take no more than ~10 days to propagate across the basin (Isoguchi et al. 1997). Generally speaking, the WBC anomaly becomes northward (southward) to induce the positive (negative) SST anomaly during strong (weak) tidal mixing, although the exact reason for the lead of ~2 yr of the transport anomalies relative to the tidal mixing is not so clear.
We can therefore conclude that the 18.6-yr modulation of tidal mixing induces the circulation anomaly not only directly by generating the local density anomaly in the Kuril Straits but also indirectly by generating the basin-scale wind stress anomaly associated with the Aleutian low variation through the midlatitude air–sea interaction. A close look at Fig. 7 shows that the amplitudes of the anomalous horizontal advection of mean temperature, the generating term of the SST anomaly, have two maxima: a larger one at the middle of the KOE region and a smaller one just south of the Kuril Straits, or around the northern edge of the KOE region, reflecting the two different mechanisms. The smaller maximum is located south of the maximum velocity anomaly around the Kuril Straits because the meridional gradient of the mean SST increases toward the south at these latitudes.
3) Barotropic and baroclinic responses of the ocean current
In this section, the vertical structure of the velocity anomaly is investigated because the simulated mean flow and the anomalous flow are both confined to the surface layer rather than distributed vertically uniformly. As a variable representative of the baroclinic response, we employ here baroclinic pressure defined as total minus depth-averaged (barotropic) following previous studies (Schneider et al. 2002; Tatebe and Yasuda 2004). Figure 12a shows the horizontal distribution of the barotropic pressure anomaly, whereas Figs. 12b and 12c show those of the baroclinic pressure anomaly at depths of 80 and 4025 m, respectively, and Fig. 12d shows the vertical cross section of the baroclinic pressure anomaly at 39°N. The spatial pattern of the barotropic pressure anomaly is very similar to that of the barotropic streamfunction anomaly shown in Fig. 8a. Figure 12 indicates that, in the KOE region, the baroclinic response is dominated by the first vertical mode, which seems to be generated near the western boundary, being synchronized with the barotropic response, and to be advected eastward by the Kuroshio and the Oyashio Extension over a distance of ~30° longitudes in ~2 yr (Nakamura et al. 2006). Since the baroclinic component is much larger than the barotropic one and they are nearly in phase with each other in the surface layer whereas they are of the same order of magnitude and are nearly out of phase in the deeper layer, the baroclinic response works to confine the velocity anomaly resulting from the barotropic response within the surface layer and to keep the deeper layer stagnant.
This adjustment process can be interpreted in terms of a meridional shift of the subtropical–subarctic gyre boundary centered around ~39°N. Because the meridional gradient of the long-term mean density is large in the latitudes around the gyre boundary (Fig. 13a), a small meridional shift of this mean density field due to a barotropic flow caused by wind stress variation is also accompanied by baroclinic motions. Actually, a large-amplitude density variation nearly out of phase with tidal mixing (a negative density anomaly in association with a northward WBC anomaly and vice versa) can be found around the gyre boundary (Fig. 13b), together with the associated zonal velocity variation on both sides of it (Fig. 13c). On the other hand, Figs. 12b and 12c do not show a clear baroclinic signal propagating westward in both the subtropical and the subarctic regions, meaning that the baroclinic Rossby waves, which are shown to carry decadal climate variability to the west by several previous observational and modeling studies (Latif and Barnett 1996; Schneider et al. 2002; Tatebe and Yasuda 2005; Kwon and Deser 2007; Zhong and Liu 2009; Qiu and Chen 2010), play a relatively minor role at least in generating the 18.6-yr variability in this particular numerical model. This discrepancy is perhaps linked to the fact that the SST and the pressure anomalies are largest in the western KOE region just east of Japan in the present numerical model (Figs. 2a, 3b, and 12a–c), while they are as large or even larger in the central to the eastern North Pacific in the real ocean or in some other numerical models, which can propagate as baroclinic Rossby waves to affect the western North Pacific.
4) Baroclinicity of the lower atmosphere
Finally, the 18.6-yr variability of the storm-track activity is investigated in order to validate our speculation that it connects the surface heat flux anomaly in the KOE region to the SLP anomaly in the Aleutian low. Since the model output is only a monthly mean so that a life cycle of each eddy is not resolved, the Eady growth rate maximum defined as
where U is the mean zonal flow, is calculated here, which represents well the storm-track activity (Hoskins and Valdes 1990). Figure 14 shows the anomaly of the calculated growth rate when the tidal mixing is strongest, with the long-term mean growth rate superimposed, both averaged in the lower troposphere (700–1000 hPa) where σ is essential for development of synoptic-scale eddies. In the North Pacific storm-track region characterized by large long-term mean growth rate (33°–45°N, 145°E–165°W), the anomaly of the growth rate largely has negative values except near the northern edge where it has weak positive values, meaning that the storm track is shifted northward while being weakened when tidal mixing is strong. This variation of the storm-track activity can result from the northward shift of the SST front accompanied by the positive SST anomaly in the KOE region (Brayshaw et al. 2008; Ogawa et al. 2012) and is qualitatively consistent with the northwestward shift and weakening of the Aleutian low (Zhu et al. 2007; Taguchi et al. 2012).
5) Results from an ocean-only model
All the above results indicate the following scenario for the generation of the SST anomaly in the western KOE region. First, as a purely oceanic response, it is induced by the horizontal circulation anomaly around the center of the Kuril Straits, which results from the density anomaly due to the modulation of tidal mixing. The induced SST anomaly then forces the overlying atmosphere through the surface heat flux anomaly to induce the SLP and the associated wind stress anomalies around the southeastern part of the Aleutian low, which then vary the WBC to enhance the SST anomaly. Therefore, the SST anomaly originally induced by the oceanic process can be strengthened through the interaction with the atmosphere whereas it is also possible that the SST anomaly is weakened while giving a heat flux to the atmosphere.
To reveal which effect is dominant, an additional numerical experiment is carried out using the ocean component of the coupled climate model into which the global 18.6-yr modulation of the tidal mixing is incorporated. The model is forced by monthly climatologies of the surface wind stress and the surface heat and salt fluxes obtained in the climate model, which are fixed excluding the 18.6-yr variability so that neither positive nor negative feedback from the atmosphere works, and is driven for 60 years from an initial state also obtained from the climate model. Figure 15 shows the SST anomaly obtained by harmonically analyzing the calculated time series of the final 20 years. The phase relation remains relatively similar to that of the climate model but large amplitudes are confined to smaller area with the maximum value reduced to ~60% and slightly moved northeastward in location (cf. Fig. 3b), demonstrating that the SST anomaly is first induced by the ocean and then amplified by the atmosphere as a net effect. The maximum amplitude is shifted to just south of the Kuril Straits, near the smaller peak of the anomalous horizontal advection of mean temperature shown in Fig. 7 because of the lack of the feedback effect from the atmosphere, although it is still located slightly south of that by ~1°, probably owing to the effect of the advection of the temperature anomaly by the mean Oyashio.
As a final remark of this section, we note that essentially the same results are obtained from the analyses of the case KURIL throughout this section except that the amplitudes of the anomalies are slightly reduced overall, again showing the leading role of the tidal mixing in the Kuril Straits and the Okhotsk Sea in generating the 18.6-yr climate variability in the North Pacific. It must also be noted that not all of the anomalies mentioned in this section can be judged as statistically significant at high confidence level; however, they seem consistent with each other, which convinces us that they are not just spurious signals.
a. Comparison with observations and potential impacts on the real climate
In this study, the amplitudes of the SST anomaly in the KOE region associated with the 18.6-yr modulation of the tidal mixing reach ~(0.2°–0.3°)C, which are ~(15%–20%) of the standard deviations of the SST in the same region. Furthermore, the resultant anomalous SST and SLP patterns are reminiscent of those associated with the observed PDO. Indeed, the power spectrum of the PDO index defined as a time series of the leading empirical orthogonal function for the modeled North Pacific SST anomaly, which captures basic features of the observed PDO, and the power spectrum of the North Pacific index both show peaks at a period of 18.6 yr (Figs. 16a and 16b, respectively). These results suggest the possibility that the 18.6-yr modulation of tidal mixing induces the PDO-like variability or regulates the phase of the PDO, although the obtained spectral peaks are relatively weak so that they cannot be judged as statistically significant at high confidence level. It should also be pointed out that the climate in the North Pacific intrinsically has bidecadal variability, which seems to be comparable in energy to that forced by the modulation of tidal mixing, as exemplified by the fact that even the case CONST exhibits such variability. Furthermore, when compared with observations (Yasuda et al. 2006; Yasuda 2009), the spectral peaks are somewhat weaker and narrower, while the lags of the PDO relative to the tidal mixing are slightly earlier [~0 vs ~(2–4) yr]. The reasons for these discrepancies must be revealed in the future to obtain a definite conclusion about the role of the modulation of tidal mixing on bidecadal climate variability. Nevertheless, the results in this study suggest the possibility that we can improve climate predictability by taking into account the completely predictable 18.6-yr modulation of tidal mixing.
b. Comparison with a previous study
The results obtained in this study are somewhat different from those of Hasumi et al. (2008), who showed that the 18.6-yr modulation of tidal mixing in the Kuril Straits generates coastal trapped waves that propagate down to the equator to cause 18.6-yr periodicity in ENSO-like decadal variability. The different results must be derived from the different spatial distribution of the ocean vertical diffusivity because the other parameters are completely the same between the two studies. Here we raise a couple of possible explanations. One is that, since the vertical diffusivity in Hasumi et al. (2008) is assumed to be vertically uniformly 200 × 10−4 m2 s−1 so that it becomes much larger than ours especially in the thermocline, its 18.6-yr modulation can generate baroclinic Kelvin waves more effectively. The other is that, since the vertical diffusivity in Hasumi et al. (2008) is horizontally uniform throughout the Kuril Straits, its 18.6-yr modulation fails to induce the velocity anomaly around the center of the Kuril Straits that triggers the SST anomaly in the KOE region in our study. Identifying the definite reason for the differences, which requires more numerical experiments, is beyond the scope of this study. Moreover, if a subtle difference in spatial distribution of vertical diffusivity in the Kuril Straits can cause substantial differences in the climate variability all over the North Pacific, further exploration of exact spatial distribution of vertical diffusivity is needed for us to incorporate it into a higher-resolution numerical model to accurately assess its effects on climate variability.
c. Future work
Although the effects of the 18.6-yr modulation of tidal mixing on climate variability in the North Pacific and a possible underlying physical mechanism have thus been presented, there remain some problems to be investigated in the future. First of all, the relative importance of the bidecadal variability forced by the modulation of tidal mixing versus that intrinsic to the coupled climate system must be evaluated quantitatively. Second, climate variability in other regions such as the equatorial Pacific and the Southern Ocean, including bidecadal variability of the amplitude of the interannual variability of ENSO, which can also be affected by the 18.6-yr modulation of tidal mixing in the neighboring region, should also be examined. Finally, we have to validate our results using a higher-resolution numerical model that can include more sophisticated parameterization of tidal mixing (e.g., Klymak and Legg 2010; Kang and Fringer 2012) and can reproduce more realistic mean states and variability of both the ocean and the atmosphere. In particular, in addition to diapycnal mixing induced by barotropic to baroclinic energy conversion and subsequent internal wave breaking focused on in this study, diapycnal mixing due to barotropic tides directly dissipating their energy through bottom boundary layer processes at shallow seas must also be taken into account as in Lee et al. (2006); for example, the 18.6-yr modulation of bottom boundary layer mixing caused by a strong diurnal tidal flow on shelf regions of the Okhotsk Sea could affect the sea ice formation and the resultant water mass formation and air–sea heat exchange (Shcherbina et al. 2003; Ono et al. 2006). Needless to say, these numerical experiments must be carefully validated through a comparison with various observational datasets including instrumental and proxy records.
In this study, the spatial distribution of diapycnal diffusivity together with its 18.6-yr oscillation estimated from a global tide model has been incorporated into a state-of-the-art numerical coupled climate model to investigate its effects on climate variability over the North Pacific and to understand the underlying physical mechanism.
We have shown that a significant SST anomaly with a period of 18.6 yr appears not only in the Kuril Straits and the Okhotsk Sea where locally enhanced modulation of tidal mixing exists but also in the KOE region where tidal mixing is weak. The SST anomaly in the KOE region has an amplitude of ~(0.2°–0.3°)C and a lag of ~0 yr, so that positive (negative) SST anomaly tends to appear during strong (weak) tidal mixing. Corresponding to this SST anomaly, the SLP around the southeastern part of the Aleutian low has also been shown to have significant 18.6-yr variability with an amplitude of ~1 hPa and a lag of again ~0 yr, so that the Aleutian low tends to be weakened (deepened) and shifted northwestward (southeastward) during strong (weak) tidal mixing, suggesting that the SST anomaly in the KOE region exerts significant effects on the atmosphere. A series of numerical experiments have demonstrated that it is the 18.6-yr modulation of tidal mixing in the Kuril Straits and the Okhotsk Sea that mainly induces this variability in the North Pacific. The obtained anomalous SST and SLP patterns during strong (weak) tidal mixing are similar to those associated with the negative (positive) phase of the PDO, qualitatively in rough agreement with the findings based on observations (Yasuda et al. 2006; Yasuda 2009).
The physical mechanism responsible for this 18.6-yr climate variability, described below, is schematically illustrated in Fig. 17. First, a horizontal circulation anomaly is developed around the center of the Kuril Straits where stratification throughout the water column is strongly varied as a direct effect of the locally enhanced modulation of tidal mixing. Since the meridional gradient of the mean SST is large along the western boundary, especially in the latitudinal range of the KOE, the induced velocity anomaly can effectively generate the SST anomaly in the western KOE region, which is then advected eastward by the mean Kuroshio and the Oyashio Extension to be extended over broad area of the North Pacific. The SST anomaly forces the overlying atmosphere through anomalous surface heat flux to vary the storm-track activity and to induce the SLP and associated wind stress anomalies around the southeastern part of the Aleutian low. The induced wind stress anomaly then varies the WBC and causes a meridional shift of the subtropical–subarctic gyre boundary to enhance the SST anomaly in the western KOE region. The variation of the WBC can be primarily explained in terms of a barotropic response to the wind stress curl anomaly, whereas a baroclinic response is generated near the western boundary connected with the barotropic response and acts to confine the velocity anomaly within the surface layer. The atmosphere, therefore, can work either to damp the SST anomaly while being forced by the anomalous surface heat flux or instead to amplify it through the variation of the WBC. An additional numerical experiment using the ocean component of the coupled climate model without any feedback from the atmosphere has shown that, as a net effect, the atmosphere enhances the SST anomaly. In summary, the SST anomaly in the KOE region, the SLP anomaly in the Aleutian low accompanied by the wind stress anomaly, and the WBC anomaly form a positive feedback system capable of amplifying the initial SST anomaly in the KOE region originally induced by the horizontal circulation anomaly around the Kuril Straits as a purely oceanic process.
In concluding this study, it should be emphasized that not all of the bidecadal climate variability can be attributed to the 18.6-yr modulation of tidal mixing. Nevertheless, we believe that the findings of this study would greatly contribute to the improvement of the bidecadal climate predictability in the North Pacific Ocean.
The authors express their heartfelt gratitude to three anonymous reviewers for their invaluable comments on the original manuscript. This work was supported by the Ministry of Education, Science, Sports and Culture of Japan via a Grant-in-Aid for Scientific Research (KAKENHI 20221002). Figures were produced using the GFD-DENNOU Library.
Current affiliation: Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo, Japan.
Current affiliation: Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan.