Analysis of results from a global eddy-resolving general circulation model has revealed the existence of a North Pacific decadal variability in subduction rate. This decadal variability corresponds well with the Pacific Decadal Oscillation (PDO). The zero-lag correlation between the two time series reaches 0.61 for the period of integration (1950–2003), and increases to as high as 0.80 after the climate shift in the mid-1970s. Much of the North Pacific decadal variability in subduction rate is due to changes in winter mixed layer depth, which in turn are closely related to changes in surface wind and heat flux.
 Coherent decadal atmospheric and oceanic variability in the North Pacific has been reported in the literature [e.g., Latif and Barnett, 1994; Mantua et al., 1997; Wu and Liu, 2003; Deser et al., 2004]. A popular index used to describe this variability is the Pacific decadal oscillation (PDO) index defined as the leading principal component of North Pacific sea surface temperature (SST) variability poleward of 20°N [Mantua et al., 1997]. As part of the North Pacific climate system, the PDO index has been shown to be closely related to the decadal variability in sea level pressure, surface wind stress, and surface heat flux [e.g., Trenberth and Hurrell, 1994; Latif, 2006]. Its influence is prevalent and believed to play a significant role in modulating precipitation patterns and many other climate characteristics across the Pacific [e.g., Minobe, 1997; Mantua et al., 1997].
 Here, we report the finding of a decadal variability in subduction rate. The subduction of North Pacific waters is part of the subtropical overturning cell (STC) that transports heat and salt from the subtropics into the equator [McCreary and Lu, 1994]. Among other hypotheses [e.g., Gu and Philander, 1997; Luo and Yamagata, 2001], the decadal variability of El Nino and Southern Oscillation (ENSO) has been related to changes in the STC [e.g., Kleeman et al., 1999]. Studies of the STC have focused on variability of gyre circulation, mostly the equatorward flow in the thermocline [e.g., McPhaden and Zhang, 2002]. Until this time, the variability of water subducting in the subtropics or the subduction rate of North Pacific waters has not been well documented, though changes in these waters' properties are widely recognized [e.g., Yasuda and Hanawa, 1997; Schneider et al., 1999; Hautala and Roemmich, 1998].
 Estimate of subduction rate, often referred to as the volume flux of mixed layer water entering the thermocline per horizontal unit area [e.g., Qiu and Huang, 1995], requires detailed information on upper layer circulation and density stratification, which are not ordinarily available from observations. Until this time, our understanding of subduction rate in the North Pacific has primarily confined to its climatological features. A comprehensive description of its variability and in particular its relationship to the PDO is not available.
 Numerical models have become a powerful tool in synthesizing observations and identifying dynamics of the ocean. Taking advantage of the rapid advance in ocean general circulation model (GCM), this study investigates the subduction rate and its decadal variability over the North Pacific using results from the eddy-resolving Ocean GCM for the Earth Simulator (OFES).
2. Model Description
 The OFES was based on the Modular Ocean Model (MOM3). Its domain covers a near-global region extending from 75°S to 75°N, with a horizontal resolution of 0.1 degree both in longitude and latitude. The vertical resolution varies from 5 m near the surface to 330 m near the bottom, with a total of 54 levels and a maximum depth of 6065 m. The model topography was constructed from the 1/30° bathymetry dataset created at the Southampton Oceanography Center. See Sasaki et al.  for more details.
 A 50-year climatological spin-up was first executed from annual mean temperature and salinity fields of the World Ocean Atlas 1998 (WOA98) with no motion. Then, the model was forced from 1950 to 2003 with daily surface wind stress, heat flux, and salinity flux based on the NCEP re-analysis data. The surface fluxes were specified with bulk formula from the re-analyzed atmospheric variables, in addition to a surface salinity restoring to the climatological value of WOA98. To suppress grid-scale noises, a scale-selective damping of bi-harmonic operator was adopted for horizontal mixing, and the K-Profile Parameterization (KPP) scheme was employed for the vertical mixing.
 With its high resolution and realistic topography, the OFES was able to reproduce most, if not all, of the detailed phenomena observed in the global ocean, suggesting that the circulation from OFES is one of the best available in a model [Sasaki et al., 2004]. Results from the 54-year hindcast integration are presented in the following sections.
3. Mean Subduction Rate
 The climatological monthly mean temperature, salinity, and velocity fields are produced by averaging their individual values over the period of integration (54 years). The mixed layer depth (MLD), defined as the depth where water potential density is 0.1 kg m−3 heavier than that at the sea surface, is determined from the mean density field. In the North Pacific, the MLD reaches its seasonal maximum in March (Figure 1a). The winter MLD is generally shallow (<50 m) along the southern rim of the subtropical gyre, but often reaches 200 m in the mixed water region at 30°–40°N. In the eastern subtropical gyre, a local maximum (>150 m) is seen, as a result of enhanced downward Ekman pumping and surface buoyancy flux stemming from a large excess of evaporation over precipitation.
 We calculate the mean subduction rate, Smean, in the same way as Qiu and Huang  and Qu et al. , by tracing water particles released at the base of winter mixed layer for one year. The mean subduction rate shows essentially the same pattern as that derived from climatological data [Qiu and Huang, 1995]. In much of the subtropical North Pacific, it is larger than 25 m yr−1, consistent with the basin-scale downward Ekman pumping (Figure 1b). It exceeds 100 m yr−1 in the mixed water region, where lateral induction associated with large winter MLD gradients is dominant. A local maximum (>90 m yr−1) is seen in the eastern subtropical gyre, corresponding well with the winter MLD maximum shown above (Figure 1a).
 Two peaks stand out in the mean subduction rate against the winter mixed layer density (Figure 1c). One is related to the formation of Subtropical Model Water (STMW) at density between 25.1 and 25.6 kg m−3, and the other has a density range of 26.0 and 26.5 kg m−3, corresponding to the formation of North Pacific Central Mode Water (CMW) [cf. Hanawa and Talley, 2001]. By integrating the mean subduction rate over the subtropical North Pacific (20°N–50°N), we obtain a total volume of 49.3 Sv. This volume is significantly larger than that derived from climatological data [e.g., Qiu and Huang, 1995], but shows a reasonable agreement with earlier modeling studies [e.g., Qu et al., 2002]. To this volume, the STMW contributes 19.2 Sv at σθ = 25.1–25.6 kg m−3 and the CMW contributes 10.5 Sv at σθ = 26.0–26.5 kg m−3.
4. Decadal Variability and Atmospheric Forcing
 Winter mixed layer depth and monthly velocity fields for the period 1950–2003 are used to examine the variability of annual subduction rate, Sann, in the North Pacific. As discussed above, the subduction of North Pacific waters is confined roughly to a density range between 24.5 and 26.5 kg m−3 (Figure 2a). The two peaks, corresponding to the formation of STMW and CMW, respectively, are visible for nearly all period of integration. The total volume subducted in the subtropical North Pacific (20°N–50°N) varies greatly from year to year (Figure 2b). In principle, this volume has a good correspondence with the PDO. To extract the dominant signal on decadal time scale, we apply a 7-year low-lass filter to both time series, and the correlation between them reaches 0.61 for the period of integration (1950–2003). This result suggests that the subduction of North Pacific waters increases in most cases during the positive phase of PDO, and vice versa. Careful examination of the two time series indicates that their correlation is time dependent. It is generally low (0.29) during the period 1950–1975, but increases to 0.80 during the later part of integration (1976–2003), showing a correspondence with the North Pacific climate shift that took place in the mid-1970s [e.g., Latif and Barnett, 1994; Mantua et al., 1997]. The causes of low correlation for the first half of integration are not clear. It could result from inaccurate forcing (winds, heat flux, etc) from the NCEP re-analysis, or from inappropriate initial condition of the model. The latter problem is likely related to the ocean's decadal variability prior to the period of integration, whose effect is expected to persist for at least a few decades.
 Two additional integrations are conducted to identify the dynamics related to the decadal variability in subduction rate, one with variable velocity and climatological winter MLD, and the other with variable winter MLD and climatological velocity. The results suggest that the North Pacific decadal variability in subduction rate is primarily due to changes in winter MLD (Figure 2c). The subduction rate for the variable MLD integration looks similar as for the fully variable integration, and the two time series become almost identical (r = 0.98) after the climate shift in the mid-1970s. Contribution from velocity variability is relatively small, and appears to counteract the effect of MLD variability in the fully variable integration.
 Prominent North Pacific decadal variability in sea level pressure, surface wind stress, and surface heat flux has been reported in the literature [e.g., Trenberth and Hurrell, 1994; Mantua et al., 1997; Wu and Liu, 2003; Latif, 2006]. This variability is expected to exert strong influence on ocean's winter mixed layer either by surface wind stirring or by surface cooling convection. When the PDO index is positive, the anomalously strong westerly winds cool the SST due to increased heat loss to the atmosphere and enhanced mixing in the ocean, thereby resulting in an anomalously deep winter MLD in the subtropical North Pacific. The deepening of winter MLD allows North Pacific waters to be easily swept into the thermocline by horizontal circulation (lateral induction), suggesting an enhanced subduction rate over the North Pacific. The situation is reversed when the PDO index turns negative.
 Combined empirical orthogonal function (EOF) analysis is used to further characterize the dominant decadal variability in subduction rate. The combined EOFs for anomalies of MLD and Sann are calculated simply by making the parameters normalized by their respective standard deviations (STDs). The leading combined EOF mode captures about 10% of the total variance over the North Pacific (Figure 3). The mode is narrowly confined in its extent to the central subtropical North Pacific at (30°N–40°N, 180°–160°W), where it explains up to 80% of the variance. In general, the simulated MLD and Sann anomalies show the same pattern, both with a positive anomaly in the central subtropical North Pacific surrounded by anomaly of opposite sign (Figure 3a). This spatial pattern is consistent with the sea level pressure, SST, surface heat flux, and winter MLD patterns shown by many previous studies [e.g., Trenberth and Hurrell, 1994; Mantua et al., 1997; Ladd and Thompson, 2002; Latif, 2006]. The time evolution of this combined EOF component is closely related to the PDO (Figure 3c). The correlation between the two time series reaches 0.86 for the period of integration (1950–2003), which is significant at the 99% confidence level, indicative of dominant atmospheric forcing associated with the PDO. The second combined EOF component, accounting for about 6% of the total variance (figure not shown), shows a similar pattern to the mean subduction rate (Figure 1b), with maximum values in the Kuroshio extension region. This and the higher mode variability in subduction rate may be related to local decadal climate modes reported by Luo and Yamagata . The detail needs to be investigated by future studies.
 Further inspection of annual subduction rate against winter mixed layer density indicates that there is a periodic shift in density of subducted water (Figure 2a). This includes peaks of annual subduction rate in 1958, 1970, 1981, 1983, and 1998 (Figure 2b). A composite of MLD, Sann, SST, wind, and surface heat flux anomalies during these periods shows that the density shift is associated with an eastward movement of the mode water core (Figure 4), a phenomenon also reported by earlier numerical studies [e.g., Xie et al., 2000; Ladd and Thompson, 2002]. Water subducted during these periods is of higher density than usual by up to 0.25 kg m−3. Strong interaction between the atmosphere (wind, heat flux, etc.) and the ocean's winter mixed layer occurs during these periods. A negative surface heat flux anomaly (>9 W m−2 in magnitude), stemming from increased evaporative cooling, is primarily responsible for the cold SST (>0.9°C in magnitude), high sea surface density (>0.2 kg m−3), and deep MLD (>40 m) anomalies, which in turn result in an enhanced subduction rate in the central North Pacific. As the winter mixed layer water in the central North Pacific is of higher density than that in the west (Figure 1a), this result implies a density shift in subducted water, namely, from the density of STMW to the density of CMW.
 The present analysis has revealed the existence of a North Pacific decadal variability in subduction rate, which appears to be closely related to the PDO reported by many previous studies. With such a prominent variability in the subtropics, one may have reasons to believe that some of the signal can be conveyed into the tropics by the STC [e.g., Gu and Philander, 1997]. Recent studies have shown evidence for a connection between the STC transport and equatorial SST anomalies [e.g., Xie et al., 2000; Nonaka et al., 2002; Zhang et al., 2001, 2007], in line with the theory proposed by Kleeman et al. . But, until this time, no similar connection between the STC transport and subduction rate anomalies has been identified, which needs to be investigated further by research.
 Existing observations have shown a decadal variability in subsurface temperature that is consistent with the climate shift in the mid-1970s [e.g., Hautala and Roemmich, 1998; Schneider et al., 1999]. Although the annual subduction rate presented in this study does not show an upward trend in its magnitude (Figure 2c), its correlation with the PDO significantly increases (r = 0.80) after the mid-1970s. No observational evidence is available for this time dependence. Further investigation could be provided by a completed, dynamically consistent data assimilation product.
 This research was supported by the NSF through grant OCE06-23533 and by the JAMSTEC, the NASA, and the NOAA through their sponsorship of research activities at the IPRC. The OFES simulation was conducted on the Earth Simulator under the support of JAMSTEC. The authors are grateful to S. Gao, I. Fukumori, R. Fine, and E. Lindstrom for valuable discussions and useful communications on the topic, to T. Yamagata and two anonymous reviewers for thoughtful comments and suggestions, and to H. Sasaki and Y. Shen for constant assistance in processing the OFES outputs. SOEST contribution 7826 and IPRC contribution IPRC-641.