Chinese Journal of Oceanology and Limnology   2016, 34 (4): 835-846     PDF       
http://dx.doi.org/10.1007/s00343-016-5036-y
Institute of Oceanology, Chinese Academy of Sciences
0

Article Information

Lingling LIU(刘玲玲), Ruixin HUANG(黄瑞新), Fan WANG(王凡)
Subduction/obduction rate in the North Pacific diagnosed by an eddy-resolving model
Journal of Oceanology and Limnology, 34(4): 835-846
http://dx.doi.org/10.1007/s00343-016-5036-y

Article History

Received: Jan. 29, 2015
Accepted: Jan. 4, 2016
Subduction/obduction rate in the North Pacific diagnosed by an eddy-resolving model
Lingling LIU(刘玲玲)1, Ruixin HUANG(黄瑞新)2, Fan WANG(王凡)1        
1. Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
2. Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
ABSTRACT: Ventilation in the North Pacific is examined using data from the eddy-resolving 1/12° global HYbrid Coordinate Ocean Model (HYCOM) and QuikSCAT wind stress data. For the period January 2004 to December 2006 and area 20°-40°N, the total annual subduction rate is estimated at 79 Sv, and the obduction rate 41 Sv. Resolving the small-scale and high-frequency components of the eddy field can increase the subduction rate by 42 Sv, and obduction by 31 Sv. Lateral induction is the dominant contributor to enhancement of subduction/obduction, and temporal change of mixed layer depth has a secondary role. Further analysis indicates that the high-frequency components of the eddy field, especially those with timescale shorter than 10 days, are the most critical factor enhancing subduction/obduction.
Key words: subduction     obduction     eddy-resolved     high frequency     North Pacific    
1 INTRODUCTION

Water mass exchange between the surface and subsurface ocean is a key component of the oceanic general circulation, which is closely linked to air-sea fluxes such as heat, freshwater, and other tracers. The common terms for quantifying these processes in the open ocean are subduction and obduction, defined as the large-scale transfer of fluid irreversibly leaving(entering)the surface mixed layer into(from)the permanent pycnocline.

Diagnostics of subduction/obd uction rate climatology have been performed throughout the world oceans, including the North Atlantic(Marshall et al., 1993), North Pacific(Qiu and Huang, 1995), South Pacific(Huang and Qiu, 1998), South Indian Ocean(Karstensen and Quadfasel, 2002a), and entire Southern Hemisphere(Karstensen and Quadfasel, 2002b). Recent studies(Trossman et al., 2009; Liu and Huang, 2012)have suggested that owing to the variability on interannual time scale should be taken into account. However, the effect of variability on shorter time scales was not addressed in the aforementioned studies.

By definition, subduction/obduction is directly associated with the cycle of mixed layer depth(MLD), vertical pumping and lateral induction of fluid across the sloping base of the mixed layer(Cushman-Roisin, 1987). Thus, the spatiotemporal variation of MLD and velocity fields can both affect subduction and obduction. Studies have indicated that during some part of the seasonal cycle, the mixed layer is also controlled by small-scale oceanic motions(Pollard and Regier, 1992; Follows and Marshall, 1994). However, given the limitation of observations and computing power available, most studies of subduction/obduction have been confined to non- eddy resolving cases. It is well known that eddy dynamics is one of the most important aspects of the oceanic general circulation, and >90% of total kinetic energy in the ocean is contained by eddies(Ferrari and Wunsch, 2009). Thus, eddies must have key roles in many physical ocean processes.

Marshall(1997)discussed the potential importance of mesoscale eddies in subduction. Hazeleger and Drijfhout(2000)suggested that eddies south of the Gulf Stream extension can enhance the annual subduction rate by almost a factor of two. With recent improvement in the technology of oceanic observation and computing power, much more effort has been directed toward revealing the role of eddies in oceanic circulation and climate. The effect of small-scale disturbances and mesoscale eddies on subduction and mode water formation has been investigated in many studies. based on observed data(Uehara et al., 2003; Qiu et al., 2006, 2007; Oka, 2009; Kouketsu et al.,2011; Xu et al., 2014)and numerical models(e.g., Rainville et al., 2007; Nishikawa et al., 2010; Xu et al., 2014). Moreover, Tandon and Zahariev(2001)found that water mass transformation is sensitive to temporal resolution of surface fluxes, even at diurnal time scale.

Regarding the basin-scale effect of eddies, Qu et al.(2002)estimated the annual subduction rate in the North Pacific at 61.6 Sv based on an oceanic general circulation model(OGCM)with horizontal resolution of 1/4 degree, in which mesoscale eddies contributed 7.8 Sv and small-scale eddies 4.6 Sv. However, as indicated by Tsujino and Fujii(2007), eddy-permitting OGCMs, with horizontal resolution 20-40 km, cannot fully resolve mesoscale eddies. As a result, the effect of eddies could be severely underestimated by such models. Here, we use the eddy-resolving HYbrid Coordinate Ocean Model(HYCOM) assimilation data and QuikSCAT wind stress data to investigate subduction/obduction rate in the North Pacific and the basin-scale effect of resolving small-scale and high- frequency components of the eddy field.

The paper is organized as follows. The data and method are described in Section 2. The subduction/ obduction rate and effect of eddy resolution are discussed in Section 3. Finally, we sum up and draw conclusions in Section 4.

2 DATA AND METHOD 2.1 Data

The HYCOM assimilation data(http://www.hycom.org/dataserver/glb-analysis) are configured for the global ocean, with HYCOM2.2 as the dynamical model. Computations were done on a Mercator grid between 78°S to 47°N(1/12 equatorial resolution). A bipolar patch was used for regions north of 47°N. Horizontal dimensions of the global grid were 4 500×3 298 points, resulting in ~7 km spacing on average, with 32 vertical layers. Surface forcing, including wind stress, wind speed, heat flux and precipitation, was from the Navy Operational Global Atmospheric Prediction System. There are several versions, based on different experiments. Here, weusedexpt_60.5, calledtheHYCOM+NCODA Global 1/12° Analysis(GLBa0.08/expt_60.5), which covered the period from November 2003 to December 2006. Additional details of HYCOM are described by Metzger et al.(2010).

The Navy Coupled Ocean Data Assimilation(NCODA)system (Cummings, 2005)was used for data assimilation. NCODA uses the model forecast as a first guess in a multivariate optimal interpolation (MVOI)scheme, and assimilates available satellite altimeter observations, satellite and in-situ sea surface temperature as well as available in-situ vertical temperature and salinity profiles from expendable bathythermographs(XBTs), Argo floats and moored buoys.

In this study, daily MLD(defined as the depth at which the temperature differs by 0.2°C from sea surface temperature)and horizontal velocity fields were directly obtained from a data server. Potential density was calculated using temperature and salinity from HYCOM. Ekman pumping velocity was estimated from QuikSCAT daily wind stress.

2.2 Annual subduction/obduction rate

Water mass formation/erosion through subduction/ obduction may be calculated in several ways. The common methods are kinematic/dynamic calculations based on either Lagrangian or Eulerian coordinates. The Lagrangian definition has been widely used in diagnosing subduction/obduction rate in non-eddy- resolving models(Qiu and Huang, 1995; Karstensen and Quadfasel, 2002a, b; Liu and Huang, 2012), because the corresponding calculation is very straightforward. However, for eddy-resolving models, strong eddy activity makes the data very noisy. A careful examination revealed that the commonly used Lagrangian definition may be inconvenient for calculating subduction/obduction rate in the case of strong eddies or other perturbations(Liu et al., 2011). The Eulerian definition, on the other hand, has not been used widely in previous studies because it requires much more refined data at each station. However, such data are available from numerical Similarly, the annual mean obduction rate is defined as models, and it turns out that the Eulerian definition is a much better choice for diagnosing subduction/ obduction from eddy-resolving model output.

In Eulerian coordinates, the annual subduction rate is defined as

    (1)

where

    (2)

is the instant detrainment rate(De Szoeke,1980; Cushman-Roisin,1987)and T =1 year. and u mb are the vertical and horizontal velocity at the base of mixed layer,and h m is MLD. w e is the Ekman pumping velocity; the second term for w mb associated with β denotes the vertical velocity reduction caused by the vertical accumulation of meridional velocity in the mixed layer. Tsed and Teed are times when eff ective detrainment starts and ends,which are determined by tracing trajectories of water parcels downstream for 1 year.

As discussed by Liu et al.(2011),because of largeamplitude perturbations induced by either typhoons or eddies,the eff ective subduction window may appear in the form of several sub-windows in time. Furthermore,to clearly explain the relevant physics,we can rewrite Eq.1 as follows:

    (3)

where

    (4)

Accordingly,subduction rate can be separated into the following three components:

    (5)

i.e.,annual mean subduction rate in Eulerian coordinates can be classified as contributions from vertical pumping(S E,VP),lateral induction(S E,LI),and the temporal change of MLD(S E,TC).

Similarly,the annual mean obduction rate is defined as

    (6)

where

    (7)

is the instantaneous entrainment rate. The effective trajectory is selected by tracing trajectories of water parcels upstream backward in time for 1 year. In the same way, obduction rate can also be separated into the following three components:

    (8)

By definition, both D and E in Eqs.1 and 6 should be positive. However, this does not mean that the corresponding three components of detrainment entrainment must be positive. In fact, in some cases, their individual terms can be negative, provided the sum is positive. The discussion below shows cases when some of these components are negative.

3 SUBDUCTION/OBDUCTIONRATEAND EFFECT OF EDDY RESOLUTION

By the definition of subduction/obduction rate, we should first determine the time windows of effective detrainment/entrainment. For a given station, water parcels are released/received at the base of the mixed layer once daily, and the corresponding forward/ backward trajectories in space and time are traced at a regular 0.2-day interval based on the velocity field(u, v, w)to ascertain whether they are effective. For the subduction calculation, if a trajectory is intercepted by the mixed layer downstream within one year of its release, this trajectory is not effective. If within this year this trajectory is never intercepted by the downstream mixed layer, it is termed an effective trajectory. The meaning of an effective trajectory for the obduction calculation is very similar, except that the trajectory is backward in both space and time domains. Then, the annual subduction/obduction rate at a given station is diagnosed as the summation of all effective detrainment/entrainment.

We wish to emphasize that we cannot separate out the effect of eddies on the mean flow in this study, and eddy-induced subduction/obduction in context indicates the enhanced subduction/obduction by resolving the small-scale and high-frequency components of the eddy fields.

Figure 1 Annual mean subduction rate in the North Pacific
3.1 Subduction rate

The spatial distribution of annual subduction rate 20averaged over 2004-2005 is shown in Fig. 1a. For convenience, this case will be referred as Exp0. It can 10be seen that subduction takes place over the entire subtropical basin, and maximizes in the northwestern part of the subtropical gyre. This can also be seen from the meridional/zonal distribution of zonal/ meridional integration (left/lower panel in Fig. 1a).

The distribution of subduction rate in potential density coordinates appears noisy(upper panel in Fig. 2)and peaks around σ θ =25.2 kg/m3,which is closely associated with the formation of North Pacific Subtropical Mode Water(Masuzawa,1969; Suga et al.,1989).

The total volume flux in the North Pacific from 20°N to 40°N is estimated at 79 Sv,and contributions from the three components are listed in Table 1. It appears that at basin scale,lateral induction is dominant in the subduction process based on the eddy-resolving data within the Eulerian framework,and temporal change of MLD has a secondary role. The zonal/meridional distribution of the meridionally/ zonally integration(red line in Fig. 3)reflects the same point.

Figure 2 Distribution of subduction/obduction rate in density coordinates for the case with(lower panel)and without(upper panel)spatial and temporal smoothing
Figure 3 Left(right)panels: zonally(meridionally)integrated term as function of latitude(longitude)for case with(black line)and without(red line)spatial and temporal smoothing
Table 1 Annual subduction/obduction rate and corresponding three components for cases with and without spatial and temporal smoothing,all with units Sv

The most important feature of the present study is that our new estimate is much larger than that reported in other studies. Qu and Chen(2009)estimated the subduction rate from 20°N to 50°N at 49.3 Sv from interannual monthly Ocean General Circulation Model for the Earth Simulator data with horizontal resolution 0.1°×0.1°. Recently,Liu and Huang(2012)estimated the global subduction/obduction rate. Based on interannual monthly-mean Simple Ocean Data Assimilation(SODA)outputs with horizontal resolution 0.5°×0.5°,the corresponding subduction rate in the North Pacific from 20°N to 40°N is estimated at 41 Sv. It appears that both the temporal and spatial resolution of their study is low. Hence,the much higher subduction rate obtained in our study may be largely attributed to the use of data with high temporal and spatial resolution,which can resolve the small-scale and high-frequency components of eddy fields.

To validate the use of eddy-resolving HYCOM data in calculating the subduction/obduction rate,we carried out an additional calculation based on data with spatial and temporal smoothing to make the spatial and temporal resolution similar to SODA. The technical specification of this equivalent dataset is as follows. In the North Pacific,a new data grid with horizontal resolution 0.5°×0.5° was constructed. Then,for a given station with longitude X0 and latitude Y0 in that grid,the mean of values in the HYCOM grid within the region(X0−0.25:X0+0.25,Y0−0.25:Y0+0.25)was defined as the value at that station(X0,Y0). Finally,a 31-day moving average(equivalent to a monthly mean)was applied at each station. For convenience,this case is referred to as Exp1. Based on this smoothed dataset,the annual subduction rate was re-estimated at 37 Sv,close to Liu and Huang’s(2012)result from SODA outputs with similar spatial pattern(Fig. 1b).

The subduction rate calculated from the eddyresolving data is about twice that calculated from smoothed data,but the spatial pattern is similar(Fig. 1). This rate reached the same peak around σθ =25.2 kg/m3(Fig. 2). The question arises as to why the subduction rate calculated from the smoothed data is so much smaller than that from the non-smoothed data. Table 1 lists the contribution of the three components in the two cases. It is readily seen that the most remarkable difference between the results of these two datasets is great enhancement of the lateral induction term in the case of eddy-resolving data,which increased from 18 to 52 Sv(Table 1). This enhancement,shown in the middle panels in Fig. 3,is prominently distributed in the Kuroshio recirculation region where strong eddy activity prevails.

Temporal change of MLD was enhanced from 18 Sv for smoothed data to 27 Sv for non-smoothed data(Table 1),with the difference distributed over all longitudes and latitudes(the lower panels in Fig. 3). The contribution from vertical pumping was small. With the eddies resolved,this contribution was greatly reduced,and this reduction was mainly south of 30°N and between 180° and 120°W(Fig. 3)However,this is a small term of the subduction rate. Thus,overall,the total subduction rate is greatly increased for the case with eddies resolved,owing to the increase of lateral induction and temporal change of MLD.

We chose two stations to examine the effects of eddy resolution on the three components of subduction rate. Figure 4 shows the MLD,daily effective detrainment,and the three components of the annual subduction rate for the two stations,calculated from data with and without spatial and temporal smoothing. In the figure,black circles(blue stars)indicate results of the original high-resolution(smoothed)data. Subduction windows with effective detrainment,mean daily contribution,corresponding subduction rate,and its three components for the two stations are listed in Table 2.

Figure 4 Mixed layer depth (m), daily eff ective detrainment, and three components of annual subduction rate (vertical pumping, lateral induction and the temporal change of MLD, all in units m/a) for two stations: (31.25°N, 136.75°E) (left panels) and (26.75°N, 145.75°E) (right panels)
Table 2 Sub-windows and days with effective subduction rate(days),daily contribution(m/a),annual subduction rate,and its three components(m/a)for two stations,for cases with and without spatial and temporal smoothing

It is evident that in the high-resolution data,the temporal MLD evolution is very noisy,and there are various perturbations. Moreover,its spatial distribution is very rough,with a strong horizontal gradient(figure omitted). However,after spatial and temporal smoothing,these perturbations were eliminated,along with their effects on subduction rate. As listed in Table 2,the effective subduction appears in the form of several sub-windows in time. With the eddies resolved,the subduction sub-windows are discrete,there are fewer effective detrainment days,and the daily contribution fluctuates more. Otherwise,for the case with spatial and temporal smoothing,the period of sub-windows is much longer,and the mean daily contribution is much smaller(Fig. 4 and Table 2). Overall,for the smoothed data,the annual mean subduction rate is greatly reduced.

It is important to note that the physics relevant to the eddy-induced enhancement of subduction rate may vary by station. As shown in Table 2,the difference of subduction rate from the use of smoothed and non-smoothed data at station(31.25°N,136.75°E)is primarily caused by temporal change of MLD,whereas the difference at station(26.75°N,145.75°E)is largely due to the lateral induction term.

In summary,it appears that at basin scale,lateral induction is the dominant factor for enhancing subduction rate in the case with eddies resolved,followed by temporal change of MLD. However,the situation is complicated and may vary by station. Furthermore,the basin-scale effect of eddy resolution on subduction rate,which has been missed in other studies based on low-resolution data,can be simply defined as the difference between the result based on data with and without spatial and temporal smoothing. That is,resolving the small-scale and high-frequency components of eddy fields could increase the subduction rate by 42 Sv in the North Pacific between 20°N to 40°N,which is mainly in the Kuroshio recirculation region with strong eddy activity. Overall,eddy resolution can greatly enhance the subduction rate in the North Pacific,by >110%.

3.2 Obduction rate

In addition to the subduction rate,which indicates how much water is pumped into the permanent pycnocline,we analyzed the effect of eddy resolution on the obduction rate. That rate is also an important part of the oceanic circulation and climate,because it indicates how fast water in the permanent pycnocline is returned to the mixed layer after cycling through the ocean interior.

The annual obduction rate based on the eddyresolving data is shown in Fig. 5a. It is readily seen that the obduction mainly takes place near the boundary between the subtropical and subpolar gyres,which can be clearly seen from the meridional/zonal distribution(left/lower,Fig. 5a)of the zonal/ meridional integration. Here again,lateral induction was the most important contributor,with the temporal change of MLD having secondary importance(red line in Fig. 6). However,the dataset used does not cover the entire North Pacific,so regrettably,the contribution to obduction in a large part of the subpolar gyre was missed.

Figure 5 Annual mean obduction rate
Figure 6 Meridional and zonal distribution of obduction rate

The obduction rate distribution in density coordinates is depicted as the histogram with negative values in Fig. 2. Similar to the subduction,the obduction has a minor peak around σ θ =25.2 kg/m3 . The fact that both the central density for subduction and obduction has the same value may seem surprising,but this is no coincidence. As discussed by Qiu and Huang(1995)and Liu and Huang(2012),in the Kuroshio recirculation area,there is both subduction and obduction. This is called an area of ambiduction.

The total obduction rate in the North Pacific(20°N,40°N)was estimated at 41 Sv,with the contribution from the three components listed in Table 1. This clearly demonstrates the importance of the lateral induction term.

Net water mass formation/erosion inferred from this dataset,defined as the difference between subduction and obduction,is shown by the solid black in the upper panel of Fig. 2. It is readily seen that there was net water transfer from the mixed layer to the permanent pycnocline,with most accumulation in the density range σ θ =23.2–26.6 kg/m3 . In the density range σ θ 26.6 kg/m3,there is net water mass erosion,i.e.,obduction is greater than subduction. We emphasize that the net water mass formation/erosion rate inferred from the dataset is subject to the strong limitation that the dataset covers only part of the subpolar basin. Consequently,this rate can be very biased toward water mass formation.

The distribution of obduction rate based on data with spatial and temporal smoothing is similar to that based on data without smoothing(Fig. 5),except that the quantity is greatly reduced. This is also seen from the obduction distribution in density coordinates(lower panel in Fig. 2). Moreover,net water transfer in the given density range(black bars in Fig. 2)is also smaller than that from eddy-resolving data.

The total obduction rate based on data after spatial and temporal smoothing is estimated at 10 Sv,with the contribution from the three components listed in Table 1. Similar to the case of subduction,lateral induction is the dominant factor causing the great reduction in obduction rate following data smoothing. In the same way,the basin-scale effect of eddy resolution on obduction rate can also be diagnosed as the difference between the results based on data with and without spatial and temporal smoothing. Thus,resolving the eddies enhanced the obduction rate by 31 Sv in the North Pacific over 20°N to 40°N.

3.3 Subduction/obduction rate based on data with

filtering at different scale As discussed above,perturbations,which were largely eliminated in previous studies with low temporal and spatial resolution,can make great contributions to the subduction/obduction rate. To examine the influence of perturbations of varying scale in calculating the subduction/obduction rate,we performed two additional experiments,one based on data with temporal filtering but retaining high spatial resolution,and the other with spatial filtering but retaining high temporal resolution.

For the case with temporal filtering but retention of high spatial resolution,three experiments,Exp2–4,were performed based on data(including both velocity and MLD)generated after 11,21,and 31-point moving averages in time; i.e.,perturbations with respective timescales shorter than 10,20,and 30-days were filtered out.

The spatial distribution of subduction/obduction rates in Exp2–4 is similar to that in Exp0(figures omitted)and the distribution in density coordinates is similar(Fig. 7a,c and e). However,actual values are different. Total subduction/obduction rates in the North Pacific for Exp2–4 are listed in Table 3. These results indicate that the use of data after time filtering alone can substantially reduce the subduction/ obduction rate.

Table 3 Subduction and obduction rate and net water formation/erosion in the North Pacific(20°N,40°N)averaged over 2004–2006,in units Sv/a
Figure 7 Subduction/obduction rates as a function of density,in units Sv/0.2 σθ

In the North Pacific,increasing the temporal resolution from 10 days to daily increased the subduction rate by 37 Sv(Table 3),and the obduction rate by 24 Sv. Maximum enhancement was approximately σ θ =25.2 kg/m3 for both subduction and obduction(Fig. 7b). This is similar for the cases with 20- and 30-day filtering,Exp3 and 4,as seen in Table 3 and Fig. 7d and f.

According to our calculation,the use of data with low temporal resolution can reduce net water mass formation(subduction minus obduction)over most of the density range(Fig. 7b,d and f. Integrated over the entire density range and domain,retaining the highfrequency perturbations can increase net water mass formation. However,this phenomenon may be linked to the intrinsic limitation of the data used because they cover only a part of the subpolar basin,leaving a large portion of the subpolar gyre uncovered. Moreover,the results are similar to Exp1 with both spatial and temporal smoothing. Comparing these results demonstrate that perturbations with timescale shorter than 10 days are the most important contributor to large-scale transfer of fluid between the mixed layer and ocean interior.

Another experiment,Exp5,was carried out to examine the effect of spatial filtering alone. In this case,the high daily temporal resolution was retained,but a spatial average applied to generate data with spatial resolution 0.5°×0.5°. For a given station(X0,Y0),where X0,Y0 indicate longitude and latitude respectively,mean values on the HYCOM grid in the region(X0−0.25:X0+0.25,Y0−0.25:Y0+0.25)are established as the value at that station.

For the datasets with spatial filtering alone,the annual subduction rate was reduced to 59 Sv,with obduction rate 20 Sv(Table 3); the spatial distribution was similar to that without spatial averaging(figure omitted). Its distribution in density coordinates(Fig. 7g)is also similar to that without spatial averaging(upper panel in Fig. 2),except that the quantity is smaller. The difference also peaks around σθ =25.2 kg/m3(Fig. 7h). However,there is a noticeable phenomenon in that spatial filtering alone does not substantially alter the basin-scale net water mass formation/erosion. However,over the density range σθ =24–24.6 kg/m3,the spatial filtering alone produces less water mass erosion(obduction minus subduction),very different from Exp1 based on data with both spatial and temporal smoothing.

Left panels show subduction/obduction rate calculated from various experiments(panel a for exp2,c for exp3,e for exp4,and g for exp5). Right panels show difference between standard Exp0 and experiments corresponding to left panels. Solid black bars indicate difference of subduction and obduction(subduction-obduction).

In summary,it appeared that altering either the temporal or spatial resolution of datasets can affect subduction/obduction. As discussed above,lateral induction is the most important process for enhancing subduction/obduction in the case of eddy resolution. The high-frequency variability,usually at small spatial scale,can frequently modify the horizontal gradient in the ocean and tilt the mixed layer base,which is propitious for water mass exchange between the mixed layer and ocean interior,i.e.,subduction/ obduction. Thus,the high-frequency variability,especially that with timescale shorter than 10 days,is the most critical for enhancing subduction/obduction.

4 SUMMARY

Subduction/obduction rate is a key index for the study of oceanic general circulation and climate. In the present study,we estimated that rate in the North Pacific and explored the effect of resolving smallscale and high-frequency components of eddy fields,based on HYCOM and QuikSCAT wind stress data.

Averaged over the period January 2004 to December 2006 and the area 20°N to 40°N,the total annual subduction rate in the North Pacific was estimated at 79 Sv,and the obduction rate 41 Sv. These values are much larger than those reported in many studies based on non-eddy-resolving data. The high rates are primarily attributed to the use of data with high temporal and spatial resolution. In retrospect,strong perturbations smoothed out in other studies were the major contributor to water mass formation/erosion in the world ocean. Thus,heavily smoothed data in the spatial and temporal domain could have markedly reduced the subduction/ obduction rate reported in those studies. In comparison with results from the same data after spatial and temporal smoothing,the eddy contribution to water mass formation/erosion was as follows. The subduction rate increased to 42 Sv and the obduction rate to 31 Sv in the North Pacific,from 20°N to 40°N. Among other factors,lateral induction was the dominant contributor to basin-scale,eddy-induced subduction/obduction.

The effects of eddy resolution on basin-scale subduction/obduction was examined in two ways. First,the effect of temporal smoothing alone was investigated,and the experiment in terms of variable time-scale filtering indicated that high-frequency components with timescale shorter than 10 days are the most important contributor to the subduction/ obduction rate. The effect of spatial smoothing alone was also examined. The results show that temporal smoothing alone and spatial smoothing alone can both reduce the subduction/obduction rate. However,the result based on data with temporal smoothing alone is much closer to that based on data with both temporal and spatial smoothing,and the result based on data with spatial smoothing alone is much larger. Therefore,it appears that the effect of eddies on water mass formation/erosion is critically dependent on temporal sampling of the eddy-resolving data,with spatial sampling of secondary importance.

Our study is only a rough estimate of basin-scale subduction/obduction rate,considering the effect of eddies. There are several factors that can induce large errors. First are errors in model circulation and mixed layer depth. According to Trossman et al.(2009),various criteria for estimating mixed layer depth can produce a large difference in subduction rate. Second,vertical velocity,which is calculated from Ekman pumping velocity plus a reduction term attributable to meridional flow in the surface layer,cannot fully represent vertical velocity in the real ocean. Therefore,the results herein may underestimate the annual subduction/obduction rate in the real ocean,because the dataset cannot resolve smaller-scale processes such as the diurnal cycle.

References
Cummings J A, 2005. Operational multivariate ocean data assimilation. Quart. J. Roy. Met eor. Soc., 131 (613) : 3583 –3604. Doi: 10.1256/qj.05.105
Cushman-Roisin B, 1987. Hawaii Inst. of Geophysics Special Publications, Hawaii. .
De Szoeke R A, 1980. On the effects of horizontal variability of wind stress on the dynamics of the ocean mixed layer. J. Phys. Oceanogr., 10 (9) : 1439 –1454. Doi: 10.1175/1520-0485(1980)010<1439:OTEOHV>2.0.CO;2
Ferrari R, Wunsch C, 2009. Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid. Mech., 41 : 253 –282. Doi: 10.1146/annurev.fluid.40.111406.102139
Follows M J, Marshall J C, 1994. Eddy driven exchange at ocean fronts. Ocean Modell., 102 : 5 –9.
Hazeleger W, Drijfhout S S, 2000. Eddy subduction in a model of the subtropical gyre. J. Phys. Oceanogr., 30 (4) : 677 –695. Doi: 10.1175/1520-0485(2000)030<0677:ESIAMO>2.0.CO;2
Huang R X, Qiu B, 1998. The structure of the wind-driven circulation in the subtropical South Pacific Ocean. J. Phys. Oceanogr., 28 (6) : 1173 –1186. Doi: 10.1175/1520-0485(1998)028<1173:TSOTWD>2.0.CO;2
Karstensen J, Quadfasel D, 2002a. Water subducted into the Indian Ocean subtropical gyre. Deep-Sea Res earch Part II: Topical Studies in Oceanography, 49 (7-8) : 1441 –1457. Doi: 10.1016/S0967-0645(01)00160-6
Karstensen J, Quadfasel D, 2002b. Formation of Southern Hemisphere thermocline waters: water mass conversion and subduction. J. Phys. Oceanogr., 32 (11) : 3020 –3038. Doi: 10.1175/1520-0485(2002)032<3020:FOSHTW>2.0.CO;2
Kouketsu S, Tomits H, Oka E, Hosoda S, Kobayashi T, Sato K, 2011. The role of meso-scale eddies in mixed layer deepening and mode water formation in the western North Pacific. J. Oceanogr., 68 (1) : 63 –77.
Liu L L, Huang R X, 2012. The global subduction/obduction rates: their interannual and decadal variability. J. Clim ate, 25 (4) : 1096 –1115. Doi: 10.1175/2011JCLI4228.1
Liu L L, Wang F, Huang R X, 2011. Enhancement of subduction/obduction due to hurricane-induced mixed layer deepening. Deep-Sea Res earch I: Oceanographic Research Papers, 58 (6) : 658 –667. Doi: 10.1016/j.dsr.2011.04.003
Marshall D, 1997. Subduction of water masses in an eddying ocean. J. Mar Res., 55 (2) : 201 –222. Doi: 10.1357/0022240973224373
Marshall J C, Williams R G, Nurser A J G, 1993. Inferring the subduction rate and period over the North Atlantic. J. Phys. Oceanogr., 23 (7) : 1315 –1329. Doi: 10.1175/1520-0485(1993)023<1315:ITSRAP>2.0.CO;2
Masuzawa J, 1969. Subtropical mode water. Deep Sea Res earch and Oceanographic Abstracts, 16 (5) : 463 –472. Doi: 10.1016/0011-7471(69)90034-5
Metzger E J, Hurlburt H E, Xu X, Shriver J F, Gordon A L, Sprintall J, Susanto R D, van Aken H M, 2010. Simulated and observed circulation in the Indonesian Seas: 1/12° global HYCOM and the INSTANT observations. Dyn. Atmos. Oceans, 50 (2) : 275 –300. Doi: 10.1016/j.dynatmoce.2010.04.002
Nishikawa S, Tsujino H, Sakamoto K, Nakano H, 2010. Effects of mesoscale eddies on subduction and distribution of Subtropical Mode Water in an eddy-resolving OGCM of the western North Pacific. J. Phys. Oceanogr., 40 (8) : 1748 –1765. Doi: 10.1175/2010JPO4261.1
Oka E, 2009. Seasonal and interannual variation of North Pacific Subtropical Mode Water in 2003-2006. J. Oceanogr., 65 (2) : 151 –164. Doi: 10.1007/s10872-009-0015-y
Pollard R T, Regier L A, 1992. Vorticity and vertical circulation at an ocean front. J. Phys. Oceanogr., 22 (6) : 609 –625. Doi: 10.1175/1520-0485(1992)022<0609:VAVCAA>2.0.CO;2
Qiu B, Chen S M, Hacker P, 2007. Effect of mesoscale eddies on subtropical mode water variability from the Kuroshio Extension System Study (KESS). J. Phys. Oceanogr., 37 (4) : 982 –1000. Doi: 10.1175/JPO3097.1
Qiu B, Hacker P, Chen S M, Donohue K A, Watts D R, Mitsudera H, Hogg N G, Jayne S R, 2006. Observations of the subtropical mode water evolution from the Kuroshio Extension System Study. J. Phys. Oceanogr., 37 (3) : 457 –473.
Qiu B, Huang R X, 1995. Ventilation of the North Atlantic and North Pacific: subduction versus obduction. J. Phys. Oceanogr., 25 (10) : 2374 –2390. Doi: 10.1175/1520-0485(1995)025<2374:VOTNAA>2.0.CO;2
Qu T D, Chen J, 2009. A North Pacific decadal variability in subduction rate. Geophys. Res. Lett., 36 (22) .
Qu T D, Xie S P, Mitsudera H, Ishida A, 2002. Subduction of the North Pacific mode waters in a global high-resolution GCM. J. Phys. Oceanogr., 32 (3) : 746 –763. Doi: 10.1175/1520-0485(2002)032<0746:SOTNPM>2.0.CO;2
Rainville L, Jayne S R, McClear J L, Multrud M E, 2007. Formation of subtropical mode water in a high-resolution ocean simulation of the Kuroshio Extension region. Ocean Modell., 17 (4) : 338 –356. Doi: 10.1016/j.ocemod.2007.03.002
Suga T, Hanawa K, Toba Y, 1989. Subtropical mode water in the 137°E section. J. Phys. Oceanogr., 19 (10) : 1605 –1618. Doi: 10.1175/1520-0485(1989)019<1605:SMWITS>2.0.CO;2
Tandon A, Zahariev K, 2001. Quantifying the role of mixed layer entrainment for water mass transformation in the North Atlantic. J. Phys. Oceanogr., 31 : 1120 –1131. Doi: 10.1175/1520-0485(2001)031<1120:QTROML>2.0.CO;2
Trossman D S, Thompson L A, Kelly K A, Kwon Y O, 2009. Estimates of North Atlantic Ventilation and mode water formation for winters 2002-06. J. Phys. Oceanogr., 39 (10) : 2600 –2617. Doi: 10.1175/2009JPO3930.1
Uehara H, Suga T, Hanawa K, Shikama N, 2003. A role of eddies in formation and transport of North Pacific Subtropical Mode Water. Geophys. Res. Lett., 30 (13) : 1705 .
Xu L X, Xie S P, Mcclearn J L, Liu Q Y, Sasaki H, 2014. Mesoscale eddy effects on the subduction of North Pacific mode waters. J. Geophys. Res. Oceans, 119 (8) : 4867 –4886. Doi: 10.1002/2014JC009861