Hydrographic observations, ocean state estimates, and ocean objective analyses are combined to investigate the decadal variations of the North Equatorial Current (NEC) in the Pacific at 137°E during the last three decades (1975–2005). Observations show that the decadal NEC transport has three maxima around 1980/1981, 1994/1995, and 2004/2005, and two minima around 1989/1990 and 1999/2000, respectively. Associated with these maxima/minima, the sea surface height (SSH) falls/rises and the subsurface isopycnals shoal/deepen in the southern part of NEC, resulting in westward/eastward zonal velocity anomalies. Results from the ocean state estimates and ocean objective analyses show good agreement with observations. Further analysis indicates that the observed zonal velocity anomalies at 137°E are part of the cyclonic/anticyclonic gyre anomalies formed in the tropical northwestern Pacific east of the Philippines, coinciding with the tropical gyre. Results from a 1½ layer reduced gravity model suggest that these oceanic variations are mainly controlled by the decadal wind forcing in the tropical western Pacific and can be attributed to both local Ekman dynamics and baroclinic Rossby wave propagation.
 The North Equatorial Current (NEC) in the Pacific Ocean is located between the subtropical and tropical gyres and bifurcates into the northward flowing Kuroshio Current (KC) and the southward flowing Mindanao Current (MC) off the Philippine coast (Figure 1a) [e.g., Nitani, 1972; Qu et al., 1998]. The NEC-MC-KC (NMK) current system has been extensively investigated based on in situ observations [e.g., Toole et al., 1988; Hu and Cui, 1989, 1991; Toole et al., 1990; Qiu and Joyce, 1992; Gu, 1996; Qiu and Lukas, 1996; Qu et al., 1997, 1998; Qu and Lukas, 2003; Yaremchuk and Qu, 2004; Wang and Hu, 2006; Kashino et al., 2009; Xie et al., 2009; Qiu and Chen, 2010; Zhai and Hu, 2012] and numerical simulations as well [e.g., Qiu and Lukas, 1996; Wang et al., 2002; Kim et al., 2004; Zhai and Hu, 2013]. Among others, the NEC has been shown to play an important role in the evolution of the western Pacific warm pool [e.g., Qu et al., 1997], in the variability of biological properties and fishery in the western Pacific Ocean [Kimura et al., 2001; Amedo et al., 2002], and in the modulation of the global thermohaline circulation and the Indonesian throughflow [e.g., Gordon, 1986].
 Studies of the NEC transport have focused on its seasonal and interannual variabilities [e.g., Qiu and Joyce, 1992; Qiu and Lukas, 1996; Kim et al., 2004; Yaremchuk and Qu, 2004; Kashino et al., 2009; Zhai and Hu, 2012, 2013], which indicate that the latter is much stronger than the former. On the interannual time scale, the variability of the NEC transport is associated with the El Niño-Southern Oscillation (ENSO), being larger during El Niño events and smaller during La Niña events. A multidecadal variability in the sea level and gyre circulation of the tropical northwestern Pacific Ocean was also reported by Qiu and Chen  using satellite altimeter sea surface height data. It has been shown that the NEC during the past 17 years has migrated southward and strengthened. Different from that on the interannual time scale, the variability of the NEC transport on the decadal time scale has been hampered by a dearth of long-term observations. However, the 37 years (1972–2008) hydrographic observations along 137°E meridian conducted by Japan Meteorological Agency (JMA) are a notable exception. Preliminary analysis of these observations indicates that there were significant decadal variations in the NEC transport with a dominant time scale of about 10 years and a magnitude (9.0 Sv) of variability comparable to that of interannual variations (Figure 4a) [Zhai and Hu, 2012, 2013]. Based on these observations combined with results from ocean state estimates and objective analyses, the present study intends to describe and explore the dynamics of the decadal NEC transport variations at 137°E in the past three decades. Though the hydrographic observations obtained by JMA may be enough to give the decadal variations of the NEC at 137°E, they could not provide any information about the associated large-scale horizontal circulation variations. By combining all available hydrographic observations to form three-dimensional global maps of oceanic temperature and salinity or through data assimilation into ocean models, the ocean objective analyses and ocean state estimates could help us to obtain a dynamically consistent description of the NEC decadal variations at 137°E and its relationship to large-scale horizontal circulation variations. Meanwhile, good comparisons between results from multiproducts would make our conclusions more tenable. In this study, we would first use the hydrographic observations to examine the decadal NEC transport variations and the current's basic characteristics at 137°E. We then use results from ocean state estimates and objective analyses to examine the relationship between the decadal NEC transport variations and the large-scale circulation changes. The remaining of the paper is organized as follows. The data and method of analyses are described in section 2, the results are presented in section 3, and a brief summary is provided in section 4.
2. Data and Method of Analyses
 The hydrographic data used for this study were obtained from the JMA website http://www.data.kishou.go.jp/kaiyou/db/vessel_obs/data-report/html/ship/efile_NoS2_e.html. As part of the Cooperative Study of the Kuroshio (CSK) sponsored by the Intergovernmental Oceanographic Commission, Unesco, JMA carried out winter oceanographic surveys along 137°E since 1967. The 137°E observations were conducted in both winter and summer seasons since 1972. The other two seasons (spring and fall) were also covered since early 1990s. In this study, only observations since 1972 are used, covering a period of 37 years from 1972 to 2008 (Figure 1b). Temperature and salinity of each cruise are meridionally interpolated onto integer latitudes and then smoothed with a Gaussian filter of 150 km e-folding scale [Qu et al., 1999] to remove interference from transient processes, such as internal waves, eddies, and other small scale motions. The smoothed data are used to calculate the geostrophic velocity and sea surface dynamic height with a reference level at 1000 db following Qiu and Joyce  and Shuto .
 We also use a merged altimetry product from Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO) [Ducet et al., 2000], which include sea surface height (SSH) and corresponding sea surface geostrophic velocity. This product is obtained through combining Topex/Poseidon, Jason, ERS-1 and -2, and ENVISAT in a 1/3° × 1/3° Mercator grid and a 1 week time interval. The altimetry data used here are from 1992 to 2006. Figure 1a shows the satellite altimeter observed mean SSH and sea surface geostrophic currents in the North Pacific Ocean, from which the westward NEC and its bifurcation near the Philippine coast can be clearly seen.
2.2. Ocean State Estimates
 The two kinds of ocean state estimates used in the present study are the European Center for Medium-Range Weather Forecasts (ECMWF) ocean analysis/reanalysis system (ORA-S3) [Balmaseda et al., 2008] and Simple Ocean Data Assimilation version 2.2.4 (SODA224) [Carton and Giese, 2008; Giese and Ray, 2011].
 Monthly mean output of ECMWF ORA-S3 used in this study covers the global ocean with a horizontal resolution of 1° × 1° and spans a period of 51 years from January 1959 to December 2009. The ocean data assimilation system for ORA-S3 is based on the Hamburg Ocean Primitive Equation model (HOPE)-Optimal interpolation (OI) scheme. The system is forced by fluxes from the 40 years ECMWF Reanalysis (ERA-40) from January 1959 to June 2002 and Numerical Weather Prediction (NWP) operational analyses thereafter. There are 29 vertical levels un-uniformly extending from 5 m to 5250 m. This data set has some innovative features, including the assimilation of salinity on temperature surfaces and the assimilation of altimetry data with global sea level trends [Balmaseda et al., 2008]. One can refer to Balmaseda et al.  for more detailed description of the data set, including the ocean assimilation scheme, the wind forcing, the data assimilated, the comparisons with observations and previous versions, and so on.
 Monthly mean output of SODA224 also covers the global ocean with a horizontal resolution of 0.5° × 0.5° and spans from 1871 to 2008. There are 40 levels in the vertical. The ocean model is based on the Parallel Ocean Program (POP) ocean model version 2.0.1 [Smith et al., 1992] and forced by the 20th Century Atmospheric Reanalysis product (20CRv2) [Compo et al., 2011]. One can refer to Carton and Giese  and Giese and Ray  for details of the ocean model, the relevant configurations and the assimilation algorithm.
2.3. Ocean Objective Analyses
 The two kinds of ocean objective analyses used in the present study are the newly developed Decadal Climate Prediction System (DePreSys) [Smith and Murphy, 2007; Smith et al., 2007] and the newest version of the Enhanced Ocean Data Assimilation and Climate Prediction (ENACT) archive version 3 (EN3v2a) [Ingleby and Huddleston, 2007; Wijffels et al., 2008; Guinehut et al., 2009].
 DePreSys contains objective analyses of temperature and salinity of the global ocean with a horizontal resolution of 1.25° × 1.25° and 20 levels in the vertical, spanning from 1950 to 2006. The analyses are based on the covariances computed directly from a realistic Hadley Center coupled global climate model (HadCM3) [Gordon et al., 2000] and with observations from the World Ocean Database 2001 (WOD01) [Conkright et al., 2002] for the period 1950–1955 and a new quality-controlled data set developed by Ingleby and Huddleston  from 1956 onward [Smith and Murphy, 2007]. One can refer to Smith and Murphy  for more details.
 EN3v2a contains objective analyses of temperature and salinity of the global ocean with a horizontal resolution of 1.0° × 1.0° and 40 levels in the vertical, spanning from 1950 to present. The new version EN3v2a is obtained with the methods of Ingleby and Huddleston  and observations from the World Ocean Database 5 (WOD05) [Boyer et al., 2006] and more recent data archived by the Global Temperature-Salinity Profile Programme (GTSPP) project [Wilson, 1998]. One can refer to Ingleby and Huddleston  for more details.
 Though DePreSys and EN3v2a have used the same temperature and salinity profiles prepared by Ingleby and Huddleston  after 1956, they adopted different methods. The results from both data sets are analyzed in the present study. Sea surface dynamic height and horizontal geostrophic velocity in the upper 1000 m are then calculated from these two data sets with the same reference level (1000 db) as adopted in the calculation of the sea surface dynamic height and zonal geostrophic velocity with the hydrographic observations at 137°E obtained by JMA. There are slight differences in the magnitudes of the calculated sea surface dynamic height and horizontal geostrophic velocity when choosing the reference level at between 1000 db and deeper depths of ∼1500–2500 db [e.g., Qu et al., 1998]. However, it has been indicated that the decadal NEC variations and associated large-scale circulation variations are insensitive to the reference level at 1000 db [e.g., Qiu and Joyce, 1992] or at deeper depths of ∼1500–2500 db [e.g., Qu et al., 1998].
 As the NEC transport variations mainly reflect the upper ocean variations, the two ocean state estimates and two objective analyses can be validated by comparing the sea level in them with tidal gauge observations which are independent of the four products. For that purpose, we select six tidal gauge stations located at low latitudes of the tropical northwestern Pacific Ocean. As the SSH from the two ocean state estimates and the sea surface dynamic height from the observations and ocean objective analyses are of different amplitudes, their original time series are normalized. Figure 2 shows the normalized time series of the sea level at the six tidal gauge stations and from the four oceanic products. It is found that high-positive correlations exist between the observed sea level fluctuations and those from the ocean state estimates and objective analyses. The correlation coefficients are overall higher than 0.70 above the 95% confidence level and can be as high as 0.80 on seasonal and longer time scales. This heightens our confidence in further assessing the decadal NEC transport variations and their associated broader-scale circulation changes using results from the ocean state estimates and objective analyses. At most stations, sea level from ORA-S3 and that from the two ocean objective analyses have higher correlations with tidal gauge observations than that from SODA224. Perhaps, these differences are because of the different methods, models, and forcing fields in producing the four different products. Overall, ORA-S3 and the two ocean objective analyses are expected to give more realistic descriptions of the circulation changes associated with the decadal NEC transport variations.
 To focus on the decadal variations, temperature and salinity observed by JMA and their derived sea surface dynamic height, zonal velocity, and volume transport of the NEC along 137°E of each year are first linearly interpolated to January (winter) and July (summer) of the year and then the total time series are filtered by a low-pass filter (>8 years). Monthly variables from the ocean state estimates and objective analyses of the same period are also filtered with the same low-pass filter. At last, the first and last 4 years of the low-pass filtered variables are excluded from further analyses. The decadal anomalies are calculated through subtracting the mean from the low-pass filtered time series.
3.1. Basic Characteristics
 We first examine the basic characteristics of the decadal NEC variations at 137°E using the repeated hydrographic observations, which include the meridional distribution of zonal velocity anomalies, the temporal variations of the maximum westward velocity, and the meridional boundaries of the NEC. Figure 3a shows the annual mean zonal velocity and its standard deviation on the decadal time scale at 137°E. The mean NEC spans from 7°N to about 19°N at the sea surface in general. Its maximum westward velocity core is located at about 11°N and moves northward with depth. The main body of the NEC with westward velocities >5 cm s−1 lies between 7°N and 20°N. As shown by the black lines in Figure 3a, the standard deviation of the decadal zonal velocity anomalies decreases northward and downward. Standard deviations >1.5 cm s−1 are mainly confined south of 17°N and above 300 m. This result suggests that circulation changes in the southern part of the section make most contributions to the decadal NEC transport variations. Figure 3b shows the decadal variations of the southern NEC boundary of zero velocity following the tropical gyre center. The magnitude of its fluctuations on decadal time scale is only about 1°N, which is much smaller than that of the full time series. Figure 3c shows the decadal variations of the maximum westward velocity of the NEC. On average, the maximum westward velocity of the NEC is about 23.5 cm s−1. The value is larger than average during the periods of 1978–1988, 1993–1997, and 2003–2005 and smaller than average during the periods of 1975–1976, 1989–1993, and 1997–2002.
 In the present study, the NEC transport (TNEC) across the 137°E is obtained by integrating the westward velocities vertically from the sea surface downward to 26.7 σθ-isopycnal surface and meridionally from 7°N to 20°N. The result is shown in Figure 4a. During the past 30 years, the NEC transport has three maxima around 1980/1981, 1994/1995, and 2004/2005, and two minima around 1989/1990 and 1999/2000, respectively. The differences between the maxima and minima are about 10.0 Sv, comparable to that of its interannual variation [e.g., Zhai and Hu, 2012, 2013]. The time intervals are about 10 years between the first maximum and first minimum, and about 5 years between the other adjacent extremes. To explore the oceanic variations associated with the decadal NEC transport variations, we calculate the composite anomalies of the SSH, the depth of 26.7 σθ-isopycnal surface, and the zonal velocities during the periods of decadal NEC transport maxima (1980–1981, 1994–1995, 2004–2005) and minima (1989–1990, 1999–2000). The results are shown in Figures 4b–4e. When the NEC transport is maximum, the sea surface falls and the 26.7 σθ-isopycnal surface shoals between 5°N and 15°N, which implies the upper layer thinning. The variation center is at about 7°N–8°N corresponding well with the tropical gyre center [Shuto, 1996]. Associated with these upper layer thickness variations, zonal velocity anomalies are westward north of 7°N–8°N and eastward south of it. The variations are reversed when the NEC transport is minimum.
 To explore the ocean processes possibly responsible for the upper layer variations, Figure 5 shows the composite anomalies of temperature, salinity, and potential density associated with the NEC transport maxima and minima on decadal time scale. During maximum transport periods, the southern part of the NEC is dominated by negative anomalies of temperature and positive anomalies of potential density extending to at least as deep as 1000 m. This is essentially consistent with the Empirical Orthogonal Function (EOF) analysis of winter temperatures along the 137°E from 1967 to 1987 conducted by Shuto . From the principal component of the second EOF mode [Shuto, 1996, Figure 13], he also noted a decadal transition from negative values to positive values around 1976, when the decadal NEC transport has increased (Figure 4a). Corresponding to the positive peak in the principal component, temperature anomalies [Shuto, 1996, Figure 12b] north and south of 12°N–13°N are positive and negative, respectively, both extending to at least as deep as 900 m. The typical temperature anomalies (Figure 5) in our current study are about −2.0°C and their negative maximum takes place at about 100–150 m depth near 7°N, coinciding with the center of composite SSH anomalies. Around this latitude, there are positive and negative salinity anomalies above and below the climatological salinity maximum depth, respectively. During minimum transport periods, the situation is reversed. The linear correlation between the depths of the salinity maximum around the center of composite SSH anomalies and the NEC transport on the decadal time scale is about −0.74 above 95% confidence level. These results indicate that the decadal variations of the upper-layer thickness are largely due to simultaneous fluctuations of isothermal and isohaline surfaces instead of variations of water mass properties.
 To the north of the center, however, the decadal salinity anomalies around the climatological salinity maximum, which represents the North Pacific Tropical Water (NPTW) [e.g., Qu et al., 1999] are positive during maximum transport periods while negative during minimum transport periods. The linear correlation between the salinity maximum of the NPTW and the NEC transport on the decadal time scale is about 0.87 above 95% confidence level. This reveals that the salinity of the NPTW has been changing accompanying the NEC transport on the decadal time scale. As shown in section 3.4, the decadal NEC transport variations across 137°E are related to the cyclonic/anticyclonic gyre anomalies formed in the tropical northwestern Pacific Ocean. The decadal salinity anomalies of the NPTW, therefore, may be mainly generated locally by the anomalous cross-front geostrophic advections induced by the gyre anomalies as in the case of the interannual salinity anomalies of the NPTW [e.g., Li et al., 2012; Zhai and Hu, 2012].
3.3. 1½ Layer-Reduced Gravity Model
 In the following, we examine the relationship between the decadal NEC transport variations and the upper ocean changes. The in-phase variations of the SSH and the depth of 26.7 σθ-isopycnal surface suggest that the ocean in this region be basically dominated by the first baroclinic mode [e.g., Wunsch, 1997]. Therefore, the variability of the upper ocean transport can be examined by a 1½ layer reduced gravity model, which can be expressed as
where h is the upper layer thickness (equivalent to the pycnocline depth), y1 and y2 are latitudes of the southern and northern NEC boundaries, u is the upper layer zonal velocity and is calculated from the SSH η or h by
 In equation (1), the negative sign is chosen to make the westward NEC transport positive. In (2), g and g′ are the gravity and reduced gravity, respectively, and f is the Coriolis parameter.
 In the reduced gravity model, h is related to η by , with C being constant. Therefore, the pycnocline depth h can be chosen as the depth of the isopycnal surface that has the highest correlation with η. The black line in Figure 6c displays the correlations between SSH and the depths of isopycnal surfaces between 23.7 σθ and 27.3 σθ, including the pycnocline. The overall correlation coefficient within this density range is above 0.71 with confidence level above 95%. The largest correlation (r = 0.98) is between SSH and the depth of 25.1 σθ-isopycnal surface. As an example, Figures 6a and 6b show the variations of SSH and the depth of 25.1 σθ-isopycnal surface, respectively. We then calculate the NEC transports between the sea surface and isopycnal surfaces of 23.7–27.3 σθ following equation (1). Their correlations with TNEC calculated in above section are shown as the red line in Figure 6c. The correlation coefficients are all >0.88 with confidence level above 95%. The NEC transport calculated with the depth of the 25.6 σθ-isopycnal surface gives the highest correlation (r = 0.94). The red and blue lines in Figure 6d show the NEC transport calculated with the depths of the 25.6 σθ and 26.7 σθ-isopycnal surfaces, respectively. One can see that the latter is slightly larger than TNEC. The above analysis confirms that the 1½ layer reduced gravity model does a good job in reproducing the variability of TNEC. In the following, we use the depth of 25.6 σθ-isopycnal surface as the upper layer thickness h and discuss why the decadal NEC transport maxima/minima are associated with the upper layer thinning/thickening and the westward velocity strengthening/weakening in the southern part of the NEC.
 The transport anomalies in the 1½ layer reduced gravity model can be expressed as
 Here, we define and to denote the transport anomalies induced by upper layer thickness anomalies and zonal velocity anomalies, respectively. These anomalies, along with the total transport anomalies, are shown in Figure 6e. The correlation of with (r = 0.91) is much higher than that with (r = −0.14). Meanwhile, the standard deviation of (7.8 Sv) is much larger than that of (2.7 Sv). This result indicates that the zonal velocity variations dominate in the NEC transport variations. Thus, though the upper layer thinning in the southern part of the NEC tends to decrease the NEC transport, it also results in westward velocity strengthening, which in turn increases the NEC transport.
3.4. Ocean State Estimates and Objective Analyses
 Before using the ocean state estimates and objective analyses to test the relationship of the decadal NEC transport variations with broader-scale circulation changes, we first validate their results by the observations. Figure 7 shows the time series of the NEC transport calculated from the ocean state estimates and ocean objective analyses. They agree well with the observations both in magnitude and phase. Their simultaneous correlation coefficients with the observations are all >0.70 significant at the 95% confidence level. On the decadal time scale, ORA-S3 gives the highest correlation (r = 0.95), while SODA224 gives the lowest correlation (r = 0.75).
 Figure 8 shows the composite decadal zonal velocity anomalies at 137°E from ocean state estimates and objective analyses, showing similar spatial patterns to the observations. During the periods of decadal NEC transport maxima, zonal velocity anomalies are westward to the north and eastward to the south of the southern NEC boundary, which roughly coincides with the center of the tropical gyre. The situation during the periods of decadal NEC transport minima is reversed. It suggests that all the four selected products capture the observed decadal NEC transport variations well and can be used further to examine the horizontal circulation variations.
 With the decadal variations of the NEC transport and zonal velocity as described above, an immediate question is whether the zonal velocity anomalies are part of the gyre circulation anomalies. In Figure 9, we present the composite decadal anomalies of SSH and horizontal velocities averaged between 50 m and 120 m from the four products. As shown in this figure, all the four products show nearly the same circulation anomaly patterns. During the maximum transport periods, the SSH anomalies in the tropical northwestern Pacific Ocean off the Philippine coast are negative, with their center basically coinciding with the mean southern NEC boundary. The sea surface falling also implies the pycnocline shoaling and thus the upper layer thinning. Geostrophically, the negative SSH anomalies result in an anomalous cyclonic gyre around their center. During the minimum transport periods, the situation is reversed; the SSH anomalies off the Philippine coast are positive and the anomalous gyre is anticyclonic. This suggests that the zonal velocity anomalies at 137°E are just part of the anomalous cyclonic/anticyclonic gyre formed off the Philippine coast, which should be associated with the decadal variability of the Mindanao Dome [e.g., Masumoto and Yamagata, 1991; Tozuka et al., 2002; Kashino et al., 2011].
 To give more support directly from observations, we present in Figure 10, the differences of the satellite altimeter observed SSH and its derived sea surface geostrophic velocity between the periods of the decadal NEC transport maxima (1992–1996 and 2003–2005) and minimum (1997–2000). From this figure, negative SSH anomalies and their associated cyclonic gyre anomaly can be clearly seen in the tropical northwestern Pacific Ocean off the Philippine coast. This result is consistent with those from the ocean state estimates and ocean objective analyses.
 The above analysis has suggested wind-driven circulation variations that are responsible for the decadal NEC transport variations in the tropical northwestern Pacific Ocean at 137°E. Furthermore, the good performance of a 1½ layer reduced gravity model in reproducing the depth-integrated NEC transport variations supports the capability of the linear vorticity equation in explaining the underlying dynamics [e.g., Meyers, 1979; Kessler, 1990; Qiu and Joyce, 1992; Capotondi et al., 2003; Qiu and Chen, 2010; Zhai and Hu, 2012, 2013]. Under the long wave approximation and assumptions of low frequency and quasi-geostrophy, the linear vorticity equation for the SSH anomaly (η′) can be written as
where is the speed of the first mode of long baroclinic Rossby waves, β is the meridional gradient of the Coriolis parameter f, λ is the baroclinic Rossby radius, is the wind stress vector anomaly, and ε is the Newtonian dissipation rate. The first two terms on the right-hand side represent the remote wind forcing through the westward propagation of Rossby waves and the local wind forcing through local Ekman pumping, respectively.
3.5.1. Local Wind Forcing
 We first examine the role of the local wind forcing. In this case, the rate of the decadal SSH change is governed by the convergence/divergence of the anomalous Ekman fluxes
with the solution
where is the initial SSH anomaly. The derived SSH anomalies are function of g′ and ε, as the initial values of SSH anomalies and wind stress can be easily obtained from the four products. To obtain optimal values of these two parameters, the percentage of decadal SSH variance from the four products explained by those calculated following equation (6) are calculated as follows:
where η′ represents the decadal SSH anomaly in the oceanic products and denotes the time average over the past 30 years. The optimal g′ and ε can be determined by maximizing VE. Figure 11 presents the simultaneous correlation coefficients between the decadal SSH anomalies from the four products and those from equation (6). In most part of the tropical North Pacific Ocean, the correlations are positive and they can reach as high as 0.80 in some part of the region. However, in the central tropical North Pacific Ocean south of about 10°N and part of the Philippine Sea, the correlations are negative, implying that local Ekman dynamics is unable to interpret the decadal SSH variations there.
3.5.2. Remote Wind Forcing
 In this section, we examine the effect of the remote wind forcing. With zonally varying ε(x) and CR(x), the solution of equation (4) can be obtained through integrating it along with the Rossby wave characteristics from the eastern basin boundary and is expressed as
where x = xe denotes the eastern ocean basin boundary, is the negative transit time needed for the first baroclinic Rossby wave generated in the east to reach the target point x. The effect of the decadal SSH variations at the eastern basin boundary is ignored because it is confined only within a few Rossby radii away from the boundary [e.g., Fu and Qiu, 2002; Qiu and Chen, 2010]. The baroclinic Rossby wave speed CR is calculated with the baroclinic Rossby radius λ derived by Chelton et al. . When the wind stress vector anomalies are given, the modeled would be a function of g′ and ε. In equation (4), the Newtonian dissipation is used to parameterize the momentum dissipation which is assumed in the form of horizontal eddy diffusion [Qiu et al., 1997] and thus, the ε should be a function of longitude. However, for the purpose of simplicity and being easy to handle, the ε is usually chosen as a constant in the literature [e.g., Capotondi et al., 2003; Qiu and Chen, 2010; Hsin and Qiu, 2012; Zhai and Hu, 2012]. It is quite time consuming to obtain the optimal ε for each longitude. In the present study, we would follow Zhai and Hu  and try to obtain an optimal ε for longitudes to the west of 180°E (εW) and another optimal ε for longitudes to the east (εE) along the latitude of interest. This may be reasonable considering that the significant circulation variations associated with the decadal NEC transport variations are mainly confined in the western tropical Pacific Ocean (Figure 9). The relatively low/high ε estimated here would indicate that the Rossby wave signals responsible for the decadal variations of the SSH in the northwestern tropical Pacific Ocean experience small/large dissipation along their way propagating westward. Optimal values of g′, εW, and εE are estimated for each product. Along each latitude of interest, the optimal g′, εW, and εE are determined by maximizing VE in the longitude band of 135°E–170°E following equation (7) but replacing by . The wind forcing data used in equation (8) for the four oceanic products are from ORA-S3 produced by ECMWF. For SODA224, we have also examined the performance using the wind forcing data in equation (8) from itself, which is originally from 20CRv2 [Giese and Ray, 2011]. The result indicates that for SODA224 the wind forcing data from ORA-S3 performs better in reproducing the circulation variations associated with the decadal NEC transport variations (comparing Figures 14c and 14d with Figures 9c and 9d) than that from itself (figure not shown). The model skill with the use of wind data from SODA224 would be better when considering different ε for more different parts of the Pacific Ocean basin than only two different parts as done here. The sensitivity of the model skill to the spatial variations of ε should be further examined in the future studies and beyond our current study. In the following, only results with the use of wind forcing data from ORA-S3 in equation (8) for all the four oceanic products are displayed and discussed.
 Figure 12 shows the optimal values of g′, εW, and εE. Though slightly different in magnitude, the four products show similar meridional distributions of the three parameters. g′ has its maximum around the center of tropical gyre and decreases both northward and southward. This result is consistent with the meridional distribution of stratification, which is strongest around the center of tropical gyre (see also Figure 5). The current result of g′ also agrees well with previous conclusions that the maximum g′ corresponds to the thermocline ridge [e.g., Kessler, 1990; Donguy and Meyers, 1996; Johnson et al., 2002]. εW is relatively small (≈ 0) at most latitudes south of 15°N but increases to about 1.0–2.0 × 10−7 s−1 at latitudes north of 15°N. Different from εW, εE is small (≈ 0) north of 13°N but increases to above 1.0 × 10−7 s−1 at low latitudes. εE for ORA-S3, DePreSys, and EN3v2a show local maxima (3.8 × 10−7 s−1) around 6°N–7°N and then decrease both northward and southward, similar to g′, while that for SODA224 shows local maxima around 5.25°N and around 8°N–10°N. The difference in the meridional variations of εE of the four products should be due to the different decadal SSH anomalies in the four products. With currently derived optimal values of g′, εW, and εE, the modeled for each product are obtained through forcing the first-mode baroclinic Rossby wave model (equation (8)) with the wind data from ORA-S3.
 Figure 13 presents the simultaneous correlations between the decadal SSH anomalies from equation (8) and those calculated from the ocean state estimates and ocean objective analyses. Comparing with the situation only considering local Ekman dynamics (Figure 11) involving baroclinic Rossby wave dynamics significantly increases the correlations and the area with positive correlations. In most part of the tropical northwestern Pacific Ocean, the correlations can be >0.80.
 With such high correlations, we then present in Figure 14 the composite mapping of the simulated decadal SSH anomalies and their derived sea surface geostrophic velocities. The composite mapping in general bears a striking resemblance to those from the ocean state estimates and ocean objective analyses (Figure 9) in both the magnitudes and spatial patterns; that is, the tropical northwestern Pacific Ocean is with negative SSH anomalies and an anomalous cyclonic gyre during the periods of the decadal NEC transport maxima, and the situation is reversed during the periods of the decadal NEC transport minima. Besides, we have also noted two minor discrepancies between the composite maps of the simulated decadal SSH anomalies and those from the four oceanic products. One is that the meridional extents of the simulated gyre anomalies in the northwestern tropical Pacific Ocean are slightly smaller than those in the oceanic products (Figure 9). This may be improved if we consider more spatial variations of ε across the Pacific basin. The other one is that the simulated decadal SSH anomalies in the eastern part of the Pacific Ocean are weaker than those in the oceanic products. This may be mainly because that we ignore contributions from the Rossby wave signals triggered at the eastern ocean boundary and also possibly because that the adopted εE values are larger than reality. Overall, the good comparisons between the composite maps of the simulated decadal SSH anomalies and those in the selected oceanic products imply that the linear vorticity equation (8) works well in reproducing the decadal circulation variations in the tropical northwestern Pacific Ocean.
 Given the good performance of the linear vorticity equation (8), it may be helpful to clarify the relative contributions of the wind forcing over different longitude bands in the Pacific Ocean. As an example, we examine the percentage of the cumulative decadal variance of the SSH at xT = 137°E explained by the wind forcing in the east as a function of longitude X. The is defined as
where denotes the SSH anomaly at 137°E forced by the wind anomaly to the west of X. The results are shown in Figure 15 and indicate that much of the decadal SSH variance is caused by the wind forcing in the western part of the tropical North Pacific Ocean.
3.6. Relations to Climate Modes
 This section clarifies the connection of the decadal circulation variations to climate modes in the tropical Pacific Ocean. Figure 16a compares the time series of the decadal NEC transport observed at 137°E, and the first EOFs of the decadal anomalies of the sea surface temperature (SST) from ORA-S3 and wind stress vector from both ORA-S3 and SODA224. As the Pacific Decadal Oscillation (PDO), which is defined as the first EOF mode of the monthly SST anomaly poleward of 20°N in the North Pacific Ocean, has been pointed out to have significant imprints on the decadal variability of the tropical Pacific Ocean [e.g., Mantua et al., 1997; Zhang et al., 1997], its time series is also shown in Figure 16a for comparison. In this study, the PDO index is downloaded from http://jisao.washington.edu/pdo/, which can also be obtained through conducting the EOF analysis of the monthly SST anomalies with ECMWF ORA-S3 and/or other SST data sets.
 The first EOF mode of the decadal SST anomalies in the tropical Pacific Ocean, often referred to as TPDV, presents the typical mode of the decadal variability in the tropical Pacific Ocean [e.g., Timmermann, 2003; Rodgers et al., 2004; Yeh and Kirtman, 2004, 2005; Sun and Yu, 2009]. To examine the robustness of the spatial patterns and temporal evolutions of the TPDV, the EOF analysis is conducted with decadal SST anomalies in the tropical Pacific Ocean of 120°E–280°E and 25°S–25°N from five different products: ORA-S3, SODA224, DePreSys, EN3v2a, and the Extended Reconstruction Sea Surface Temperature version 3b (ERSSTv3b) [Xue et al., 2003; Smith et al., 2008]. Basically, the five products show the same spatial patterns and time evolutions of the TPDV and thus only results from ORA-S3 are shown here in Figure 16. In these five products, the TPDV explains 55%, 54%, 62%, 50%, and 61% of the decadal SST variance in the tropical Pacific, respectively. In general, the spatial pattern of the TPDV shows a broad triangular shape in the tropical Pacific with an anomalous warming center in the central Pacific (Figure 16b). The current result is similar to that derived from a coupled GCM [Yeh and Kirtman, 2004]. So, it suggests that the TPDV is robust in the tropical Pacific Ocean.
 On the other hand, as discussed above, the circulation variations associated with the decadal NEC transport variations are mainly induced by the surface wind forcing in the tropical Pacific, it is therefore useful to clarify the wind forcing pattern by conducting an EOF analysis of the wind stress vector anomalies. The first EOF of the decadal wind stress vector anomalies is calculated for both the entire tropical Pacific Ocean of 120°E–280°E and 25°S–25°N and the northwestern tropical Pacific Ocean of 130°E–180°E and 5°N–21°N (figure not shown), which gives about the same spatial patterns and time evolutions in the northwestern tropical Pacific Ocean. The spatial patterns of the first EOF modes of the decadal wind stress anomalies from ORA-S3 and SODA224 are shown in Figures 16c and 16d, respectively, both explaining 43–44% of the decadal wind stress variance. Basically, the two products show the same spatial patterns of the first EOF modes except in the northwestern and southeastern part of the basin. Comparing Figure 16b and Figures 16c and 16d, one can see that the first EOF mode of the wind stress anomalies is dynamically consistent with that of the SST anomalies, that is, the wind stress anomalies are mainly across lines of equal SST anomalies from cold SST anomaly regions to warm SST anomaly regions. The wind stress anomalies are westerly along the equator and northwesterly north of it in the western part of the tropical North Pacific Ocean, and they are essentially westerly east of the dateline. The westerly wind anomalies west of the dateline in SODA224 extend to higher latitudes than those in ORA-S3. These wind anomalies produce upward Ekman pumping velocity anomalies during the warm phase of the TPDV over the western-central tropical North Pacific Ocean, which then trigger westward propagating upwelling Rossby waves. The correlation coefficients of the principal components of the first EOF of the decadal wind stress anomalies in ORA-S3 and SODA224 with the TPDV reach 0.95 and 0.94 above 95% confidence level, respectively. Though with comparable correlations with the TPDV index, the decadal evolution of the wind forcing in SODA224 agrees better with the TPDV than that in ORA-S3 in terms of the occurring time of extrema in the TPDV index and principal components of the first EOF modes of the decadal wind forcing. This difference could be due to the different methods adopted in preparing the two products.
 The decadal NEC transport has high correlations with the PDO (r = 0.80) with a lead of 21 months, with the TPDV (r = 0.78) with a lead of 7 months, with the first EOF mode of the wind forcing from ORA-S3 (r = 0.64) with a lead of 1 month and from SODA224 (r = 0.79) with a lead of 6 months. The TPDV has a high correlation with the PDO (r = 0.79) with a lead of 17 months. All the correlations presented here are significant above the 95% confidence level. These results indicate that the decadal NEC transport in the tropical northwestern Pacific Ocean is highly correlated with the TPDV, as well as the PDO, though the latter has its influence center at higher latitudes than the former. At the same time, we note that the time difference between each pair of peaks or troughs of the TPDV and the decadal NEC transport is slightly different from case to case, possibly due to different wind anomalies and contributions from other processes.
 Combining repeat hydrographic observations along 137°E with ocean state estimates and objective analyses, the decadal NEC transport in the tropical northwestern Pacific Ocean and its associated large-scale circulation changes are investigated. Over the past 30 years (1975–2005), the decadal NEC transport has three maxima around 1980/1981, 1994/1995, and 2004/2005, and two minima around 1989/1990 and 1999/2000, respectively. Associated with these transport maxima/minima, the SSH falls/rises and the subsurface isopycnals shoal/deepen in the southern part of the NEC, resulting in westward/eastward zonal velocity anomalies. The composite decadal anomalies of temperature, salinity, and potential density indicates that the decadal variations of the upper layer thickness are mostly due to simultaneous fluctuations of isothermal and isohaline surfaces instead of variations of water mass properties. Results from the ocean state estimates and ocean objective analyses confirm the observed decadal variations of the NEC transport and zonal velocity at 137°E. Using the ocean state estimates and ocean objective analyses along with the altimeter observations, we further found that the decadal zonal velocity anomalies at 137°E are part of the anomalous cyclonic/anticyclonic gyres formed in the tropical northwestern Pacific Ocean off the Philippine coast, whose center is around that of the tropical gyre.
 With the linear vorticity equation governing a 1½ layer reduced gravity model, it is shown that the decadal circulation variations in the tropical northwestern Pacific Ocean are mainly controlled by sea surface wind forcing in the western part of the tropical Pacific Ocean. These variations can be further attributed to the local Ekman dynamics and the westward propagation of baroclinic Rossby waves. The decadal sea surface wind forcing is in turn closely related to the tropical Pacific decadal variability.
 We are much obliged to Kentaro Ando for providing the web link to the hydrographic observations at 137°E obtained by Japan Meteorological Agency. We are also grateful to Bo Qiu for valuable discussions. Detailed comments from two anonymous reviewers helped improve an early version of the manuscript. The present study is sponsored by Project of State Strategic Program of Global Change (2013CB956202) and the National Basic Research Program of China (2012CB417401). T.Q. is also supported by NSF through grants OCE10-29704 and OCE11-30050. SOEST contribution 9005, and IPRC contribution number IPRC-1013. F.Z. is also supported by China Postdoctoral Science Foundation through grant 2013M530331.