 Research article
 Open Access
 Published:
Spatiotemporal vertical velocity variation in the western tropical Pacific and its relation to decadal ocean variability
Progress in Earth and Planetary Science volumeÂ 9, ArticleÂ number:Â 57 (2022)
Abstract
Prior to the cold phase of the Pacific decadal oscillation (PDO), sea surface water in the western tropical North Pacific is heated. To evaluate the impact of the subsurface water on the upperocean (\(<100\)Â m depth) temperature variation, we examined the vertical velocity variation. We applied altimetrybased gravest empirical mode (AGEM) method to Argo hydrographic profile (2001â€“2017) and altimetric sea surface height (1993â€“2017) data in the western tropical Pacific and obtained a timevarying threedimensional (3D) potential density field in the layer from 100 to 1000Â m depth. From the AGEMderived potential density, we derived a 3D field of vertical velocity below 100Â m depth by the Pvector inverse method, which is based on potential density and vorticity conservations, and examined the spatiotemporal characteristics, focusing on the seasonal to quasidecadal (QD) variations. In the mean state, substantial upward current (\(>10^{6}\,{\text {m\,s}}^{1}\)) is observed in the region of \(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\) in the North Equatorial Current, southern part of the North Pacific subtropical gyre. Possibly besides the Ekman upwelling, the upward current contributes to the cooling of the upper ocean in the western tropical North Pacific through the upward advection of the deep cold water. The upward current was found to be intensified (attenuated) by the strengthening (weakening) of the subtropical gyre interior southward flow on the QD timescale in association with frequent occurrences of La NiÃ±a (El NiÃ±o) events. The weakening of the upward current is responsible for the QD increase in upperocean temperature in the western tropical North Pacific, which is equivalent to or larger than \(0.2~^{\circ }\)C, several years after the warm phase of the PDO. The QD temperature variation may affect the phase reversal of the PDO through the heat transport of the western boundary current of the subtropical gyre, i.e., the Kuroshio.
1 Introduction
The subtropical gyre of the North Pacific is a basinscale anticyclonic circulation, consisting of the northward swift western boundary current, socalled the Kuroshio, and the southward weak flow in the interior region. The subtropical gyre transports a huge amount of heat northward (e.g., Bryden and Imawaki 2001; Nagano etÂ al. 2009, 2010). Through the variation in the northward heat transport, the subtropical gyre of the North Pacific is considered to play a critical role in interannual and longer timescale midlatitude climate variations such as the Pacific decadal oscillation (PDO) (e.g., Kawai etÂ al. 2008), the most dominant variation in sea surface temperature (SST) in the North Pacific, (e.g., Mantua etÂ al. 1997; Mantua and Hare 2002). Similar decadal oscillations were produced in ocean and atmosphere coupled numerical models (Latif and Barnett 1994, 1996; Gu and Philander 1997).
The spatial pattern of the PDO is defined as the first empirical orthogonal function (EOF) mode of SST in the North Pacific. A map of regression slope of SST to the PDO index (the time coefficient of the first EOF mode of the SST) is illustrated in Fig.Â 1a. In the positive (warm) phase of the PDO, the pattern exhibits a negative SST anomaly in the central part of the North Pacific and a positive SST anomaly in the central and eastern equatorial Pacific (Mantua etÂ al. 1997; Mantua and Hare 2002). Thermal disturbances excited at the northern periphery of the subtropical gyre due to the strengthening of the Aleutian Low are observed to subduct in the upper main thermocline (pycnocline), to propagate southward in the interior region of the subtropical gyre, and, longer than 10 years after the subduction, reaches a subsurface (up to approximately 100Â m depth) layer around a latitude of \(18^{\circ }\)N of the western tropical North Pacific (e.g., Deser etÂ al. 1996; Schneider etÂ al. 1999).
By combined use of altimetric sea surface height (SSH) data, expendable bathythermograph temperature data, and Argo salinity data at lines from San Francisco to Hawaii and from Hawaii to Japan, Nagano etÂ al. (2016a) studied the quasidecadal (QD) variation in the subtropical gyre net heat transport due to the variation of the interior flow with periods of 8â€“12 years (e.g., Tourre etÂ al. 2001; White etÂ al. 2003; Hasegawa and Hanawa 2003; Hasegawa etÂ al. 2013). Up to 4Â years after the positive (warm) PDO phase, the volume transportweighted temperature in the subtropical gyre interior region increases due to the enhancement in volume transport in a potential density layer between 25.0 and 25.5Â \({\sigma }_{\theta }\) (\({\sigma }_{\theta } =\) potential density \( 1000~{\text {kg\,m}}^{3}\)). As a result, because the temperature difference of the water masses transported by the Kuroshio and the gyre interior flow decreases, the northward net heat transport decreases. The reduction in the northward heat transport accumulates heat in the western tropical North Pacific, where climatological SST is very high, and enhances the warm pool SST (Nagano etÂ al. 2016a), as is recognized in the map of the regression slope with a 3year lag (Fig.Â 1d). In other words, the warm pool SST increases prior to the negative phase of the PDO.
The QD variation in the subsurface volume transport in the interior region of the subtropical gyre is suggested to contribute to the SST variation in the region of \(10^{\circ }\)â€“\(20^{\circ }\)N, \(125^{\circ }\)â€“\(160^{\circ }\)E in the western North Pacific warm pool (Nagano etÂ al. 2016a) possibly through the enhancement of the upwelling of deep water from layers deeper than 100Â m depth. If we obtain a threedimensional (3D) field of vertical velocity, we can confirm this idea. The spatiotemporal characteristics of upward currents in the western tropical North Pacific are, however, unknown because vertical current velocity is too small (\(<10^{4}\)Â \({\text {m\,s}}^{1}\)) to be directly measured by oceanographic instruments such as current meters, the accuracy of current measurements being of the order of \(10^{3}\)Â \({\text {m\,s}}^{1}\) at best for now (e.g., Thomson and Emery 2014). Therefore, vertical velocity should be estimated from other physical variables such as 3D water density field under some hydrodynamic assumptions.
Based on the conservations of potential density and potential vorticity, Needler (1985) derived a formula of 3D absolute velocity vector (\({{\varvec{v}}}\)), in the interior region of subtropical gyres as
where \({\rho }\) is the potential density, f is the Coriolis parameter, g is the gravitational acceleration, \(q=f/{\rho } (\partial {\rho }/{\partial }z)\) is Ertelâ€™s potential vorticity neglecting the relative vorticity, and \({{\varvec{k}}}\) is the unit vertical vector. In addition to potential density and potential vorticity, the Bernoulli function of a water parcel advected by the flow is conserved if the flow is steady and the diffusion can be neglected (e.g., Needler 1985; Pedlosky 1987a, b). For the estimation of the 3D current velocity field from hydrographic data, several methods have been proposed by past investigators (e.g., Stommel and Schott 1977; Olbers etÂ al. 1985; Killworth 1983, 1986; Chu 1995, 2006). These methods are expected to provide similar 3D current velocity fields because they are based on the same assumptions, i.e., conservations of potential density and potential vorticity.
Chu (1995, 2006) developed a sophisticated method, called the Pvector inverse method, to calculate 3D absolute velocity vector from observed hydrographic data, avoiding cases that isosurfaces of potential density and potential vorticity are parallel (i.e., \({\nabla }{\rho }\,{\times }{\nabla }{q}\)Â =Â 0), as described in the following section. For example, he applied the Pvector inverse method to the circulations in the upper layer of the North Atlantic and demonstrated a very strong downward velocity around a depth of the main pycnocline (500Â m depth) in the area south of Iceland, where the subduction zone of the global ocean conveyor belt is possibly located (Schmitz 1995). Therefore, the Pvector inverse method provides reasonable 3D distributions of vertical velocity and may be used to diagnose vertical velocity in the western tropical and subtropical North Pacific.
By applying the Pvector inverse method to the 3D potential density field in the tropical and subtropical North Pacific, we expect to obtain a vertical velocity field in the upper ocean layer and to reveal its seasonal to decadal variations. In other words, we can identify the location where the QD variation in the subsurface volume transport in the interior region of the subtropical gyre reported by Nagano etÂ al. (2016a) emerges in the western Pacific region and how the QD variation of the vertical transport to the east of the Philippines is related to the variation in the interior region. Further, the impact of the vertical transport on the upper ocean to the east of the Philippines may be estimated.
In general, potential vorticity is not conserved along streamlines with horizontal and vertical diffusion. To obtain the absolute velocity vector field by the Pvector method and other methods based on the potential vorticity conservation, a timevarying 3D gridded water density field with sufficient spatial resolution is required. As a candidate of such a dataset, we may use gridded hydrographic data such as the grid point value of the Monthly Objective Analysis using the Argo (MOAA GPV) data (Hosoda etÂ al. 2008) based on global Argo float data collected since 2000. Using this dataset, we first attempted to compute the Pvectorderived vertical velocity. However, the vertical velocity computed from the MOAA GPV data applying the Pvector method is unreasonably large (\(>10^{4}\,{\text {m\,s}}^{1}\)) probably because the effective resolution (\({\sim }1000\)Â km) is too low to apply the conservation of potential vorticity. Hence, we must use a finer gridded dataset to obtain reliable vertical velocity estimates by the Pvector inverse method.
Satellite observations have extensive coverage and sufficient resolutions in space and time to resolve the ocean variations on scales ranging from mesoscale to global scale. SSH maps with a horizontal resolution of \(1/4^{\circ } {\times } 1/4^{\circ }\) are available to examine current variations (Pujol and Mertz 2020). Particularly, because SSH is a physical parameter, which corresponds to integrated specific volume (i.e., reciprocal of water density) through the water column from the bottom to the sea surface, variations in altimetric SSH should be related to those in water density through the water column. Thus, combined use of the Argo hydrographic profile data and altimetric SSH data might produce a sufficiently fine resolution 3D hydrographic dataset.
The altimetrybased gravest empirical mode (AGEM) method has been applied to spatiotemporally sparse hydrographic data to estimate variations of hydrographic and current fields all over the world from SSH data (e.g., Sun and Watts 2001; Swart etÂ al. 2010; Nagano etÂ al. 2016a, b). Because AGEMderived hydrographic fields have the same horizontal resolution as that of the altimetric SSH data, they are sufficient to resolve regional scale circulations and their temporal variations. Nagano et al. (2016a, b) applied the AGEM method to hydrographic data and altimetric SSH data, and estimated sections of potential temperature and salinity (therefore, potential density) at a line from San Francisco to near Japan via Hawaii across the interior region of the North Pacific subtropical gyre and 3D hydrographic fields in the western subarctic North Pacific.
In this study, we compute the 3D monthly potential temperature, salinity, and therefore potential density fields from the AGEM for areas divided by applying cluster analysis to Argo hydrographic profile data. We then estimate the vertical velocity field by the Pvector inverse method and examine the variations on seasonal to decadal timescales. In Sect.Â 2, we describe Argo conductivityâ€“temperatureâ€“depth (CTD) profile data, altimetric SSH data, and the AGEM method. In Sects.Â 3 and 4, we analyze the AGEMderived potential density and the Pvectorbased vertical velocity fields, focusing on their variations related to the QD variations in the tropical and subtropical North Pacific and examine the impact of the vertical velocity variation on the upperocean temperature through the vertical advection of the deep cold water. Summary and conclusion are provided in Sect.Â 5.
2 Data and methods
2.1 Argo data
To construct AGEM fields, we used more than 7000 temperature and salinity profiles from the near sea surface (10Â dbar) to a pressure level of 1000Â dbar (equivalent to a depth of approximately 1000Â m) collected for each month by Argo floats (Advanced automatic QC Argo Data versionÂ 1.2) from January 2001 to May 2017 in the region of \(10^{\circ }\)Sâ€“\(25^{\circ }\)N, \(120^{\circ }\)Eâ€“\(180^{\circ }\). A total of 90192 hydrographic profiles were used in this study. The accuracies of the Argo temperature, salinity, and pressure data were reported to be \({\pm }0.005\)Â \(^{\circ }\)C, \({\pm }0.01\) (psu), and \({\pm }5\)Â dbar by Argo Science Team, respectively (Hosoda etÂ al. 2008). Following the Akima (1970) method, temperature and salinity profiles were interpolated onto the vertical grids at intervals of 10Â dbar from 10 to 1000Â dbar.
From the Argo temperature and salinity profile data, we calculated spiciness parameter by using the polynomial proposed by Flament (2002), which isopleths are orthogonal to those of potential density on the temperatureâ€“salinity diagram. The orthogonal character of the spiciness parameter permits us to identify water masses in terms of potential density by the single parameter. Because of this, spiciness analyses are useful to distinguish water masses, as demonstrated in the Kuroshio and North Pacific subtropical gyre interior regions by Nagano et al. (2009, 2010, 2012). We performed cluster analysis, applying Wardâ€™s criteria (e.g., Ward 1963; Anderberg 1973) to spiciness values averaged between isopycnal layers at intervals of 0.01Â \({\text {kg\,m}}^{3}\) from 24.06 to 26.46Â \({\sigma }_{\theta }\) and changing the number of clusters from 3 to 9. The number of clusters being set to 7, the classification based on the cluster analysis is found to be roughly consistent with the distributions of water masses in the western tropical and subtropical Pacific such as the North/South Pacific Tropical Waters and the North Pacific/Antarctic Intermediate Waters (e.g., Fine etÂ al. 1994; Kashino etÂ al. 2011; Talley etÂ al. 2011). Thus, we classified Argo hydrographic profiles into 7 clusters.
We divided the study region (\(10^{\circ }\)Sâ€“\(25^{\circ }\)N, \(120^{\circ }\)Eâ€“\(180^{\circ }\)) into pieces of \(5^{\circ }\) on each side based on this cluster analysis result. Next, the dominant (the most frequent) cluster of hydrographic profiles for each piece was determined. Based on the dominant clusters in all pieces, the study region was separated into 7 areas in individual months except for January (6 areas) and February (5 areas). The area division based on the cluster analysis is found to be roughly consistent with the regional current and water mass pathways (Fig.Â 2) (e.g., Reid 1997; Talley etÂ al. 2011).
Using the Argo temperature and salinity profiles, we calculated the dynamic height with the reference pressure level of 1000Â dbar, \(H_{\text {CTD}}\), in meters as
where p is pressure and \({\delta }={\rho }^{1}  {\rho }^{1} (0, 35, p)\) is the specific volume anomaly relative to the specific volume of seawater with temperature 0Â \(^{\circ }\)C and salinity 35 (e.g., Gill 1982) calculated from Argo CTD data. The vertical integral in Eq.Â (2) was discretized into the summation of 10dbar averaged \({\delta }\) multiplied by the vertical interval of 10Â dbar from 10 to 1000Â dbar. The error in the Argoderived \(H_{\text {CTD}}\) was estimated to be smaller than 0.8Â cm, which is small compared with the altimetric SSH data error (\({\sim }3\)Â cm).
2.2 Altimetric SSH data
We used daily altimetric absolute SSH (\(H_{\text {ALT}}\)) \(1/4^{\circ }\) \(\times\) \(1/4^{\circ }\) gridded map data in the region of \(10^{\circ }\)Sâ€“\(25^{\circ }\)N, \(120^{\circ }\)Eâ€“\(180^{\circ }\) from January 1993 to May 2017. The absolute SSH data are derived from the delayedtime updated SSH (Level 4) anomaly data (DT_SLAH) (Pujol and Mertz 2020) added to the mean dynamic topography data (MDT_CNESCLS13) provided by Rio etÂ al. (2011). Because the SSH data are erroneous near the coasts, we did not use SSH data in regions of water depths less than 1000Â m to estimate AGEM fields and AGEMderived 3D potential temperature and salinity fields.
\(H_{\text {ALT}}\) is linearly correlated with the dynamic height derived from Argo CTD data, i.e., \(H_{\text {CTD}}\), with correlation coefficients of 0.60â€“0.98 (Fig.Â 2), which are much higher than the 1% significance level (i.e., within the 99% confidence limit) based on the Studentâ€™s tÂ test. Therefore, we performed linear regressions and based on those equations, converted values of \(H_{\text {ALT}}\) to dynamic height, which is required to construct 3D potential temperature and salinity fields by the AGEM method described in the next subsection. Note that the correlation coefficients in the equatorial and South Pacific are relatively low possibly because of highfrequency (time scales shorter than days) variations by internal gravity waves or small scale patchy water masses as observed by Richards etÂ al. (2015) and others, which cannot be fully resolved by the altimetric SSH observations.
2.3 Areawise AGEM method
Vertical structures of temperature and salinity are considered to be greatly different among the areas classified by the cluster analysis and seasons. Thus, to consider the spatial and seasonal variations, for each month and each area, we constructed AGEM fields, i.e., the relations between hydrographic profiles and dynamic height, \(H_{\text {CTD}}\), based on all the Argo CTD data in the area during the month. The AGEM fields were smoothed for \(H_{\text {CTD}}\) by a Gaussian weight function with an efolding scale of 2.5Â cm to remove noisy features due to the highfrequency variability.
As an example, the AGEM potential temperature and salinity fields down to a depth of 1000Â m for 6 areas in January are shown in Figs.Â 3aâ€“f and 3gâ€“l, respectively. The main thermocline illustrated by the sharp potential temperature decrease from 25Â \(^{\circ }\)C to 8Â \(^{\circ }\)C commonly deepens as the dynamic height \(H_{\text {CTD}}\) increases. Along with the main thermocline, the salinity maximum layer deepens with \(H_{\text {CTD}}\) although the salinity values are different for each area. Salinity in the areas in the Southern Hemisphere (Fig.Â 3i, k) is higher than that in other areas (Fig.Â 3g, h, j, l), as illustrated by Reid (1997) and others. Corresponding to the regional differences in salinity, there are also regional variations in potential temperature and density.
We identify differences in the vertical distributions of potential temperature and salinity for the season (not shown). In the upper layer shallower than 100Â m, potential temperature, and salinity seasonally vary associated with the development of the mixed layer in winter and the stratification in summer. Because, in this AGEM estimation, we used Argo hydrographic data during approximately 17Â years from 2001 to 2017, the constructed AGEM fields should account the interannual to decadal variations. Such spatial and seasonal variations of the AGEM fields beside the SSH variations are responsible for those of the horizontal circulation and vertical current and their interannual to decadal modulations, as described in the following sections.
By converting monthly altimetric SSH, \(H_{\text {ALT}}\), to \(H_{\text {CTD}}\) and referring to the AGEM fields, we estimated the temporal changes of the 3D fields of potential temperature and salinity, and that of potential density on the horizontal grids of \(1/4^{\circ }\) at the vertical grids of 10Â m from 10 to 1000Â m. Ranges of converted SSH, i.e., dynamic height, variations in individual areas were within those of the dynamic height of the AGEM fields (abscissa in Fig.Â 3). This suggests that the AGEMderived 3D potential temperature and salinity fields involve the seasonal to decadal variations that are consistent with the SSH variations. To eliminate noisy features and to suppress artificial gaps between the areas in AGEMderived potential temperature and salinity fields for reasonable estimation by the Pvector inverse method, spatial smoothing was performed using a Gaussian filter with a damping scale of 150Â km. For the following analysis, we used the smoothed AGEMderived potential temperature and salinity fields. In Fig.Â 4, we show the rootmeansquare (RMS) potential density differences between Argo and AGEMderived data at depths of 100, 200, 400, and 800Â m; the RMS potential density difference at each grid was computed by using data collected in the month by Argo floats within a radius of 1000Â km. The RMS potential density differences are reduced with the depth from approximately 1.2Â \({\text {kg\,m}}^{3}\) at 100Â m to 0.1Â \({\text {kg\,m}}^{3}\) at 800Â m due to the weakening of the variations on shorter timescales than approximately 1Â month. In addition, note that there are no artificial spatial gaps in the RMS potential density differences due to the area division based on the cluster analysis.
FigureÂ 5a shows the horizontal distribution of potential density at a depth of 200Â m averaged in all months during the study period. In addition, according to Rintoul etÂ al. (2002) and Nagano etÂ al. (2016b), we calculated the streamfunction defined as
The streamfunction in the mean state integrated from the sea surface to a pressure level of 1000Â dbar (approximately 1000Â m depth) is illustrated by contours in Fig.Â 5a. The estimated mean current circulations are similar to those observed by past investigators (e.g., Nitani 1972; Reid 1997; Qu etÂ al. 1998; Qu and Lukas 2003). The North Pacific subtropical and tropical gyres to the north and south of approximately \(13^{\circ }\)N are characterized by high and low potential density. Associated with the northward sharp decrease in potential density at a latitudinal band between \(10^{\circ }\)N and \(15^{\circ }\)N, there exists a strong current toward the western boundary of the Pacific basin, i.e., the North Equatorial Current (NEC), which consists of the westward current of the southern part of the subtropical gyre and that of the northern part of the tropical gyre.
The Mindanao Dome (MD) is produced in the region off the eastern coast of the Mindanao Island (\(4^{\circ }\)â€“\(10^{\circ }\)N) and the eastern edge of the circulation extends to the east of \(140^{\circ }\)E in boreal spring (Fig.Â 5c) and to the east of \(150^{\circ }\)E in boreal autumn (Fig.Â 5e). The remarkable seasonal change of the circulation observed by Qu etÂ al. (1998), Qu and Lukas (2003), and others, and produced in a numerical model by Tozuka etÂ al. (2002) are reproduced in this AGEM estimation.
2.4 Pvector inverse method
By using a unit vector \({{\varvec{P}}}\), called the perfect vector (Pvector); and the magnitude of the velocity vector \({\gamma }\), called the speed parameter, at location \({{\varvec{x}}}=(x, y, z)\), Chu (1995, 2006) expressed Eq.Â (1) as \({{\varvec{v}}}({{\varvec{x}}})\) \(= {\gamma } {{\varvec{P}}}\). Here, using potential density \(\rho\) and potential vorticity \(q=f/{\rho } (\partial {\rho }/{\partial }z)\), \({{\varvec{P}}}\) is defined as
Using the thermal wind equation, \(\gamma\) at a depth level of \(z_{k}\) (\({\gamma }_{k}\)) is calculated as
where (\({\Delta }u_{k}\), \({\Delta }v_{k}\)) is the vertical shear vector of horizontal velocity relative to the reference depth level, \(z_{r}\). In this study, we set \(z_{r}\) to 1000Â m.
Using the monthly 3D potential density fields estimated by the areawise AGEM method, we calculated the 3D velocity vector below a depth of 100Â m, where the AGEMbased potential density is reliable. Note that we did not conduct the calculation in the equatorial region between \(3^{\circ }\)S and \(3^{\circ }\)N because f is close to zero approaching the equator. There are two necessary conditions for the solution to exist. Isosurfaces of potential density and those of potential vorticity are not parallel (\({\nabla }{\rho }\,{\times }{\nabla }{q}\) \(\ne\) 0), and the denominator of Eq.Â (5) does not vanish (for the existence of the Pspiral). By examining the two necessary conditions for the existence of the absolute velocity vector, we can remove inappropriate solutions. In this study, we did not calculate the Pvector and the speed parameter in the locations where these necessary conditions are not satisfied. The necessary conditions are satisfied in areas exceeding 86% of the calculation region every month. Values of \({{\varvec{P}}}\) and \(\gamma\) in areas with no data were interpolated with a spatial Gaussian weight function with a horizontal efolding scale of 150Â km, which is much smaller than spatial scales of the phenomena of our interests (\(> 500\)Â km).
The estimation of the 3D absolute current velocity field was conducted under some assumptions. In particular, the neglect of relative vorticity may produce significant error in the vertical velocity. Taking the curl of the momentum equation and using the continuity equation for incompressible fluid, we obtain \({\partial }w/{\partial }z = (1/f)({\partial }{\zeta }/{\partial }t)\), where \({\zeta }={\partial }v/{\partial }x  {\partial }u/{\partial }y\) is relative vorticity (e.g., Gill 1982). The horizontal velocity is no more than 50Â \({\text {cm\,s}}^{1}\) in the NEC and the horizontal scale of the variation is larger than 1000Â km, so that the magnitude of \({\zeta }\) is order of \(10^{7}\)Â \({\text {s}}^{1}\) except in the western boundary region. Taking into account the vertical and time scales of the w variation, 100Â m and 1Â month, respectively, the contribution of relative vorticity except in the western boundary region is less than \(10^{6}\)Â \({\text {m\,s}}^{1}\), which is smaller than the w variation. In the western boundary region, the error larger than \(10^{6}\)Â \({\text {m\,s}}^{1}\) is considered to be included in the estimated vertical velocity data.
By using the thermal wind equation, the vortexstretching equation, \(v = (f/{\beta }) {\partial }w/{\partial }z\), gives \({\rho }{\partial }^2 w/{\partial }z^{2} =  ({\beta }g/f^2){\partial }{\rho }/{\partial }x\), where \(\beta\) is the latitudinal variation of f (Killworth 1983). On the basis of this equation, the error of the estimated vertical velocity attributed to the potential density error can be evaluated. The RMS difference between Argo and AGEMderived potential density data in layers deeper than the main thermocline, where variations possibly due to highfrequency internal gravity waves are relatively small, may be regarded as the AGEM potential density error. If we set the error of the potential density to 0.1Â \({\text {kg\,m}}^{3}\), we evaluate the error of the w variation with a horizontal scale of 1000Â km and a vertical scale of 100Â m to be \(10^{7}\)Â \({\text {m\,s}}^{1}\). The error is one order of magnitude smaller than the variation in w on the seasonal and longer time scales, as will be discussed in the following sections.
To examine the characteristics of interannual and longer timescale variations in vertical velocity, we smoothed the data by a 15month running mean filter. We decomposed the interannual vertical velocity variation by EOF modes to reveal regionalscale variation patterns, as the EOF mode decomposition is helpful to examine the spatiotemporal characteristics of the variations (e.g., Thomson and Emery 2014). Based on the EOF mode patterns, we determine the upwelling region where we compute volume and temperature transports.
2.5 SST data
To examine the impact of vertical velocity on upperocean (\(<100\)Â m depth) temperature in the region east of the Philippines, we used monthly US National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation Sea Surface Temperature (SST) V2 (NOAA_OI_SST_V2) data (Reynolds etÂ al. 2002) from January 1993 to May 2017 in the region of \(10^{\circ }\)Sâ€“\(25^{\circ }\)N, \(120^{\circ }\)Eâ€“\(180^{\circ }\). We smoothed the data by a 15month running mean filter to eliminate the seasonal variation and evaluated the temporal tendency of the temperature by taking the smoothed data to the water temperature averaged in the top 100Â m.
2.6 Climate indices
We used the NiÃ±oÂ 3.4 index from January 1993 to December 2016, which is defined as the monthly mean SST anomaly from the seasonal variation in the central and eastern equatorial region of \(5^{\circ }\)Nâ€“\(5^{\circ }\)S, \(170^{\circ }\)Wâ€“\(120^{\circ }\)W as an El NiÃ±oâ€“Southern Oscillation (ENSO) index by Trenberth (1997). Anomalously high and low SST events in the central and eastern equatorial Pacific, i.e., El NiÃ±o and La NiÃ±a events, are indicated by the NiÃ±oÂ 3.4 index. In addition, the PDO index from January 1993 to December 2016, defined as the time coefficient of the first EOF mode of SST in the region poleward of \(20^{\circ }\)N for the period from 1900 to 1993 (Mantua etÂ al. 1997), was used to calculate the regression slope between the PDO index and SST in the Pacific (Fig.Â 1) and to conduct comparison with the time series of the vertical current transports in the western tropical North Pacific.
3 Results
3.1 Mean circulation and vertical velocity fields
The areawise AGEM estimation produced the horizontal upperocean circulations in the western parts of the North Pacific subtropical gyre and the North/South Pacific tropical gyres, as illustrated by the streamfunction in Fig.Â 5a. Feeding the subtropical gyre interior southward flow, the westward flowing NEC is strengthened toward the western boundary from \(148^{\circ }\)E to \(135^{\circ }\)E (Fig.Â 5a). The cyclonic circulation of the MD centered around \(8^{\circ }\)N, \(130^{\circ }\)E is separated from the eastern tropical cyclonic circulation east of \(165^{\circ }\)E. Associated with the westward shrinkage of the MD in boreal winter (Fig.Â 5b) and spring (Fig.Â 5c), the westward current of the southern part of the NEC around a latitude of \(8^{\circ }\)N is attenuated in longitudes between \(145^{\circ }\)E and \(168^{\circ }\)E as illustrated by the widening and undulation of the \(\chi _{1000}\) contours. When the MD is weak, the NEC approaches the North Equatorial Countercurrent (NECC), and it generates wavy patterns between the currents. The wavy patterns may be attributed to fluctuations due to the barotropic instability (e.g., Pedlosky 1987a), which can occur in the enhanced horizontal shear between the opposing currents, as observed in the central and eastern equatorial regions (e.g., Tanaka and Hibiya 2019). In boreal summer (Fig.Â 5d) and autumn (Fig.Â 5e), the MD extends eastward and strengthens the NEC.
Upward (positive) velocities of approximately \(1 {\times } 10^{6}\)Â \({\text {m\,s}}^{1}\) are found in a part of the NEC, 10â€“\(16^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\), in layers of 100Â m (Fig.Â 6a) and 200Â m (Fig.Â 6b) depths. This upwelling region is located in the boundary between the subtropical and tropical gyres, where the meridional gradients of the potential density and streamfunction are remarkable (Fig.Â 5a). Meanwhile, at a depth of 400Â m, there is no systematic pattern of vertical velocity. As indicated by the vertical velocity maps at 100Â m depth in Fig.Â 7, the upward velocity is extensively observed in the region north of approximately \(10^{\circ }\)N, mostly in the subtropical gyre region, in boreal winter (Fig.Â 7a) and spring (Fig.Â 7b) but is limited in the latitudes south of \(15^{\circ }\)N in summer (Fig.Â 7c) and autumn (Fig.Â 7d). The magnitudes of the vertical velocity tend to be amplified in low latitudes near the western boundary regions because of \(\gamma {\sim } f^{1}\) as derived from Eq.Â (5). Although values of vertical velocity at individual grids are similar to or a little larger than the error (\(10^{6}\)Â \({\text {m\,s}}^{1}\)) estimated in Sect.Â 2.4, the error of mean value across such a regional scale (\(>2000\)Â km) is evaluated to be \(10^{8}\)Â \({\text {m\,s}}^{1}\). Therefore, we focus on the variations with spatial scales equivalent to or larger than the upwelling region in the NEC. In Sect.Â 3.3, we will discuss the vertical volume and temperature transports across the upwelling region.
The seasonal changes in vertical velocity are also identifiable in the zonal and meridional sections; for example, we show zonal sections at the latitude of \(12.6^{\circ }\)N (Fig.Â 8) and meridional sections at the longitude of \(145.4^{\circ }\)E (Fig.Â 9). The upward and downward velocities were produced in a layer down to a depth of approximately 350Â m in association with the undulation of the isopycnal surfaces of 25.0â€“26.5Â \({\sigma }_{\theta }\) in the longitudinal band between \(140^{\circ }\)E and \(170^{\circ }\)E. The intensity of the vertical velocity is greatest in boreal winter (Figs.Â 8b, 9b) and spring (Figs.Â 8c, 9c). In the region from \(140^{\circ }\)E to \(160^{\circ }\)E, the upward velocity appears to be stronger than the downward velocity; particularly, in the layer shallower than 150Â m, upward velocity is predominant (Fig.Â 8).
The considerably large vertical velocity (\(> 5 {\times } 10^{6}\)Â \({\text {m\,s}}^{1}\)) is generated in winter and spring around a latitude of \(12^{\circ }\)N, where the main pycnocline sharply shoals toward the equator along with the strongly baroclinic NEC, as illustrated in Fig.Â 9b, c. The strong vertical velocity in boreal winter to spring is considered to be driven by the winter intensification of the NEC, which may be partly attributed to the variation of the subtropical gyre interior flow volume transport in a potential density layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) reported by Nagano et al. (2012, 2016a). Despite the great seasonal change in a layer between 150 and 350Â m depths, the seasonal change in the shallower layer around a latitude of \(10^{\circ }\)N between \(140^{\circ }\)E and \(180^{\circ }\) is remarkably small. Beneath a depth of approximately 350Â m, where the vertical potential density gradients are less than those in the overlying layer, the magnitudes of the vertical velocity are unsubstantial.
3.2 Interannual and longer timescale variations in vertical velocity
The vertical velocity field varies on various time scales longer than 1Â year. As described in Sect.Â 2.4, we obtained the interannual variation in vertical velocity by a 15month running mean filter and calculated the EOF modes. The percentages of variance explained by the first and second EOF modes are 66% and 11%, respectively, and the sum of these modes explains 77% of the total variance. Each higher EOF mode accounts for no more than 3% of the total variance. Therefore, the leading two EOF modes can explain most of the interannual to decadal vertical velocity variations.
The horizontal patterns of the first EOF mode at depths of 100 and 200Â m are shown in Fig.Â 10a, b, respectively. At 100Â m depth, apart from the western boundary region, the first EOF mode varies with a zonal scale exceeding 2000Â km such as in the negative loading region of \(10^{\circ }\)â€“\(15^{\circ }\)N, \(150^{\circ }\)Eâ€“\(180^{\circ }\) (Fig.Â 10a), where the mean vertical velocity is largely upward, containing smaller scale (\({\sim }1000\)Â km) variations (Fig.Â 6a). The positive and negative alternating large loadings are present to the east of Mindanao Island (\(3^{\circ }\)â€“\(10^{\circ }\)N, \(125^{\circ }\)â€“\(140^\circ\)E), but, because relative vorticity was not taken into account, the vertical velocity estimated in the western boundary current region may be unreliable.
At a depth of 200Â m (Fig.Â 10b), remarkably large positive and negative loadings are aligned alternatively along a latitude of \(12^{\circ }\)N with a zonal scale of approximately 500Â km. The zonal scale of the vertical velocity variation at this depth is smaller than that at 100Â m depth. The area of either sign of the loading at 200Â m depth appears not to be dominant in the region \(10^{\circ }\)â€“\(15^{\circ }\)N, \(150^{\circ }\)Eâ€“\(180^{\circ }\). In both zonal (Fig.Â 10c) and meridional (Fig.Â 10d) sections of the EOF mode, the remarkable variation is observed down to a depth of approximately 350Â m, below which vertical gradient of potential density is small and the vertical velocity variation is weak. Therefore, the first EOF mode variation of the vertical velocity is responsible for the intensity change of the upward current above approximately 350Â m depth in the region of \(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\) shown in Figs.Â 6, 8a, and 9a.
The second EOF mode of the vertical velocity at a depth of 100Â m has a large negative loading in a region similar to the first EOF mode but is limited within the region of \(10^{\circ }\)â€“\(15^{\circ }\)N, \(155^{\circ }\)Eâ€“\(180^{\circ }\) (Fig.Â 11a). Regions equatorward of \(10^{\circ }\)N and \(10^{\circ }\)S show mostly positive values. At a depth of 200Â m (Fig.Â 11b), positive and negative loadings with spatial scales smaller than approximately 500Â km are sporadically distributed in the region south of \(15^{\circ }\)N. The spatial patterns of the vertical velocity are identifiable in the zonal and meridional sections down to a depth of 290Â m, but in layers deeper than 300Â m, we find noisy features with vertical scales of 10â€“20Â m (Fig.Â 11c, d).
The time coefficient of the first EOF mode (black solid line in Fig.Â 12a) has peaks several months after peaks of the NiÃ±oÂ 3.4 index (gray solid line), i.e., El NiÃ±o events, as in 1997â€“1998, 2002â€“2003, 2004â€“2005, 2009â€“2010, and 2015â€“2016. Similarly, troughs of the time coefficients are found after La NiÃ±a events such as in 1995â€“1996, 1998â€“2001, 2007â€“2008, and 2010â€“2011. The timelagged correlation coefficient between the first EOF mode and the NiÃ±oÂ 3.4 index shows the maximum of 0.52 with a lag of 8Â months (black solid line in Fig.Â 13, TableÂ 1). The maximum correlation coefficient is higher than the 5% significance level (i.e., within the 95% confidence limit) based on the Studentâ€™s t test. Therefore, the first EOF mode variation is significantly related to the ENSO.
Peaks of the time coefficient of the second EOF mode are found almost simultaneously with those of the NiÃ±oÂ 3.4 index (Fig.Â 12b). With a lag of 1Â month, the correlation coefficient reached the maximum of 0.74, which is higher than the 5% significance level and is therefore statistically significant (black dashed line in Fig.Â 13, TableÂ 1). The second EOF mode variation is excited by the ENSO before the first EOF mode variation and is more highly correlated with the ENSO than the first EOF mode variation. The first EOF mode lags 9Â months behind the second EOF mode with the maximum correlation coefficient of 0.71, which is much higher than the 5% significance level and is statistically significant (pink solid line in Fig.Â 13).
3.3 Impacts of vertical velocity variation on SST
In this subsection, we examined the impact of the interannual and longer timescale variations in the vertical velocity on the upperocean temperature in the region 10â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\), referred to as Region A in what follows, where the vertical velocity at 100Â m depth is prominently upward on average (shown by a solid square in Fig.Â 6a) and quite variable (Fig.Â 10a).
We calculated vertical volume transport (\(V_{z}\)) and temperature transport (\(F_{z}\)) at a depth of 100Â m in Region A, which are defined as
and
where \(C_p\) is the specific heat capacity of seawater at constant pressure and \(\theta\) is the potential temperature. \({\rho } C_p\) is set to \(3.99 {\times } 10^6\)Â \({\text {J\,K}}^{1}\,{\text {m}}^{3}\).
Time series of the vertical volume and temperature transports are shown by thick black and green lines in Fig.Â 14a, respectively. Both modes of transports in Region A are always positive, i.e., upward, and fluctuates inversely related to the PDO and NiÃ±oÂ 3.4 indices with correlation coefficients of \(0.80\) and \(0.79\), respectively (TableÂ 1), being consistent with the EOF analysis in Sect.Â 3.2. In addition, the transport is relatively low (high) due to frequent occurrences of El NiÃ±o (La NiÃ±a) events during periods such as 1994â€“1998 and 2002â€“2005 (1999â€“2001 and 2007â€“2014). This relationship is clearly shown by the QD component of the NiÃ±oÂ 3.4 index smoothed by a 37month running mean filter (Hasegawa etÂ al. 2013) (thin magenta line in Fig.Â 14a), which is inversely related to the vertical volume transport (thin black line in Fig.Â 14a).
When the volume transport reached the maximum over 1.5Â Sv in summer (July) of the 2008 La NiÃ±a year (downward arrow in Fig.Â 14a), the upward current velocity exceeded \(1 {\times } 10^{6}\)Â \({\text {m\,s}}^{1}\) in the region from \(150^{\circ }\)E to \(180^{\circ }\) around \(12^{\circ }\)N (Fig.Â 15b). The strong upwelling was driven principally by the southward current greater than 1Â \({\text {cm\,s}}^{1}\) at 100Â m depth (contours in Fig.Â 15b) existing above the isopycnal zone of 25.0â€“25.5Â \({\sigma }_{\theta }\) at 200Â m depth (vertical line mesh), which impinged on the slope of the isopycnals shoaling southward. In this period, the southward current in the isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) was mostly distributed in the subtropical gyre interior region (\(10^{\circ }\)â€“\(25^{\circ }\)N, \(145^{\circ }\)Eâ€“\(180^{\circ }\)) (Fig.Â 16b). The westward velocity of the NEC in this isopycnal layer was higher than 15Â \({\text {cm\,s}}^{1}\) to the east of \(160^{\circ }\)E.
Meanwhile, in the summer (July) of the 1997 El NiÃ±o year (upward arrow in Fig.Â 14a), the vertical velocity in Region A was weakly upward or downward, and the corresponding southward current was observed only in a limited region centered around \(14^{\circ }\)N, \(175^{\circ }\)E (Fig.Â 15a). The area of the subtropical gyre interior southward current in the isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) and the intensity of the NEC are both smaller than those in the 2008 summer (Fig.Â 16a). The QD variations in the vertical velocity just beneath a depth of 100Â m are expected to contribute to the QD variation in SST in the western tropical North Pacific related to the PDO as illustrated in Fig.Â 1.
Because the water temperature and vertical velocity at 100Â m depth are not horizontally uniform, the temperature of upwelling water is not necessarily identical to the areaaveraged temperature within Region A. The water temperature of water mass transported by the vertical current can be examined by the volume transportweighted temperature (\({\Theta }\)) at a depth of 100Â m defined as
The volume transportweighted temperature (gray solid line in Fig.Â 14b) varies on the QD timescale in opposite phase with the NiÃ±oÂ 3.4 index (magenta line in Fig.Â 14b) because of the anomalously warm (cold) water in the upper layer of the western Pacific warm pool in La NiÃ±a (El NiÃ±o). Therefore, the increase in \(\Theta\) just below a depth of 100Â m in La NiÃ±a years acts to reduce the cooling effect of the enhancement of the upward velocity. Because of the nonuniformity of w, \(\Theta\) is approximately 0.1Â \(^{\circ }\)C higher than the areaaveraged temperature, \(T_{100}\) (gray dashed line in Fig.Â 14b). However, note that, as will be shown below, the volume transportweighted temperature variation is much less effective in the upperocean temperature variation than the upward current variation.
The upward volume and temperature transports in Region A decrease with the depth because, in layers deeper than 150Â m, upward currents are compensated by similar magnitude downward currents (Fig.Â 8). For example, the volume and temperature transports at 200Â m depth are mostly positive (upward) but smaller than 0.8Â Sv and 50Â TW, respectively. Their correlation coefficients with respect to the NiÃ±oÂ 3.4 index are \(0.44\), absolute values of which are smaller than the 5% significance level.
To examine the impact of the vertical velocity and temperature variations at 100Â m depth on the temperature in the overlying layer, we estimate temperature tendency (\({\partial } T_{w}/{\partial } t\)) averaged in the top 100Â m due to the vertical velocity variation, w, i.e., vertical advection of temperature (\(w{\partial }T/{\partial }z\)), by the following formula:
where \(h_{\text {u}}\) is the depth of the uppermost level of the estimation of w (i.e., 100Â m), \(T_{\text {d}}\) is the potential temperature just below 100Â m depth, and \(T_{\text {u}}\) is the upperocean (\(<100\)Â m depth) temperature. \(T_{\text {d}}\) and \(T_{\text {u}}\) are set to the AGEMderived potential temperature at the 110Â m depth and monthly gridded value of SST prepared by Reynolds etÂ al. (2002), respectively. We assigned to w the timevarying vertical velocity at a depth of 100Â m derived from the Pvector inverse method. When the vertical velocity is negative (or downward), w is set to zero, i.e., \(w=0\).
The temperature tendency, \({\partial } T_{w}/{\partial } t\), based on Eq.Â (9) and averaged in Region A is shown in Fig.Â 14c. The QD variability (red line in Fig.Â 14c) is remarkable and is almost in phase with the PDO index (cyan line in Fig.Â 14b) with a significant correlation coefficient of 0.63 (TableÂ 1). Associated with the enhancement of the vertical volume transport (Fig.Â 14a), the temperature tendency has substantial troughs in 2000, 2009, and 2014, which occur 6â€“8 years after the peaks of the volume transport in the isopycnal layer between 25.0 and 25.5Â \({\sigma }_{\theta }\) in the subtropical gyre interior region in 1994, 2001, and 2006 estimated by Nagano etÂ al. (2016a). The minimum value of the temperature tendency (\(0.04\)Â \({^{\circ }{\text {C}}}\,{\text {month}}^{1}\)) in the spring of 2000 is approximately 30% of the annual mean cooling rates of the mixed layer due to the vertical entrainment and the net surface heat flux, which were individually estimated to be approximately \(0.13\)Â \({^{\circ }{\text {C}}}\,{\text {month}}^{1}\) by Qu (2003); thus, the variation in the upward advection of the deep cold water due to the vertical velocity variation has a critical influence on the QD upperocean temperature variation.
4 Discussion
4.1 Relation of the upward current cooling to the PDO
The temperature variation obtained by temporally integrating the anomaly of \({\partial }T_{w}/{\partial }t\), i.e., \(T^{\prime }_{w} = \int {\partial }T^{\prime }_{w}/{\partial }t \,{\text {d}}t\), exhibits a smooth QD variation with peaks in 1999 and 2006 (blue line in Fig.Â 14c). These peaks largely coincide with those of the QD SST variation in the North Pacific warm pool region calculated by Nagano etÂ al. (2016a) in the region marked by the dotted square (Figs.Â 6, 7, 10a, 11a) and the troughs of the QD variation in the net heat transport examined by Nagano etÂ al. (2016a). The peak values of \(T^{\prime }_{w}\) reach or exceed 0.2Â \(^{\circ }\)C, which is equivalent to the regression slope in the western tropical North Pacific with a lag of 3Â years as illustrated in Fig.Â 1d. \(T^{\prime }_{w}\) inversely varies leading 34Â months to the PDO index with a significant correlation coefficient of \(0.65\) (TableÂ 1). The leading time (34Â months) is a little longer than a leading time (2Â years) of the variation in coral nitrogen isotope concentrations in Tatsukushi Bay, Japan, a possible proxy for the surface Kuroshio water temperature, to the PDO index reported based on 36year time series by Yamazaki etÂ al. (2016). The discrepancy (8 months) between the time leads of this study and that of Yamazaki etÂ al. (2016) can be explained by the advection time of approximately 9Â months evaluated by Nagano et al. (2014, 2017) from the northward propagation of sea surface salinity variation along the western subtropical North Pacific.
Therefore, 6â€“8 years after the variation in the volume transport in the isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) in the subtropical gyre (Nagano etÂ al. 2016a), the vertical volume transport in the region east of the Philippines (\(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\)) changes and it modifies the upperocean temperature through the vertical advection of the cold deep water to the upper ocean. Considering the horizontal advection time scale of water masses in the subtropical gyre interior region (\({\sim }10\)Â years) (e.g., Sasaki etÂ al. 2010), the time lag between the variations in the vertical volume transport to the east of the Philippines and the volume transport in an isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) (6â€“8Â years) appears to be reasonable.
The relations of the upwelling strength in the NEC to the positive and negative phases of the PDO are summarized in Fig.Â 17a, b, respectively. In the positive phase of the PDO, the subtropical gyre interior flow in the isopycnal layer between 25.0 and 25.5Â \({\sigma }_{\theta }\) is strengthened (Fig.Â 17a). The strengthened interior flow disturbance proceeds southwestward and, 6â€“8 years after, reaches the east of the Philippines, and cools the upper ocean in the western tropical North Pacific (Fig.Â 17b), leading to the negative phase of the PDO.
The excessive accumulated heat in the western tropical North Pacific during approximately 4Â years by the attenuation of the vertical velocity is considered to be advected northward by the Kuroshio (Fig.Â 17a) as inferred from the extension of the positive regression slope (high SST after the positive PDO phase) in the western subtropical Pacific (Fig.Â 1d). Note that the high SST anomaly is attributable not to the positive PDO phase 3â€“4 years before but to the negative PDO phase approximately 10Â years before. The anomalously warm water is transported to the midlatitude region of the North Pacific by the Kuroshio and the Kuroshio Extension, yielding the next negative phase of the PDO. The strengthening (weakening) of the upward transport in Region A in the negative (positive) phase of the PDO is critically related to the reversal of the PDO phase. Note that, in the region east of the Philippines, there are mixed layer depth and barrier layer thickness variations (Sato etÂ al. 2004; Nagano etÂ al. 2018), which may change responses of SST to the surface heat flux and vertical current variations but cannot be accounted in this study. In particular, it is unclear how the barrier layer thickness varies and affects the SST variation. Future comprehensive studies are necessary to better understand the SST variation in the western North Pacific related to the reversal of the PDO phase.
4.2 Effect of vertical eddy diffusion
The upward transport in Region A can be attributed to both the adiabatic and diabatic processes. The adiabatic process contributes to the upward transport through the upward displacement of the main pycnocline (around \(10^{\circ }\)N latitude) associated with the intensification of the northern part of the NEC. On the other hand, the isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\), where Nagano etÂ al. (2016a) found the QD volume transport variation in the subtropical gyre interior region, does not reach the mixed layer base (\(<100\)Â m depth) (de BoyerÂ MontÃ©gut etÂ al. 2004) in Region A, although the upward velocity in this region extends from 250 to 100Â m in all seasons (Figs.Â 8, 9). The mechanism of the water mass transport across the isopycnal surfaces, i.e., the diabatic process, is considered to be of importance in the process that the subsurface watermass volume fluctuations are entrained into the sea surface mixed layer.
In this subsection, we examine whether or not the eddy diffusive mechanism is important, by estimating the order of the magnitude of diapycnal eddy diffusivity from the AGEM potential density and vertical velocity. Assuming that the vertical advection is balanced with the diapycnal diffusion:
where \(K_{\rho }\) is diapycnal eddy diffusivity (e.g., Pedlosky 1987b), we can estimate \(K_{\rho }\). On the basis of the AGEMbased potential density, we set \({\partial }{\rho }/{\partial }z\) and \({\partial }^2{\rho }/{\partial }z^{2}\) to \(1.0 \times 10^{2}\)Â \({\text {kg\,m}}^{4}\) and \(1.0 \times 10^{4}\)Â \({\text {kg\,m}}^{5}\), respectively, and for \(w=\) \(1.0 \times 10^{6}\)Â \({\text {m\,s}}^{1}\), \(K_{\rho }\) is estimated to be \(1.0 \times 10^{4}\)Â \({\text {m}}^{2}\,{\text {s}}^{1}\). Considering that the isopycnals can move adiabatically in the real ocean, this value is considered to be the upper limit of the diffusivity that should be observed.
Whalen etÂ al. (2012) estimated global distribution of diapycnal eddy diffusivity based on Argo hydrographic data obtained in the period from 2006 to 2011, during which La NiÃ±a events frequently occurred. The estimated value of \(K_{\rho }\) in the present study is of the same order of magnitude as globally averaged diffusivity at a depth of 200Â m (Fig.Â S.5a of Whalen etÂ al. 2012) calculated by Whalen etÂ al. (2012). Note that the vertical transports are relatively large (black and green lines in Fig.Â 14a) in Whalen et al.â€™s study period (2011â€“2016). There exists noticeably enhanced diffusivity in a layer from 250 to 500Â m depths over the rough ocean bottom in the western tropical North Pacific (Figs.Â 2a and S.1 of Whalen et al. 2012), which covers Region A. Even though the diapycnal process is not accounted for in the Pvector inverse method, the enhancement of the eddy diffusivity in La NiÃ±a condition by the rough bottom topography is consistent with the La NiÃ±arelated strengthening of the vertical velocity estimated in this study. Future observations of vertical eddy diffusion by microstructure profilers in addition to CTD data in both phases of the ENSO may be useful to clarify the relationship between the vertical velocity in Region A and the bottom topography.
4.3 Vertical currents by the Ekman current divergence near sea surface
Note that the vertical currents near the sea surface cannot be studied by the Pvector method because they are considered to be strongly affected by the Ekman currents. Near the sea surface in the tropical (south of \(13^{\circ }\)N) and subtropical (north of \(13^{\circ }\)N) western North Pacific, the winddriven Ekman currents are divergent and convergent, causing upwelling and downwelling, respectively (e.g., Fig.Â 7 of Tozuka etÂ al. 2002). The upward velocity induced by the Ekman currents is particularly strong in winter and reaches the order of \(10^{6}\)Â \({\text {m\,s}}^{1}\). Although the thickness of the Ekman layer is approximately 20Â m even in the tropical North Pacific (Fig.Â 4 of Ralph and Niiler 1999), which is remarkably less than 100Â m depth, the upward current at 100Â m depth in the western tropical region may be strengthened by the Ekman upwelling.
5 Conclusions
Prior to the negative (positive) phase of the PDO, the SST in the western tropical North Pacific is heated (cooled). The SST variation is suggested to be related to the QDtimescale (8â€“12 years) variation in the volume transport in the subsurface layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) (Nagano etÂ al. 2016a). To reveal where the QD variation in the volume transport in the subsurface layer emerges in the western tropical North Pacific and how great the impact of the variation on the upperocean temperature is, we examined the spatiotemporal characteristics of the 3D field of vertical velocity. By the areawise AGEM method, we estimated 3D potentialÂ temperature and salinity fields in the region of \(10^{\circ }\)Sâ€“\(25^{\circ }\)N, \(120^{\circ }\)Eâ€“\(180^{\circ }\) during the period from January 2001 to May 2017 using altimetric SSH data and CTD profile data collected by Argo floats. The 3D potential density field was computed from the AGEMderived potentialÂ temperature and salinity. The streamfunction in the top 1000Â dbar calculated from the AGEMderived potential density is consistent with previous studies.
Applying the Pvector inverse method to the 3D AGEMderived potential density field, we obtained the timevarying 3D vertical velocity field. Vertical velocity is observed in a layer down to a depth of approximately 350Â m. Associated with the seasonal westward shrinkage of the MD in boreal winter and spring, the westward flowing NEC approaches to the NECC and wavy patterns of the streamfunction and corresponding vertical velocity fluctuations are generated between the currents possibly through the barotropic instability due to the enhanced horizontal shear. Furthermore, the regionalscale upward current was found in the NEC, \(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\), called Region A in this paper. In this region, the southward shoaling of the isopycnal surfaces between 25.0 and 26.5Â \({\sigma }_{\theta }\) produces a mean substantial upward velocity of approximately \(1 {\times } 10^{6}\)Â \({\text {m\,s}}^{1}\) at a depth of 100Â m depth. Possibly in addition to the Ekman upwelling in the western tropical North Pacific, the upward current driven by the southward current impinged on the isopycnal slope advects the deep cold water to the upper ocean.
To examine the spatiotemporal characteristics, the interannual to decadal variations in the vertical velocity were decomposed by the EOFs. The first and second EOF modes represent the ENSOtimescale enhancement (attenuation) of the upward velocity at 100Â m depth in the region of \(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\) (Region A) with peaks approximately 8 and 1Â months after La NiÃ±a (El NiÃ±o) events, explaining 66% and 11% of the total variance, respectively. Furthermore, due to frequent occurrences of La NiÃ±a (El NiÃ±o) events, the upward velocity was observed to vary on the longer timescale, i.e., the QD timescale. The volume and temperature transports of the vertical velocity in the region of \(10^{\circ }\)â€“\(17^{\circ }\)N, \(140^{\circ }\)Eâ€“\(180^{\circ }\) vary on the QD timescale. The maxima of the volume and temperature transports are estimated to be approximately 1.5Â Sv and 150Â TW in the La NiÃ±a year of 2008, respectively. At this time, the upward current reached the maximum exceeding \(1 {\times } 10^{6}\)Â \({\text {m\,s}}^{1}\) in Region A, being forced by the southward current greater than 1Â \({\text {cm\,s}}^{1}\) impinged on the sloping isopycnal surfaces.
The cooling effect of the upper ocean (\(<100\)Â m depth) due to the upward current advection was examined. The attenuation (intensification) of the upward transport in the positive (negative) phase of the PDO keeps the upperocean temperature tendency, i.e., temporal change in the temperature, anomalously high (low) approximately 6â€“8 years after the decrease (increase) in the volume transport in an isopycnal layer of 25.0â€“25.5Â \({\sigma }_{\theta }\) in the subtropical gyre interior region, as reported by Nagano etÂ al. (2016a), and increase (decrease) SST in the western tropical North Pacific, as schematically illustrated, respectively, for the positive and negative PDO phases in Fig.Â 17. The decreases in the vertical volume transport cause the upperocean temperature increase by 0.2Â \(^{\circ }\)C or greater, which is equivalent to the SST change associated with the PDO. The QD variation in the vertical velocity in Region A can be critically related to the reversal of the PDO phase through the heat transport of the Kuroshio. This result, as well as atmospheric teleconnections from the tropical region (Alexander etÂ al. 2002), suggests that there is a significant oceanic link connecting the mid and highlatitude regions to the tropical region.
Availability of data and materials
Qualitycontrolled Argo profile data (Advanced automatic QC Argo Data versionÂ 1.2) were provided in the Japan Argo database (ftp://ftp2.jamstec.go.jp/pub/argo/). Daily altimetric SSH data and monthly NOAA Optimum Interpolation SST V2 data were produced by the EU Copernicus Marine Environment Monitoring Service (CMEMS) (ftp://my.cmemsdu.eu/) and the US NOAA/OAR/ESRL (https://psl.noaa.gov/data/gridded/data.noaa.oisst.v2.html).
Abbreviations
 3D:

Threedimensional
 AGEM:

Altimetrybased gravest empirical mode
 CTD:

Conductivityâ€“temperatureâ€“depth
 ENSO:

El NiÃ±oSouthern Oscillation
 EOF:

Empirical orthogonal function
 MOAA GPV:

Grid point value of the Monthly Objective Analysis using the Argo
 MD:

Mindanao Dome
 NEC:

North Equatorial Current
 NECC:

North Equatorial Countercurrent
 NOAA:

US National Oceanic and Atmospheric Administration
 PDO:

Pacific decadal oscillation
 QD:

Quasidecadal
 RMS:

Root mean square
 SSH:

Sea surface height
 SST:

Sea surface temperature
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Acknowledgements
The 3D hydrographic field estimation by the AGEM method applying to Argo profile data owes a lot to discussion with Prof. Kimio Hanawa and Prof. Shoichi Kizu (Tohoku University). The authors are grateful to the editors, Dr.Â MichioÂ Kawamiya (JAMSTEC) and Prof.Â Eiji Ohtani (Tohoku University), and anonymous reviewers for constructive review comments.
Funding
This work was partly supported by the Japan Society for the Promotion of Science, GrantinAid for Scientific Research (Grant Nos. JP15H04228, JP17K05660, JP20K04072, JP20H02236, JP20H04349, JP20KK0097).
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TH currently belongs to Japan Meteorological Agency. He contributed to this study when he belonged to Tohoku University and Hokkaido University. AN proposed the topic, conceived, designed the study, analyzed the data, and constructed the manuscript. TH analyzed the data and collaborated with the corresponding author (AN) in the construction of manuscript. MW discussed the results in cooperation with AN and TH. All authors read and approved the final manuscript.
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Nagano, A., Hasegawa, T. & Wakita, M. Spatiotemporal vertical velocity variation in the western tropical Pacific and its relation to decadal ocean variability. Prog Earth Planet Sci 9, 57 (2022). https://doi.org/10.1186/s40645022005133
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DOI: https://doi.org/10.1186/s40645022005133
Keywords
 Western tropical Pacific
 ENSO
 PDO
 Vertical velocity
 Pvector inverse method
 AGEM