Variations in the Central Mode Water in the North Pacific as a manifestation of the Pacific Decadal Oscillation

Abstract

The North Pacific Central Mode Water (CMW) is examined from the viewpoint of its volume variations. The volume of the CMW layers thicker than $150 m$ is used as an index of CMW variations, which successfully represents the year-to-year and decadal variations in the CMW volume. The CMW index shows the variation close to that of the Pacific Decadal Oscillation (PDO). The CMW variation is strongly tied with large-scale, dominant variations in sea surface temperature (SST), surface dynamic height (SDH), and sea surface height (SSH) anomalies in the North Pacific, with a significant correlation with the PDO. Year-to-year and decadal variations of CMW volume in May to July are significantly correlated with the wintertime Aleutian Low and 500$hPa$ geopotential height variations, which indicates that the Aleutian Low induces the eastward extension/retreat of the strong winter westerlies and resultant net surface heat flux anomaly over the CMW distribution region. Thus, the CMW volume variation can be regarded as a significant manifestation of the PDO. The SST, SDH, and SSH anomalies are associated with the surface cooling in the northern sector of the CMW distribution region. On the other hand, the SDH and SSH anomalies throughout a year and the SST anomaly in the cold season in the southeastern sector of the CMW region are formed due to the heaving of isopycnal surfaces in the subsurface layer above the CMW in response to its volume variations.

1 Introduction

The North Pacific Central Mode Water (hereafter referred to as CMW) is one of the major mode waters in the North Pacific and was first documented by Nakamura (1996) and Suga et al. (1997). Major body of the CMW occupies subsurface layers above $500 m$ between $25^\circ N$ and $40^\circ N$, $180^\circ$ and $140^\circ W$ in the central North Pacific throughout a year. Small amount of the CMW is also seen in the region between $20^\circ N$ and $25^\circ N$, $160^\circ E$ and $180^\circ$, just north of the subtropical front (e.g., Kobashi et al. 2006). Thick CMW is also found in the region from the International Dateline to around $160^\circ E$ between $35^\circ N$ and $40^\circ N$ in winter and spring. Typical potential density anomaly (potential density minus $1000 {kgm}^{-3}$), potential temperature, and salinity ranges of the CMW have been reported as $25.7{-}26.6 kg m^{ - 3}$, $7{-}15^\circ C$, and $33.6{-}34.6$, respectively (Oka and Qiu 2012). The CMW has been categorized into lighter and denser varieties based on hydrographic observations (e.g., Mecking and Warner 2001; Yasuda 2003; Oka and Suga 2005) and based on numerical model studies (e.g., Tsujino and Yasuda 2004). The formation area of the lighter variety, called L-CMW, is thought to be the region between the Kuroshio Extension Front and the Kuroshio Bifurcation Front, while the formation of the denser variety, called D-CMW, is considered to be formed in the region between the Kuroshio Bifurcation Front and the Subarctic Front (e.g., Nakamura 1996; Suga et al. 1997; Yasuda and Hanawa 1997; Yasuda 2003; Kobashi et al. 2006; Oka et al. 2020). Once the CMW is formed, it is advected and spread to the east until reaching $140^\circ W$ on isopycnal surfaces, then it migrates/expands to the south and southwest to the subtropical region (e.g., Suga et al. 1997, 2008; Oka et al. 2011). Aoki et al. (2002), Kobashi et al. (2006), Xie et al. (2011), Sugimoto et al. (2012) , and Xu et al. (2022) have proven that the advected CMW plays a crucial role in the formation, maintenance, and variations of the subtropical fronts between $180^\circ$ and $160^\circ W$ around $25^\circ N$. Kimizuka et al. (2015) revealed that the CMW affects the vertical structure of the subtropical gyre, suggesting a dynamic effect of the CMW on the large-scale circulations of the subtropical gyre.

As noted by Suga et al. (1997), the major CMW distribution area seems to coincide with the center of action of the dominant sea surface temperature (SST) anomaly pattern described using the empirical orthogonal function (EOF) (e.g., Davis 1976; Weare et al. 1976; Iwasaka et al. 1987). This fact suggests that the CMW variations are related to the decadal variations of the SST anomaly, i.e., the Pacific Decadal Oscillation (PDO; Mantua et al. 1997; Newman et al. 2016). Toyoda et al. (2015) revealed that the dominant mode of the maximum mixed layer depth in the CMW formation region shows the variation similar to the PDO based on the ensemble of 17 ocean reanalysis data. Decadal and abrupt changes in the subsurface conditions and their connection to the CMW have been investigated based on historical hydrographic observation data by Deser et al. (1996), Yasuda and Hanawa (1997), and Schneider et al. (1999) for the periods including the regime shift (Kawasaki 1983) that occurred in 1976/77 (e.g., Nitta and Yamada 1989) and by Suga et al. (2003) for the 1988/89 change, for example. On the other hand, Inui et al. (1999), Xie et al. (2000), Ladd and Thompson (2000), Kubokawa and Xie (2002), Ladd and Thompson (2002), Hosoda et al. (2004), Xie et al. (2011), and Sugimoto et al. (2012) examined decadal variations and/or regime shifts of the mode waters such as the CMW using either ideal or realistic numerical ocean models. They showed that abrupt changes in strength and position of the surface westerlies over the North Pacific during the regime shifts (e.g., Nitta and Yamada 1989; Yasunaka and Hanawa 2002; 2003) were closely related to the long-term change in the CMW.

There were few studies on year-to-year variations of the properties of the CMW before early 2000s except for Suga et al. (2003), which showed year-to-year variations and the 1988/89 change in the temperature and salinity in the core of the CMW in a repeat hydrography section along $180^\circ$. Since mid-2000s, however, observational studies on the CMW have been prospering thanks to the Argo Project (Argo Science Team, 1998; Wong et al. 2020). Oka et al. (2007), Oka et al. (2009), and Oka et al. (2011), for example, described details of the formation, subduction, distribution, and properties of the CMW based on the Argo data. Oka et al. (2009) and Kouketsu et al. (2012) showed importance of the role of meso-scale eddies on the formation of the CMW in the subtropical and subarctic frontal zones based on the float observation data. In situ, ship observations of the CMW were also actively conducted in the last two decades (e.g., Oka et al. 2014). High-resolution, shipboard observations in 2013 and 2016 have revealed the relation between formation region of L- and D-CMW and fronts, and confirmed the importance of the role of eddies in formation of the CMW (Oka et al. 2020). Interannual variations of the formation and distribution of the CMW have also been studied based on the Argo and other observation data. Oka et al. (2007) examined the mixed layer properties and their seasonal changes in the formation regions of the mode waters in the North Pacific using the Argo float observations. Kawakami et al. (2016) revealed that the deep mixed layers in the L-CMW formation region were found in the region of $180^\circ {-}160^\circ W$, $30^\circ {-}40^\circ N$ during the periods of strong westerlies while those were seen in $140^\circ {-}155^\circ E$, $36^\circ {-}40^\circ N$ during the unstable Kuroshio Extension path periods.

The previous studies of the CMW on time scales from a few years to decades have already shown that there are significant year-to-year and decadal variations in the properties and distributions of the CMW and these variations have deep connection to the large-scale SST anomaly variations, i.e., the PDO. There are few studies, however, on the volume variations of the CMW on year-to-year and decadal time scales. Relationships between the CMW variations and the sea surface height (SSH) in the North Pacific have not been examined yet although large-scale SSH variations are significantly related to the dominant SST variations in the North Pacific as pointed out by Casey and Adamec (2002) and Cummins et al. (2005). For better understanding of the relationship between the CMW variations, the SST, surface dynamic height (SDH), and SSH anomalies in the North Pacific, it is beneficial to make direct comparisons of the CMW variations to the SST, SDH, and SSH anomalies to find any relationships between the CMW volume variations and the PDO which have not seen in the previous researches.

Thus, in the present study, we will draw the pictures of year-to-year and decadal variations in the CMW and their relations to the SST and SSH anomalies, and to atmospheric conditions which are favorable for the formation of CMW based on observation data. We also examine how the CMW variations tie with the variations in the subsurface layers which may affect the sea surface conditions. We will examine variations in the whole CMW, rather than separating the variations of L- and D-CMW, because our preliminary study indicated that year-to-year volume variations in L- and D-CMW are similar to each other (see Appendix).

2 Data

We use the Grid Point Values of the Monthly Objective Analysis attained from the Argo data (hereafter referred to as MOAA GPV) to detect and describe the CMW distributions and variations. The MOAA GPV dataset is a global monthly dataset of temperature and salinity based on the Argo floats, the Triangle Trans-Ocean Buoy Network and available conductivity–temperature–depth casts from the sea surface to the 2000$dbar$ level, produced by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) Argo Team (Hosoda, 2007; Hosoda et al. 2008). After careful quality controls, a two-dimensional optimum interpolation was applied to the profile data to obtain monthly mean temperature and salinity for every $1^\circ \times 1^\circ$ latitude–longitude grid box for $25$ pressure levels from 10$dbar$ to 2000$dbar$, as the World Ocean Atlas 2001 (Conkright, et al., 2002). Decorrelation radii are from $10$ to $20$ degrees in longitude and from $5$ to $11$ degrees in latitude. The data domain in the present study is the North Pacific from $15^\circ N$ to $60^\circ N$, between $120^\circ E$ and $80^\circ W$. The analysis period is from January 2004 to December 2021 although the dataset is available since 2001. We have excluded the data before 2004 following previous studies such as Toyama et al. (2015) and Kawai et al. (2021) because the Argo observations were very sparse before 2004 in the North Pacific.

We use satellite altimeter SSH data to analyze the relationship between the CMW and SSH anomalies. The satellite altimeter SSH dataset used here is dataset-duacs-rep-global-merged-twosat-phy-l4, a product of the Data Unification and Altimeter Combination System (DUACS), which is an operational production of sea level products for the Copernicus Marine Environment Monitoring Service (CMEMS). The horizontal resolution is $0.25^\circ \times 0.25^\circ$ latitude–longitude, and the temporal resolution is 1 day. The analysis period and area are the same as those of the MOAA GPV dataset. The monthly mean and $1^\circ \times 1^\circ$ latitude–longitude averages are calculated from the daily data before the analyses to minimize the calculation time while retaining the large-scale features of the SSH anomaly.

The SST dataset used in the present study is the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation (OI) SST V2 (Reynolds et al. 2002), provided by NOAA. The horizontal resolution is $1^\circ \times 1^\circ$ latitude–longitude. The dataset covers the entire Earth, from $89.5^\circ N$ to $89.5^\circ S$ and $0.5^\circ E$ to $359.5^\circ E$. The dataset is produced mainly from meteorological satellites and in situ SST observations. The monthly means from 2004 to 2021, the same period as the MOAA GPV data, are obtained through the NOAA website.

The Japanese 55-year Reanalysis (JRA-55) dataset (Kobayashi et al. 2015; Harada et al. 2016) is used to analyze the relationship between the CMW variations and the overlying atmospheric conditions. JRA-55 is a product of a highly sophisticated data assimilation system operated by the Japan Meteorological Agency (JMA). We use monthly mean sea level pressure (SLP), $500 hPa$ geopotential height (Z500), surface fluxes such as latent and sensible heat fluxes, net longwave and net shortwave radiation fluxes and momentum flux (wind stress). The horizontal resolution is $1.25^\circ \times 1.25^\circ$ latitude–longitude. Monthly mean products are used. The period of use is from 2004 to 2021.

A PDO index (PDOI) provided by JMA is used to examine the relationships between decadal variations seen in the CMW and the PDO phenomenon. According to the website of JMA, the PDOI is “defined as the projections of monthly mean SST anomalies onto their first EOF vectors in the North Pacific (north of $20^\circ N$). The EOF vectors are derived for the period from 1901 to 2000, and climatology is defined as the monthly mean for the same period. Globally averaged monthly mean SST anomalies are subtracted from each monthly mean SST anomaly before calculation of the first EOF vector to eliminate the effects of global warming”. The definition of the PDOI by JMA is the same as those by other institutes, such as the University of Washington and the National Center for Atmospheric Research.

The annual subduction rate (ASR) estimated by Kawai et al. (2021) is used to discuss the formation of the CMW. They applied the Eulerian definition of subduction and estimated the ASR from the MOAA GPV data by tracing the trajectory of water parcels, which are released at the base of the mixed layer (ML), on an isopycnal surface for 1 year. The ASR is evaluated as follows:

$$ASR=\frac{1}{{T}_{a}}{\int }_{{t}_{s}}^{{t}_{e}}{s}_{i}dt, {s}_{i}=\frac{\partial D}{\partial t}+\overrightarrow{{u}_{mb}}\cdot \overrightarrow{{\nabla }_{h}}D+{w}_{mb}=\frac{\partial D}{\partial t}+\overrightarrow{{\nabla }_{h}}\cdot \left(D\overrightarrow{{u}_{m}}\right)$$

(1)

where ${T}_{a}$ is the time of the average, taken as 1 year here. ${s}_{i}$ is the instantaneous subduction rate, $\overrightarrow{{u}_{mb}}$ and ${w}_{mb}$ are horizontal and vertical velocity at the base of the ML. $\overrightarrow{{u}_{m}}$ is mean horizontal geostrophic velocity within the ML. ${t}_{s}$ and ${t}_{e}$ are times when effective detrainment starts and ends. The “effective detrainment” means that a water parcel that is detrained is never entrained again within ${T}_{a}$. We determine whether each detrained water parcel is effective or ineffective by tracing a trajectory on an isopycnal surface of a parcel released at the base of the ML downstream at every time step ($1 day$). If the detrained water is below the ML and not in any land grid throughout 1 year, it is regarded as effective detrainment, that is, subduction. Details of the estimation methods are given in Kawai et al. (2021). We will use the ASR evaluated for the period from 2004 to 2020, not 2021 because the estimation of the ASR in 2021 requires the MOAA GPV data for 2022, which has not been available yet as of summer 2023.

3 Methods

The CMW in the present study is defined as a layer with the three following characteristics: the potential density anomaly, ${\sigma }_{\theta }$, of which reference pressure is the sea surface pressure, must fall in the range between $25.7 kg{m}^{-3}$ and $26.4 kg{m}^{-3}$; the potential vorticity, $PV,$ is less than $2\times {10}^{-10}{ m}^{-1}{s}^{-1}$; and the potential temperature, $\theta$ is in the range between $7.0^\circ{\rm C}$ and $15.0^\circ{\rm C}$.

That is,

$$25.7kg{m}^{-3}\le {\sigma }_{\theta }\le 26.4kg{m}^{-3}$$

(2)

$$PV\equiv -\frac{f}{{\rho }_{\theta }}\left(\frac{\partial {\rho }_{\theta }}{\partial z}\right)=fg\left(\frac{\partial {\rho }_{\theta }}{\partial p}\right)\le 2\times {10}^{-10}{m}^{-1}{s}^{-1}$$

(3)

and

$$7.0^\circ{\rm C} \le \theta \le 15.0^\circ{\rm C}$$

(4)

where ${\rho }_{\theta }$ is the potential density, $f$ is the Coriolis parameter, and $g$ indicates the gravitational acceleration. The lighter limit of the ${\sigma }_{\theta }$ range, $25.7 kg{m}^{-3}$, almost corresponds to that of L-CMW (Oka et al. 2011; Oka and Qiu 2012). The denser limit, $26.4 kg{m}^{-3}$, corresponds to the denser limit of the density range of the D-CMW (e.g., Mechking and Warner, 2001; Oka and Suga 2005; Oka et al. 2011); however, other studies, such as Yasuda (2003), Suga et al. (2004), Tsujino and Yasuda (2004), and Suga et al. (2008), adopted slightly larger values than $26.4 kg{m}^{-3}$. Since the ${\sigma }_{\theta }$ range of the transition region mode water (TRMW) is $26.3{-}26.6 kgm^{ - 3}$ (Saito et al. 2011), we adopt the limit of $26.4 kg{m}^{-3}$ to minimize the risk of confusion in identifying the CMW layer with the TRMW. The lower temperature limit of D-CMW and the higher temperature limit of L-CMW in Oka et al. (2011) are adopted as the lowest and highest limits of the temperature range of the CMW in the present study. The criterion of the potential vorticity is the same as that in Nakamura (1996) but slightly larger than the upper limit for the CMW core shown in Suga et al. (2004), which is 1.5–1.75$\times {10}^{-10}{ m}^{-1}{s}^{-1}$. Since we aim to capture the CMW layer from density profiles computed from the MOAA GPV dataset, of which decorrelation radii are so large that they might obscure the CMW characteristics, we adopt a slightly soft criterion of the potential vorticity here.

We first calculated the potential density at each depth using the temperature and salinity profiles of the MOAA GPV dataset. The calculations were performed using the Gibbs Seawater Oceanographic Toolbox (McDougall and Barker 2011), which is based on the international thermodynamic equation of seawater-2010 (TEOS-10) (IOC, SCOR and IAPSO, 2010). Then we applied the Akima method (Akima 1970) to interpolate potential density into every 1$dbar$ depth for each grid, from 10$dbar$ to 900$dbar$. The vertical gradient of the potential density was then calculated from the interpolated potential density profile with a central difference method. A simple nine-point running mean was applied to smooth out the vertical gradient profiles. The Coriolis parameter at the center of each grid box was multiplied by the smoothed vertical gradient profile to calculate the potential vorticity for every 1$dbar$ level at each grid box.

If the potential density anomaly of the layer falls in the density range (2), the potential vorticity satisfies the criterion (3), and the potential temperature is in the range (4), then the layer is identified as a CMW layer. Note that the definition of the CMW allows the CMW layer to outcrop in winter and early spring. When more than one CMW layers are detected for a density profile, the first and second shallowest layers are adopted as the CMW layers, but the third and deeper layers are ignored because most of the third and deeper layers, if they exist, occupy a tiny fraction of the volume with the potential density range (2) and potential temperature range (4). The CMW thickness is defined as sum of the two CMW layers when multiple layers are detected at the same time at the same horizontal location. Mean properties, such as the potential density of the CMW for the two layers, are treated as the mean properties of the multiple CMW layers.

To describe year-to-year variations in the CMW, we adopt variations of the volume of the CMW following Oka et al. (2015) and Oka et al. (2021) because one can make quantitative comparison between the CMW volume variations and annual subduction rate. The CMW volume will be evaluated for the thick CMW distribution region, rather than adding up the volume from all regions, because the index will be able to express the CMW volume properly regardless of the horizontal extent and migration of the thick CMW. In the volume evaluation, the area of each grid is multiplied by the CMW thickness in the grid box to evaluate the CMW volume for the grid. The volume is summed up in the thick CMW distribution region, which will be defined in Sect. 4. We have recognized that there are other indices such as potential temperature, potential density, and potential vorticity at the core of the mode water used in the previous studies (e.g., Taneda et al. 2000; Suga et al. 2003; Oka and Suga 2005; Xu et al. 2022), but if one adopts the property of the CMW core as an index, multiple CMW layers, which are often detected, are hard to define the core.

To concentrate our attention on year-to-year and decadal variability, we exclude long-term trends from the time series to be analyzed because, as Trenberth and Fasullo (2013) mentioned, variations in such time scales in the CMW properties can be distorted by long-term, global warming trends. One of the important climate indices we use, PDOI, is calculated based on the sea surface temperature anomaly for which the global mean anomaly has been removed, as mentioned in Sect. 2. Although Trenberth and Fasullo (2013) recommended to subtract global mean values to remove such global warming trends, we will remove the linear trend of the entire analysis period for simplicity.

ML is determined as the layer in which the potential density at the bottom is $0.125 kg{m}^{-3}$ $\text{larger}$ than that at the 10$dbar$ surface, same as that in Kawai et al. (2021) because the surface values are not available in the MOAA GPV. ML depth (MLD), potential temperature, and salinity are evaluated based on the potential density profile and corresponding potential temperature and salinity profiles interpolated every $1 dbar$ for each grid using the Akima method similar to the potential vorticity estimation.

The total annual subduction volume (referred to as ASV) concerning the CMW is computed for every winter, which is evaluated by multiplying the area of each grid box and the ASR in the gird box and summed up over the probable CMW formation region (referred to as PCF region) in the North Pacific from $30^\circ N$ to $55^\circ N$ between $140^\circ E$ and $140^\circ W$. ASV is also estimated for the zones of $35^\circ {-}40^\circ N$, and $40^\circ {-}45^\circ N$ for the western basin ($140^\circ E{-}180^\circ$), the eastern basin ($180^\circ {-}140^\circ W$), and most of the basin ($30^\circ N{-}55^\circ N$, $140^\circ E{-}140^\circ W$), respectively. The PCF region is defined as the area where the density and temperature of the maximum ML fall in the ranges (2) and (4) mentioned above. The mixed layer volume (MLV) was also evaluated for the month of the maximum MLD in the PCF region every winter (January to March).

4 Climatological mean state and year-to-year variations of CMW

The horizontal distributions of the 2004–2021 mean annual average thickness of the CMW (Fig. 1a) show that the thickest CMW, thicker than $250 m$, is found in $32^\circ N{-}35^\circ N$, $165^\circ W{-}170^\circ W$, and the CMW layers thicker than $150 m$ can be seen in the region of $180^\circ {-}150^\circ W$, $25^\circ N{-}40^\circ N$. Depth and the CMW thickness estimated in pressure are converted into length, i.e., 1$dbar$ is regarded as 1 $m$ for simplicity. The southern bound of the thick CMW region is just to the north of the northern subtropical front between $180^\circ$ and $160^\circ W$ around $26^\circ N$, and the southern bound of the CMW in $140^\circ E{-}180^\circ$ coincides well with the southern subtropical front identified by Kobashi et al. (2006). Frequency of detection of the thick CMW is defined as the ratio of the number of months when the CMW thicker than $50 m$ is detected to all months of the analysis period, i.e., 216 months. Frequencies higher than $90\%$ are found mostly in the region where the climatological annual mean thickness is greater than $150 m$ (Fig. 1a). The annual mean meridional-vertical distribution of the CMW averaged over $180^\circ {-}160^\circ W$ is shown in Fig. 1b. The CMW is most frequently detected on the isopycnal surfaces around $\sigma_{\theta } = 26.1{-}26.3 kgm^{ - 3}$ between $27^\circ N$ and $36^\circ N$. The depth range of the CMW detection frequency of more than 50% is from $100 m$ to $470 m$. The horizontal and meridional-vertical distributions of the annual mean CMW described here are well consistent with those shown in the previous studies (e.g., Nakamura 1996; Suga et al. 1997; Oka et al. 2011). Seasonal mean distributions of the thickness of the CMW are shown in Fig. 2 for the seasons from January to March (JFM), April to June (AMJ), July to September (JAS), and October to December (OND), respectively. The thick CMW occupies the area of $180^\circ {-}150^\circ W$, $27^\circ N{-}40^\circ N$ throughout a year. The horizontal extent of the thick CMW of thicker than $150m$ shrinks as the season progresses. The thick CMW in $150^\circ E{-}170^\circ W, 35^\circ N{-}40^\circ N$ in JFM retreats to the east in AMJ and eventually disappears in OND. The 2004–2021 mean annual average CMW volume in the North Pacific, estimated for the region of $140^\circ E{-}140^\circ W$, $25^\circ N{-}50^\circ N$, is $1.26\times {10}^{15} {m}^{3}$. Approximately 92% of the total volume is found in the $25^\circ N{-}40^\circ N$ zone. Seasonal variation in the CMW volume (Fig. 3) dominates in the zone of $35^\circ N{-}40^\circ N$, and is smaller in the zones of $30^\circ N{-}35^\circ N$ and $40^\circ N{-}45^\circ N$.

Fig. 1

Long-term annual mean distribution of CMW. a Horizontal distribution of the 2004–2021 mean annual average thickness of the CMW. Colors indicate the thickness. Thick and thin red contours show the annual frequency of detection of the CMW layers thicker than 50 m for 0.5 and 0.9, respectively. Background black contours are the geostrophic streamlines on the annual mean potential density surface of σ_θ = 26.2 kgm⁻³. White circles indicate positions of the northern subtropical fronts, and green asterisks show those of the southern subtropical fronts (Kobashi et al. 2006). b The annual mean frequency of detection of CMW in the meridional section of 180° – 160°W. Colors indicate the frequency at each pressure level in the meridional section. Background contours show the annual mean potential density in the section. Thick solid contours are for σ_θ = 25.7 kgm⁻³ and 26.4 kgm⁻³ and thick solid and dotted line is for σ_θ = 26.2 kgm⁻³, while thin solid contours are drawn every 0.2 kgm⁻³ (color figure online)

Fig. 2

Long-term seasonal mean distribution of thick CMW layers. Seasonal distributions of the CMW thickness of 150 m are drawn by solid lines. Red, black, blue, and green lines show the mean thickness of 150 m for the season of JFM, AMJ, JAS, and OND, respectively. The climatological maximum ML densities of σ_θ = 25.7 kgm⁻³, 26.2 kgm⁻³ and 26.4 kgm⁻³ are drowned with thin black contour lines. Shadings show the climatological maximum MLD in March, which are deeper than 150 m. The contour lines of the MLD are drawn every 25 m (color figure online)

Fig. 3

Seasonal variations of the CMW volume in each 5° zonal belt. Black lines show climatological seasonal variations in the CMW volume between 140°E and 140°W in each 5° latitude zone from 25°N – 30°N to 45°N – 50°N. The red line indicates the CMW150 volume. See the text in Sect. 4 for the definition of the CMW150 volume (color figure online)

The 2004–2020 mean annual subduction of the CMW is evaluated. Distributions of the mean ASR are shown in Fig. 4, together with the climatological maximum MLD. The mean ASR distribution is almost same as Fig. 3b of Kawai et al. (2021). Deep mixed layer areas are found in large ASR areas west of $160^\circ E$; however, to the east, they do not coincide with each other very well. Large ASR area to the north of the contour line of ${\sigma }_{\theta }=25.7 {kgm}^{-3}$ between $180^\circ$ and $165^\circ W$ can be treated as the major PCF region, where two ASR maxima are found. The ASR maxima in the areas where the surface density is not in the range of the CMW density (2) do not contribute to the formation of CMW. It is not surprising that the local maxima of MLD do not completely agree with those of ASR because, if water parcels move to a higher density region, or density surfaces become shallower (slants upward) downstream; for example, water parcels tend not to subduct much even if ML is deep because much of them is re-entrained into ML in downstream regions. Not only MLD but also the direction of isopycnal advection and the gradient of density surface, and vertical velocity are important for ASR. The ASV and MLV in the PCF region are summarized in Tables 1 and 2. The long-term mean ASV and MLV in the entire North Pacific are $1.99\times {10}^{14}{ m}^{3}{yr}^{-1}$ and $6.19\times {10}^{14} {m}^{3}$, respectively. The ASV estimated in the zones of $35^\circ N{-}40^\circ N$ and $40^\circ N{-}45^\circ N$ are comparable and accounts for more than $85\%$ of the total ASV in the North Pacific, while the MLV in the zone of $35^\circ N{-}40^\circ N$ is more than twice as much as that in the zone of $40^\circ N{-}45^\circ N$. On the other hand, contribution of the ASV in the western basin, to the west of the major CMW distribution region, is about one-tenth of the total ASV, as expected from the distribution of ASR (Fig. 4), although the MLV in the western region and that in the eastern region are comparable. The estimation of ASV suggests that most of the CMW subducts in the region east of $180^\circ$, between $35^\circ N$ and $45^\circ N$. This is consistent with Kawakami et al. (2016), in which they have shown the L-CMW formation region is in the region of $180^\circ {-}160^\circ W$. As discussed/speculated in Oka et al. (2011), Ladd and Thompson (2000) and Mecking and Warner (2001), subduction in the region might be preconditioned by the processes in the zone west of $180^\circ$.

Fig. 4

Distribution of the annual subduction rate. The 2004–2020 mean distributions of ASR and maximum MLD are shown. Colors indicate ASR (myr^-1). Climatological maximum MLDs are indicated by white contour lines every 25 m from 150 to 250 m. Red lines are the maximum ML density in winter. Solid lines are for σ_θ = 25.7 kgm⁻³ and 26.4 kgm⁻³, and dotted and dashed lines are for σ_θ = 26.2 kgm⁻³. The climatological minimum ML temperature of 7.0 ℃ is indicated by a yellow line (color figure online)

Table 1 Mean and standard deviation of annual subduction volume (ASV) in each probable CMW formation region. Figures in parentheses in each cell of the table indicate the standard deviation

Table 2 Mean and standard deviation of maximum mixed layer volume (MLV) in each probable CMW formation region. Figures in parentheses in each cell of the table indicate the standard deviation

To describe year-to-year variations of the CMW, we adopted the CMW volume in the thick CMW distribution region as an index of the CMW variations, as mentioned in Sect. 3. The thick CMW region is defined as the region where the thickness of the CMW layers defined in Sect. 3 is thicker than 150 m (hereafter the layer is referred to as CMW150) because the frequency of detection of the CMW is more than $90\%$ in the region where the climatological annual mean thickness of the CMW is thicker than $150 m$ (Fig. 1a). The volume of the thick CMW is evaluated for the CMW150. The 2004–2021 mean seasonal variation in the CMW150 volume is shown in Fig. 3. The 18-year mean annual average volume of CMW150 is $7.84\times {10}^{14} {m}^{3}$, approximately $68\%$ of the CMW volume in the region of $140^\circ E{-}140^\circ W$, $25^\circ N{-}40^\circ N$. Figure 5a shows the CMW150 volume variation during the analysis period. The figure clearly shows seasonal variations together with year-to-year and decadal variations in the CMW150 volume. The 2004–2021 mean annual cycle of the CMW150 volume (Fig. 3) was removed from the time series of the CMW150 volume to obtain the CMW150 volume anomaly (Fig. 5b). The root mean square of the time series for the anomaly is $1.92\times {10}^{14} {m}^{3}$. The CMW150 volume anomaly also shows large decadal variations; the volume anomaly is large in 2004–2005 and 2014–2017, while they are small in 2009, 2011–2013, and 2019–2021. The volume anomaly variations are well consistent with those in the sum of the annual subduction and obduction rates for the CMW density range (Fig. 12c of Toyama et al. 2015) and those in the observation frequency of the deep MLs with the L-CMW property to the east of $180^\circ$ (Fig. 4 of Kawakami et al. 2016). A trend toward decrease of $-1.24\times {10}^{13} {m}^{3}{yr}^{-1}$ is also seen in the CMW150 volume anomaly variation. We subtracted the trend from the CMW150 volume anomaly time series to produce the CMW index (CMWI) as mentioned in Sect. 3 (Fig. 5b). The index will be used in the following sections.

Fig. 5

Monthly mean volume variations in CMW150. a Time series of the monthly mean volume of CMW150. b The CMW150 volume anomaly (black) and the detrended the CMW150 volume anomaly, i.e., the CMW index (CMWI) (red) (color figure online)

5 Relationships between the CMW volume variations and oceanic and atmospheric conditions

To see how the CMW volume variations are related to the variations in the sea surface conditions, we are examining the relationship between CMWI and the SST anomaly. The SST anomalies are compared with CMWI for each quarter of a year. Figure 6a and b shows the distributions of simultaneous correlation coefficients between the SST anomaly and CMWI for JFM and AMJ. Statistically significant coefficient at the 10% significance level is 0.47 based on an estimation of the effective sample size of the seasonal mean CMWI. Significantly large negative coefficients are found in the middle latitude central basin, and significantly large positive coefficients appear in the eastern basin. The results indicate that when a large volume of CMW is formed during cold seasons, the SST anomaly is negative in the area of $180^\circ {-}150^\circ W$, $25^\circ N{-}45^\circ N$. These results suggest that year-to-year variations in CMWI in JFM and AMJ are strongly tied with those in the SST anomaly, while the relationship between CMWI and the SST anomaly in the other seasons becomes obscure.

Fig. 6

Distribution of the correlation coefficients between CMWI and the SST anomaly. a The correlation coefficients for JFM. Thick lines indicate 0, and black dotted contour lines indicate negative correlation coefficients. Thick yellow lines are the 150 m contour lines of the annual mean CMW thickness. Statistically significant coefficients at the 10% significance level are indicated by colors. b Same as a, except for AMJ (color figure online)

We then compare CMWI with the leading EOF of the SST anomaly computed using all-month, normalized time series in the North Pacific (Fig. 7). The leading mode accounts for $22\%$ of the normalized SST anomaly variations. The leading EOF pattern is quite similar to the correlation patterns shown in Fig. 6a and b. As shown in Fig. 7b, the overall features of decadal variations in CMWI and the time coefficient of the EOF1 are almost the same, although there are small differences in 2009–2011 and 2017–2020. The correlation coefficient between the leading EOF of the SST and CMWI is $0.64$. The PDOI is also drawn in Fig. 7b and shows a variation similar to that of the EOF1. The correlation between the EOF1 and the PDOI is 0.90, which is not surprising because the time coefficient is virtually the same as the PDOI as its definition, while that between the PDOI and CMWI is 0.66. The EOF1 time series and the PDOI lead CMWI by approximately 5 months (Fig. 8). The lag relationship will be discussed in Sect. 6.

Fig. 7

The leading EOF of the SST anomaly in the North Pacific. a Spatial pattern of the leading EOF of the SST anomaly (color). b The normalized time coefficient of the leading EOF of the SST anomaly (red), the normalized PDOI (blue), and normalized CMWI (black) (color figure online)

Fig. 8

Lag correlation coefficients between PDOI and CMWI. Lag correlation coefficients between PDOI and CMWI are plotted as a function of lag (months). A black line with asterisks shows the lag correlations evaluated based on monthly mean values. A positive lag implies that PDOI leads CMWI (color figure online)

The surface dynamic height anomaly (actually that at the 10$dbar$ surface) relative to $2000dbar$ (here after referred to as SDH) was calculated at each grid box. The SDH was calculated from MOAA GPV dataset. Because the CMW volume variations can change the subsurface density, they are expected to affect the SDH. Distribution of the correlation coefficients between the SDH and CMWI is examined for each season (Fig. 9). Negative correlation coefficients appear in the region of $180^\circ {-}145^\circ W$, $25^\circ N{-}50^\circ N$ with positive coefficients to the northeast and to the southeast of the negative correlation region. In contrast to the correlation patterns for the SST anomaly and CMWI (Fig. 6), the significant correlation distribution is persistent throughout a year. A negative maximum regression coefficient on the normalized CMWI, $-2.0 cm$, is found in the area where a negative correlation stronger than $-0.6$ is found, and a positive maximum regression coefficient of $2.3 cm$ is found in the positively correlated area where the correlation coefficients are larger than $0.6$ (figures not shown). Almost the same correlation and regression patterns are found for the SSH anomaly variations. The magnitudes of the regression coefficients for SSH are comparable to those of SDH (figure not shown). Since these correlation patterns dominate the entire North Pacific, one can reasonably expect that the leading EOF pattern of the SDH and that of the SSH anomalies in the North Pacific show similar spatial patterns to the correlation patterns.

Fig. 9

Distribution of the correlation coefficients between CMWI and SDH in each season. Distribution of correlation coefficients between CMWI and SDH is drawn for JFM (a), AMJ (b), JAS (c), and OND (d)

The first EOF of the SDH anomaly in the North Pacific is shown in Fig. 10. Almost identical spatial patterns and time coefficients are obtained for the SSH anomaly (Fig. 11). The leading mode accounts for more than $20\%$ for the normalized SDH anomaly and $22\%$ for the normalized SSH anomaly. The spatial structure of the EOF1s of the SDH and the SSH anomalies well resemble those of the correlation patterns (Fig. 9). The time coefficients of the SDH and SSH are almost identical; the correlation coefficient between them is $0.96$. The correlation coefficient between the SST EOF1 and the SDH EOF1 is $0.87$ and that between the SST EOF1 and the SSH EOF1 is $0.81$.

Fig. 10

Same as Fig. 7 but except for SDH. Spatial pattern (a) and time coefficient (b) of the leading EOF of SDH anomaly (red). PDOI (blue) and CMWI (black) are also drawn in (b) (color figure online)

Fig. 11

Same as Fig. 10, except for SSH anomaly. The time coefficient of the EOF1 of the SSH anomaly is indicated by red (color figure online)

A comparison of the spatial patterns of the EOF1 for the SDH anomaly and that for the SSH anomaly with that for the SST anomaly indicates a resemblance, but the negative region in the middle latitude central basin of the SDH and the SSH anomalies expands to the north to reach the Aleutian Islands, while in the EOF1 of the SST anomaly, the positive region in the eastern basin advances just south of the Aleutian Islands in the northern basin, and the negative region in the central basin is confined to the south of $45^\circ N$. The spatial patterns of the SDH and the SSH anomalies can be considered a straightforward reflection of the subsurface conditions. On the other hand, the spatial pattern of the EOF1 of the SST anomaly seems to suffer from a weak correlation between the SST anomaly and CMWI in JAS and OND which must be affected by SST anomalies in the shallow surface mixed layers developed in summer and early autumn.

These results shown above confirm that the CMW volume variations have strong connection with the SST anomaly variations concerning the PDO (Figs. 6 and 7). The dominant SDH and SSH anomaly patterns are also closely related to the CMW volume variations (Figs. 10 and 11), which is expected by the previous studies such as Casey and Adamec (2002) and Cummins et al. (2005). All the results indicate that the PDO phenomenon consists of the dominant SST, SDH, and SSH anomaly patterns in the North Pacific, described by each EOF1, and that the CMW volume variation is also one important constituent of the PDO.

We next examine the large-scale atmospheric circulation anomalies and surface forcings that are related to the CMW volume variations. Year-to-year variations in the net surface heat flux (${Q}_{net}$), the vertical component of rotation of the surface wind stress ($curl\overrightarrow{\tau }$), SLP and $Z500$ averaged over winter, from January through March, are compared with mean CMW volume in the following early summer, i.e., May to July (hereafter referred as CMWImjj). We choose CMWImjj to explore the relationship between the surface forcings in winter and the variations in the resultant CMW that are completely isolated from the surface mixed layer. We also examine the relationships between surface and middle level atmospheric conditions in winter to understand the relationships between dominant atmospheric anomalous conditions and the CMW volume variations.

Relationships between the winter ${Q}_{net}$ anomaly and CMWImjj are examined (Fig. 12a). Here, ${Q}_{net}$ is sum of the sensible, latent, net shortwave and net longwave radiation fluxes at the sea surface, and positive ${Q}_{net}$ implies heat release from the ocean to the atmosphere. There are high positive correlation coefficients more than $0.7$ in the center of the CMW region around $31^\circ N{-}38^\circ N, 180^\circ {-}165^\circ W$, while the regression coefficients of ${Q}_{net}$ on the normalized CMWI, which are more than $20{ Wm}^{-2}$, are found in the northern half of the thick CMW region around $33^\circ N{-}40^\circ N, 180^\circ {-}160^\circ W$, which is southeast of the climatological mean deepest mixed layer regions (Fig. 2). The relationship with turbulent heat flux is almost the same as that with ${Q}_{net}$ (figures not shown). The correlation pattern suggests that during the positive CMWI periods, the large positive ${Q}_{net}$ anomaly in the CMW region contributes to the development and southward expansion of the CMW formation region, while in the negative CMWI periods, the formation region retreats to the north due to the negative ${Q}_{net}$ anomaly. This inference can be supported by examining the location of the outcrop lines of the CMW in March for positive and negative extreme CMWI years. The outcrop line is defined as the isopycnal line of ${\sigma }_{\theta }=25.7{ kgm}^{-3}$ in ML in March of each year. The positive or negative extreme CMWI years are defined as the years when CMWImjj exceeds the long-term mean by more than 0.8 standard deviation (Fig. 13a). The outcrop lines during the negative CMWI extreme years locate north of $34^\circ N$, while those during the positive extreme years, migrate to the south and southeast by a few hundreds of kilometers to the east of $175^\circ W$ as shown in Fig. 13b. This is consistent with Toyoda et al. (2015) and Kawakami et al. (2016).

Fig. 12

Distribution of correlation and regression coefficients for winter Qnet and curlτ⃗ with CMWImjj. a The correlation and regression coefficients between CMWImjj and winter Qnet anomaly. Colors indicate statistically significant correlation coefficients. Black solid and dotted lines show positive and negative correlations, respectively. Thick solid, black lines indicate zero-coefficients. White solid contour lines indicate positive regression coefficients on the normalized CMWImjj for 20.0 Wm⁻²and 25.0 Wm⁻². Arrows are the regression vectors of wind stress anomaly on the normalized CMWmjj. b Same as a, except for winter curlτ⃗ anomaly. White contour lines for the regression coefficients are drawn every 0.5 × 10⁻⁷ Nm⁻³ from 1.0 × 10⁻⁷ Nm⁻³ to 2.5 × 10⁻⁷ Nm.⁻³ (color figure online)

Fig. 13

Time series of CMWImjj and distribution of isopycnal lines of σ_θ = 25.7 kgm⁻³ in ML in March for positive and negative CMWI extreme years. a Time series of CMWImjj. The years when CMWImjj is positive and more than 0.8 times of the standard deviation are indicated by red dots, and those when the index is negative and exceeds − 0.8 times of the standard deviation are shown by blue dots. b Isopycnal lines of σ_θ = 25.7 kgm⁻³ in ML in March for positive and negative CMWI extreme years shown in a. The isopycnal lines for the positive years are indicated by red solid lines and those for the negative years are shown by blue dotted lines. The green lines are for other years. Background shadings indicate distribution of the standard deviation of MLD in March (color figure online)

Correlation coefficients between the winter $curl\overrightarrow{\tau }$ anomaly and CMWImjj are shown in Fig. 12b. Correlation coefficients higher than $0.6$ and high positive regression coefficients larger than $2.5\times {10}^{-7} {Nm}^{-3}$ are seen in the region to the northeast of the major CMW distribution area. The high positive correlation area coincides well with the strong negative correlation region between CMWI and the SDH anomaly shown in Fig. 9.

Correlation and regression analyses are performed between the winter SLP and CMWImjj and those for Z500 (Fig. 14a and b). For SLP, the strong negative regression region centered at $42.5^\circ N$, $155^\circ W$ is almost the same as the region of positive regression coefficients for the winter $curl\overrightarrow{\tau }$ anomaly (Fig. 12b), while the center of the strong negative correlation region is located at the eastern end of the CMW region, $31.3^\circ N$, $152.5^\circ W$. The regression pattern of the SLP anomaly is virtually identical to the SLP regression pattern on the PDOI shown in the previous studies as expected (i.e., Mantua et al. 1997; Newman et al. 2016) because CMWI and the PDOI show almost the same variations on the decadal time scale (Fig. 7b). Negative correlation and regression coefficients for Z500 (Fig. 14b) and other pressure surfaces in the troposphere (figures not shown) appear in the almost same region for SLP. The pattern resembles the Pacific/North American teleconnection pattern (Wallace and Gutzler 1981), as indicated by Mantua et al. (1997), but the locations of each center of action are slightly different from those of the PNA pattern. The strong negative correlation region, more than $-0.81$, is located around $35^\circ N, 160^\circ W$, and a large negative regression coefficient of more than $-60 m$ appears around $40^\circ N$, $160^\circ W$. The negative regression center is slightly southwest of the center of action at $45^\circ N, 165^\circ W$ of the PNA pattern, as defined by Wallace and Gutzler (1981). The Z500 regression pattern is almost identical to that in Mantua et al. (1997), as expected, too. These results also strongly support the notion that the CMW volume variation is an important manifestation of the PDO.

Fig. 14

Distribution of correlation coefficients between CMWImjj and SLP, and those with Z500. a The correlation and regression coefficients for SLP anomaly. Colors show the significant correlation coefficients. White solid lines and white dotted lines indicate the positive and negative regression coefficients, respectively, drawn every 1 ℎPa. b Same as a except for the Z500 anomaly. Contour lines of the regression coefficients are drawn every 10 m (color figure online)

It is also interesting to see how the CMW volume variations are related to the subsurface and deeper layers of the North Pacific Ocean because the SST, SDH, and SSH must reflect the subsurface conditions as well as the influences of the atmospheric forcings. Figure 15 shows distribution of the correlation coefficients between CMWI and potential density anomalies in the $175^\circ W{-}155^\circ W$ meridional section. Those between CMWI and the dynamic height anomalies relative to $2000dbar$ are also drawn. The correlation coefficients were calculated for the zonal mean values averaged over $175^\circ W{-}155^\circ W$ on each pressure level. Significant positive coefficients, more than 0.7, for the potential density are found in the layer between $75 m$ and $150 m$, in the zone of $28^\circ N{-}37^\circ N$, just above and around the climatological mean isopycnal surface of ${\sigma }_{\theta }=25.7{ kgm}^{-3}$. Significant negative coefficients for the dynamic height anomaly are seen in the layer from the surface to $100 m$ in the same zone, above the high correlation layer for the potential density. These facts suggest that, when the CMW volume is larger (smaller) than normal, isopycnal surfaces in the area of $175^\circ W{-}155^\circ W$, $28^\circ N{-}37^\circ N$, are lifted (lowered) above the CMW layer; in other words, the surface and subsurface layers become denser (lighter), resulting in lower (higher) dynamic height anomaly in the layers. This can be confirmed by examining correlation between the isopycnal depth anomalies and the CMW thickness anomaly in the area (Fig. 16). The depth (positive downward) of each isopycnal surface above the CMW layer in the area is negatively correlated, the coefficients lower than $-0.9$, to the CMW thickness anomaly and the rate of shoaling of the isopycnal surface is up to $1 m$ per $1 m$ of increase in the CMW thickness in the layer between $100 m$ and $150 m$ (figures not shown). These situations are also clearly seen in the composites of the potential density in the meridional section for the positive and negative extreme CMWI years (Fig. 17). When CMWImjj is positive, isopycnal surfaces in the layer from $50 m$ to $200 m$ between $25^\circ N$ and $45^\circ N$ shoal by a few tens of meters while they are lowered during negative CMWImjj years. Thus, one can expect that the CMW thickness causes the SDH and SSH anomalies through shoaling/lowering of the isopycnal surfaces in the seasonal pycnocline below the surface mixed layer. This mechanism is other than the “re-emergence” of the CMW but is the same as that have been revealed by Kobashi et al. (2021) and Kobashi et al. (2023) for the North Pacific Subtropical Mode Water. This mechanism also works in the SST anomaly variations in the region in JFM and AMJ, while during warm seasons, i.e., JAS and OND, the SST anomalies do not show significant correlation in the region as mentioned above.

Fig. 15

Distribution of correlation coefficients between CMWI and zonal mean dynamic height anomaly and that of the potential density in the meridional section of 175°W – 155°W. Colors indicate distribution of statistically significant correlation coefficients between CMWI and zonal mean dynamic height anomalies averaged over 175°W – 155°W at each pressure level relative to 2000dbar and those for the potential density anomaly are drawn with white solid and dotted lines, except for zero-correlation contours which is indicated by thick white lines. Red contours indicate the climatological mean σ_θ = 25.7 kgm⁻³ and σ_θ= 26.4 kgm⁻³ lines (color figure online)

Fig. 16

Correlation coefficients of the isopycnal surface depth with the CMW thickness in the area of 175°W – 155°W, 27°N – 35°N. Black contour lines indicate the climatological mean depth in meter of the potential density surface. Red lines indicate the denser and lighter limits of the CMW. Statistically significant coefficients are drawn with colors. Contour lines are drawn every 0.1 for the correlation coefficients (color figure online)

Fig.17

Composites of the zonal mean potential density averaged between 175°W and 155°W for positive and negative extreme periods of the CMWImjj. The red contours are the MJJ mean potential density for positive extreme periods, and the blue lines are those for negative extreme periods. The black contours show the climatological MJJ mean potential density in the meridional band. The gray shadings are the long-term annual mean frequencies of CMW detection of 0.1, 0.5, and 0.9 (color figure online)

Another striking feature of the distribution of correlation coefficients in Fig. 15 is the significantly negative correlations for the dynamic height anomaly in the region between $38^\circ N$ and $52^\circ N$ from the surface to $600 m$ and the significant positive correlations for the potential density anomaly in the same region below $150 m$. These features are actually seen to $1750 m$ (figures not shown). The vertically homogeneous correlation column is confined between $175^\circ W$ and $150^\circ W$ in the zonal section of $38^\circ N{-}52^\circ N$ (figures not shown). The high correlation column is reflection of the response of the ocean to the atmospheric surface forcing such as the rotation of wind stress seen in Fig. 12b, i.e., the $curl\overrightarrow{\tau }$ anomaly causes the Ekman suction to uplift isopycnals throughout the water column, reducing SDH and SSH, but details of the mechanisms are beyond the scope of the present study and should be addressed in future works.

6 Conclusion and discussion

We have examined the CMW distributions and seasonal, year-to-year and decadal variations of the CMW using MOAA GPV. Most of the CMW is found in the region of $25^\circ N{-}40^\circ N$, $180^\circ {-}150^\circ W$ annually and subducts in the region to the east of $180^\circ$, between $35^\circ N{-}45^\circ N$, as some previous studies have inferred (e.g., Oka et al. 2011). All the results in Sect. 5 have led us to conclude that the CMW volume variation with year-to-year and decadal time scales is a significant manifestation of the PDO. That is, when CMWI is positive, i.e., the CMW volume is larger than normal, the PDO is in positive phase. The Aleutian Low is more deepened than normal and locates to the east of its long-term mean position during the positive CMWI phase. The anomalously strong Aleutian Low extends westerlies far to the east, over the central North Pacific region between $35^\circ N{-}40^\circ N$, $170^\circ E{-}160^\circ W$, which is the CMW subduction region inferred from the ASV analysis. The anomalous westerlies enhance heat loss of the ocean to the atmosphere in the region, producing deeper and denser ML there. As a result, the outcrop line of the ${\sigma }_{\theta }=25.7 {kgm}^{-3}$ is pushed to the south/southeast of its mean position in late winter. The deeper ML in the PCF region and southward extent of the outcrop line of the ${\sigma }_{\theta }=25.7 {kgm}^{-3}$ results in larger volume of the CMW. The situations are reversed when CMWI is negative, i.e., the PDO is in negative phase.

Three mechanisms are involved in the SDH/SSH anomaly concerning the CMW variations, depending on the regions. In the southern/southeastern sector of the major CMW region, the SDH/SSH anomalies are caused by the CMW volume variation there, which alter the dynamic height anomalies above the CMW by the mechanism revealed by Kobashi et al. (2021) and Kobashi et al. (2023). In the northern sector of the thick CMW distribution region, negative (positive) SDH/SSH anomalies are caused by the negative (positive) SST and thicker (thinner) ML due to the surface cooling anomaly since the region corresponds to the stability gap (Roden, 1970, 1972; Yuan and Talley 1996) that allows the formation of the deeper ML during the positive CMWI phase. The relationship between the SDH/SSH anomalies and the CMW volume variation in the region to the north of $40^\circ N$, thus north of the subarctic front, differs from those indicated above because the permanent halocline below $100 m$ in the region prevents developing deep ML there. Therefore, the volume change in the CMW does not directly affect the SDH/SSH anomalies in the region. Rather, the SDH/SSH anomalies in the region are considered as the response to the wind stress curl anomaly in the area to the northeast of the major CMW distribution region, which is concurrent with the surface cooling anomaly in the major CMW region due to the anomalous westerly. The positive (negative) wind stress curl anomaly causes the anomalous Ekman suction to uplift (lower) isopycnals throughout the water column to lower (raise) the SDH and SSH, but details of the mechanisms are beyond the scope of the present study and should be addressed in future works.

Because the potential density and SST anomalies in the layer above the CMW are two sides of the same coin, the SST anomaly concerning the CMW variations can be attributed to two major processes, similar to those of the CMW variations in the thick CMW distribution region. One is the surface cooling in the northern sector of the CMW distribution region, which corresponds to the stability gap, resulting in the formation and subduction of a large volume of CMW there. Another process is the SST variation influenced by subsurface isopycnal surface variations in the southern/southeastern sector. That is, the SST anomaly in the southern/southeastern sector of the CMW region is formed due to the shoaling or lowering of isopycnal surfaces in the subsurface layer above the CMW in response to its volume variations as discussed in Kobashi et al. (2021) and Kobashi et al. (2023). This relationship is, however, not clearly seen in JAS and OND, when the SST anomalies in the seasons show insignificant correlations with CMWI. This is probably due to the temperature anomalies above the shallow surface mixed layer which is isolated from the subsurface conditions by the seasonal thermocline in JAS and OND.

Based on the estimation of the ASV shown in Sect. 4, we can expect that approximately $33\%$ of the mixed layer water in the PCF region in the entire North Pacific is subducted every winter, CMW150 ($7.84\times {10}^{14} {m}^{3}$) is replaced every $4$ years, and the CMW in the entire North Pacific is replaced every $6.7$ years on average. The renewal time of CMW is one order of magnitude smaller than those estimated in Suga et al. (2008), which are a few tens of years. This fact, however, does not imply that our results contradict Suga et al. (2008). They evaluated the renewal time for the water of the density range of $\sigma_{\theta } = 26.0 kgm^{ - 3} {-}26.6 kgm^{ - 3}$ in the North Pacific, which is quite different from the density range (2) shown in Sect. 3. The volume is estimated as $6\times {10}^{15}{ m}^{3}$, which is approximately 7.5 times larger than that of CMW150. When we estimate the renewal time for the water of the same density range as Suga et al. (2008), the renewal time for the water, not the entire CMW volume in the present study, is 30 years, which is comparable to Suga et al. (2008).

The lag relationship between CMWI and PDOI seen in Figs. 7 and 8 is reasonable because the SST anomaly, which concerns the CMW, forms in winter, while the CMW continues subducting and expanding to the east and southeast of its formation region after development in the deep winter mixed layer. The CMW seems to be almost settled a few months after its isolation from the surface mixed layer. Here, lag correlation analyses are performed to see how the signal of the CMW thickness variations propagates from the region near the formation areas within a year. Distributions of the lag correlation coefficients between the areal mean CMW thickness and those of all grid boxes are shown in Fig. 18. The regional mean CMW thickness time series is calculated for the area of $180^\circ {-}160^\circ W$, $35^\circ N{-}40^\circ N$. A 13-month running mean is applied to each time series before evaluating the lag correlations. A positive lag means that the regional mean CMW thickness leads the CMW thickness variation at each grid box. One can recognize that the high positive correlation area, more than 0.7, gradually expands/migrates to the east/southeast. The migration seems to occur along the geostrophic streamlines on the ${\sigma }_{\theta }=26.2 {kgm}^{-3}$ surface. The lag regression coefficients of the zonal mean CMW thickness on the regional mean thickness in $180^\circ E{-}160^\circ W$, $35^\circ N{-}40^\circ N$ are evaluated for the meridional belt between $180^\circ$ and $160^\circ W$ (Fig. 19). High positive regression coefficients expanse to the south as the lag increases. The maximum regression coefficients are found around $32^\circ N{-}33^\circ N$ at lag of $5$ months. High positive correlation coefficients, more than 0.7, are found around $30^\circ N$ at the lag of a year. The high positive correlation region well corresponds to the high regression areas on the lag-latitude section. This result suggests that the signal of the CMW variation in the northern part of the major CMW distribution area propagates to the south and reaches around $30^\circ N$ 1 year later in the meridional belt and the amplitude of the signal has its maximum around $32^\circ N{-}33^\circ N$ 5 months later, where the climatological maximum thickness of CMW is found (Fig. 1a). The phase speed is estimated to be approximately $1.7{cms}^{-1}$, which is twice as fast as those of the potential vorticity anomaly propagation along almost the same meridional belt shown by Xie et al. (2011), approximately $0.81{cms}^{-1}$, and Sugimoto et al. (2012), approximately $0.88 {cms}^{-1}$. To date, we have not fully understood the relationship between the propagation of the CMW volume variation signal and that of the potential vorticity anomaly variation signal. This relationship must be addressed in future works.

Fig. 18

Distributions of the lag correlation coefficient between the areal mean CMW thickness and those in the North Pacific. Lag correlation coefficients between the area average CMW thickness and those in the North Pacific are drawn. Positive lags indicate that the areal mean CMW leads that of each grid point. Black, blue, red, magenta, and cyan lines are the contour lines of 0.7 of the correlation coefficient for the lags of 0, 3, 6, 9, and 12 months, respectively. The black rectangle shows the region where the areal mean CMW thickness is calculated. Black dotted lines show 150 m contour lines of the annual mean CMW thickness. Background contours are the geostrophic streamlines on the annual mean potential density surface of σ_θ = 26.2 kgm⁻³ (color figure online)

Fig. 19

Lag-latitude section of the regression coefficient of the zonal mean CMW thickness in the meridional belt of 180°E – 160°W on that averaged over the area of 180°E – 160°W, 35°N – 40°N. The lag regression coefficient of the zonal mean CMW thickness in the meridional belt of 180°E – 160°W for every 1° latitude belt on the areal mean CMW thickness averaged over 180°E – 160°W, 35°N – 40°N for each lag is drawn. The vertical axis indicates latitude, and the horizontal axis shows lag in month. Positive lags indicate that the areal mean CMW leads the zonal mean at each latitude. The white rectangle indicates the latitude of the areal mean. Thick black lines indicate zero-coefficient contours. Three white broken contours indicate the correlation coefficients of 0.7, 0.8 and 0.9, respectively (color figure online)

Appendix: L- and D-CMW variations

A density criterion of ${\sigma }_{\theta }=26.2 kg{m}^{-3}$ is set to distinguish L-CMW from D-CMW following Oka et al. (2011), although other previous research defined the density range of the denser limit of L-CMW as $\sigma_{\theta } = 26.2{-}26.3 kgm^{ - 3}$ and that of the lighter limit of D-CMW as $\sigma_{\theta } = 26.1{-}26.4kgm^{ - 3}$. Thus, the density criterion for L-CMW as $25.7 kg{m}^{-3}\le {\sigma }_{\theta }\le 26.2 kg{m}^{-3}$ and for D-CMW as $26.2 kg{m}^{-3}\le {\sigma }_{\theta }\le 26.4 kg{m}^{-3}$ are adopted to evaluate L-CMW and D-CMW volumes. The PV and temperature criteria are the same as in (3) and (4). L- and D-CMW volumes are evaluated in the same manner as the estimation of CMW150. Volume variations in CMW, L-CMW and D-CMW and their anomalies are shown in Fig.

Fig. 20

CMW, L-CMW, and D-CMW volume variations are drawn. a Volume variations in CMW150 (red), L-CMW (black), and D-CMW (blue), b their anomalies, and c the normalized anomalies (color figure online)

20a and b, respectively. The normalized anomalies are drawn in Fig. 20c. All three volume time series show almost the same variations. The correlation coefficient for CMW150 and L-CMW variations is 0.98, and that for CMW150 and D-CMW is 0.94.