Influence of North Pacific subtropical mode water variability on the surface mixed layer through the heaving of the upper thermocline on decadal timescales

Decadal variability of the North Pacific subtropical mode water (STMW) and its influence on the upper thermocline and mixed layer are examined in a four-dimensional variational ocean re-analysis for the Western North Pacific over 30 years (FORA–WNP30). The STMW that forms south of the Kuroshio Extension becomes thick/cold and thin/warm on decadal timescales. These variations are subducted and advected to the south, where thick (thin) STMW causes the upper thermocline to heave up (down) above the STMW, producing cold (warm) temperature anomalies at subsurface depths, with especially large anomalies at the depths of the seasonal thermocline. Temperature anomalies also appear in the mixed layer from March to November, except in September. These anomalies have the same sign as the temperature anomalies of the STMW, although they are due not to the reemergence of the STMW at the surface but to the heaving of the upper thermocline. In the FORA–WNP30, because the formation of the mixed layer temperature anomalies owes much to the increment introduced by data assimilation, the mechanism remains unclear. A heat budget analysis of the mixed layer, however, suggests the importance of entrainment and/or vertical diffusion at the base of the mixed layer for conveying temperature anomalies from the upper thermocline to the mixed layer. The STMW also affects the mixed layer depth. A thick (thin) STMW shoals (deepens) the seasonal thermocline, enhancing (weakening) stratification at depths below the mixed layer and thus hindering (favoring) mixed layer development from July to September.


Introduction
The Kuroshio and the Kuroshio Extension encounter cold and dry monsoon winds blowing from the Asian continent in winter, losing a large amount of heat into the atmosphere and resulting in the formation of a deep mixed layer south of the Kuroshio and the Kuroshio Extension (Fig. 1a). The deep mixed layer water is subducted into the thermocline in the south by the mean circulation and eddies (Huang and Qiu 1994;Suga et al. 2008;Nishikawa et al. 2010;Xu et al. 2014), producing a thick homogeneous layer between the upper and main thermoclines. This layer is called subtropical mode water (STMW; Masuzawa 1969;Hanawa and Talley 2001;Oka and Qiu 2012). The STMW spreads by the Kuroshio recirculation gyre (Bingham 1992;Suga and Hanawa 1995) and eddies (Uehara et al. 2003;Nishikawa et al. 2010;Xu et al. 2016Xu et al. , 2017 to a wide region of the western subtropical gyre (Fig. 1b). The STMW is dynamically characterized by low potential vorticity (PV) and conserves the PV on its way south, shaping the subtropical thermocline (Kubokawa 1999;Dewar et al. 2005).
The formation of the STMW varies on decadal timescales (e.g., Qiu and Chen 2006), which influences physical and biogeochemical properties in the subtropical thermocline 1 3 downstream (Oka et al. 2015(Oka et al. , 2017(Oka et al. , 2019. The decadal variations in the STMW also lead to changes in the subtropical front (Kobashi et al. 2021) and subtropical countercurrent (Xie et al. 2011), both maintained by the STMW along the southern boundary of the STMW distribution area (Kobashi and Kubokawa 2012), exerting a significant impact on the atmosphere over the subtropical front and countercurrent (Xie et al. 2011;Zhang et al. 2017).
Recently, from an analysis of summertime repeat hydrographic observations along 137°E that have been conducted since 1972 by the Japan Meteorological Agency (JMA; Oka et al. 2018), Kobashi et al. (2021) showed that the decadal variations in the pycnoclines are associated with variations in the STMW thickness. When the STMW is thicker (thinner) than normal, the seasonal pycnocline shoals (deepens) significantly, while the main pycnocline tends to deepen (shoal). This vertical displacement of the pycnocline due to the mode water thickness anomalies has been commonly recognized in numerical models (e.g., Yamanaka et al. 2008;Nonaka et al. 2012;Sugimoto et al. 2012) and understood as the baroclinic adjustment of the pycnocline (Xie et al. 2011). Kobashi et al. (2021) further point out that the heaving of the seasonal pycnocline produces density anomalies at subsurface depths. These density anomalies seem to extend up to a near-surface layer, which is indicative of the change in the mixed layer. However, how the variations in the STMW are related to those of the mixed layer and the mechanism of the mixed layer variations have not yet been examined.
The STMW plays a role in the reemergence of winter sea surface temperature (SST) anomalies (Hanawa and Sugimoto 2004;Sugimoto and Hanawa 2005). Winter SST anomalies that form in the deep mixed layer are isolated from the atmosphere by a shallow mixed layer from spring to summer and are retained at subsurface depths. When the mixed layer deepens in the following fall to winter, the SST anomalies are entrained into the deepening mixed layer and recur at the surface Born 1970, 1974;Alexander and Deser 1995;Alexander et al. 1999).
Two areas have been identified as areas where the STMW reemerges. One area is the central North Pacific, where the STMW that forms south of the Kuroshio Extension in the winter of the previous year is transported eastward and reemerges at the surface in the current winter Hanawa 2005, 2007). This reemergence alters the surface thermal inertia and influences the Pacific Decadal Oscillation (PDO; Newman et al. 2016). The PDO is a leading mode of Pacific decadal SST variability (Mantua et al. 1997;Mantua and Hare 2002) that exerts great influences on global climate (Newman et al. 2016), marine ecosystems and fisheries (Mantua et al. 1997;Francis et al. 1998). Another area is located in the western part of the subtropical gyre. Comparing yearto-year SST variability at the same location between late winter and the other months, Hanawa and Sugimoto (2004) show that winter SST anomalies tend to recur at the surface in the fall in that location. Compared to the central North Pacific, this area has not been studied much thus far. It is still unclear how the STMW is involved in the reemergence of winter SST anomalies.
The present study examines the decadal variations in the STMW and their influence on the upper thermocline and mixed layer using long-term ocean reanalysis data. We focus on the STMW subducted to the south of the formation region, where the STMW hardly outcrops at the surface. We show that the variations in the STMW thickness make the upper thermocline heave up and down above the STMW and produce temperature anomalies in the mixed layer that have the same sign as those of the STMW. The rest of the paper is organized as follows: Sect. 2 describes the data and methods. In Sect. 3, we first show the decadal variations in the STMW and their relationship with variations in the wintertime mixed layer south of the Kuroshio Extension. Then, we explore the influence of the STMW on the overlying upper thermocline and mixed layer. The variations in the mixed layer temperature (MLT) are further diagnosed based on a heat budget analysis to explore their mechanism. Section 4 provides a summary and discusses the results in relation to the reemergence phenomenon. Climatological mean of (a) the maximum daily mixed layer depth (MLD) in March (colors) and the sea surface height (contours every 10 cm), and (b) subtropical mode water (STMW) thickness (colors) and 1000 m isobaths (contours). The box denotes the S region (25-30°N, 143-155°E) that is mainly analyzed in the present study (color figure online)

Data
We utilize ocean reanalysis data of a four-dimensional variational ocean re-analysis for the Western North Pacific over 30 years (FORA-WNP30;Usui et al. 2017). The data are produced by the Japan Agency for Marine Science and Technology (JAMSTEC) and the JMA Meteorological Research Institute (MRI) with the use of the four-dimensional variational analysis scheme version of the MRI Multivariate Ocean Variational Estimation system (MOVE-4DVAR; Usui et al. 2015) to assimilate in situ observations and satellite observations. This assimilation is performed using Japanese 55-year Reanalysis (JRA-55; Kobayashi et al. 2015) daily atmospheric forcing. The data are available as daily values at eddy-resolving resolutions of 0.1° grid (0.17° grid east of 160°E or north of 50°N) and at 54 vertical levels from the surface to a 6300 m depth for the period from 1982 to 2016. The FORA-WNP30 reproduces the decadal variability of the STMW fairly well (Usui et al. 2017). In addition, we also analyze the FORA-WNP30 that does not assimilate any observations (hereafter called Free FORA-WNP30). These data are available at the same grid points and vertical levels as the FORA-WNP30 for the period from 1982 to 2015.
In this study, the STMW is defined as a layer of PV that is less than 2.0 × 10 -10 m −1 s −1 between 15.0 and 19.5 °C (Oka et al. 2019) below the surface mixed layer. PV is calculated from the vertical gradients of potential density ( ) as PV = −(f ∕ ) ∕ z , ignoring relative vorticity, where is the density, f is the Coriolis parameter and z is the vertical coordinate (positive upward). The mixed layer depth (MLD) is computed as the shallower depth where either the potential temperature or the density differs by 0.5 °C or 0.125 kg m −3 , respectively, from the corresponding values at a depth of 10 m (Hosoda et al. 2010). The STMW thickness is defined as the total thickness of the STMW below the MLD at each grid point on a daily basis. The STMW temperature is calculated as the vertical mean of the potential temperature in the STMW layer.
To focus on decadal variations, we employ a Butterworth low-pass filter with a half-power period of 6 years. Cross-correlation and regression coefficients are computed using the low-pass filtered and detrended time series. The statistical significance is assessed at the 95% confidence limit using the degrees of freedom estimated from the length of the time series, assuming a dominant timescale of a decade. Figure 1 shows the maps of the annual mean STMW thickness and the mean maximum MLD in March, both of which are calculated using the FORA-WNP30 data. The mean maximum MLD in March is computed from the maximum daily MLD each year, which is a good precursor for STMW formation in subsequent seasons (Yu et al. 2020). A thick STMW appears in the area of 25-32°N, 143-155°E, which is to the south of the deep winter mixed layer south of the Kuroshio Extension. The thickness decreases markedly west of 140°E. This is partly due to the large meander of the Kuroshio. The Kuroshio sometimes detours offshore south of Japan (Kawabe 1995), which separates the recirculation gyre south of the Kuroshio and blocks the westward transport of the STMW (Suga and Hanawa 1995;Sugimoto and Hanawa 2014;Oka et al. 2021). In addition, the Izu-Ogasawara Ridge along 140°E (Fig. 1b) decays westward-migrating eddies that carry a large portion of the STMW, hampering the westward transport of the STMW (Xu et al. 2016. Another thick STMW is found at approximately 136°E south of Japan, which forms in a spatially isolated, deep winter mixed layer (Fig. 1a). The present study focuses on the region of 25-30°N, 143-155°E east of the Izu-Ogasawara Ridge (Fig. 1b), which is hereafter called the S region. The S region nearly corresponds to the area of the reemergence of winter SST anomalies identified by Hanawa and Sugimoto (2004).

STMW and its decadal variations
The daily time series of the STMW thickness and temperature are averaged in the S region and plotted in Fig. 2. These time series exhibit distinct seasonal and decadal variations, and the temperature also shows a noticeable warming trend. The decadal variations are similar to those previously reported by Oka et al. (2021) from Argo float observations after 2005 in the area of 15-28°N, 140°E-170°W and by Sugimoto et al. (2017) from historical hydrographic observations in the entire STMW region. The thickness and temperature vary in almost opposite phases; that is, when the STMW is thick (thin), it is cold (warm). The correlation based on the monthly time series shows a significant coefficient of − 0.89, with a slight time lag where the temperature leads by 7 months (figures not shown).
The STMW has a temperature of approximately 16-18 °C in the S region ( Fig. 2b), which forms in the deep mixed layer south of the Kuroshio Extension (Suga and Hanawa 1990;Suga et al. 2004;Oka et al. 2021). We detect the maximum MLD in March and the MLT on the same day each year and then average them in the formation January to March, April to June, July to September, and October to December are shown in gray, green, red and blue curves, respectively. d is the same as (a) but the mixed layer temperature (MLT) on the day of the maximum MLD. e and f are the same as in b and c, respectively, but the STMW temperature (color figure online) region of [30][31][32][33][34][35][143][144][145][146][147][148][149][150][151][152][153][154][155][156][157][158][159][160]d). We use only profiles with a temperature greater than 16 °C at a 200 m depth to exclude subarctic profiles north of the Kuroshio Extension from the average, following the methods of Sugimoto and Kako (2016). The MLD and MLT both vary on decadal timescales, with almost opposite phases, indicating that when the mixed layer is deep (shallow), it is cold (warm). The correlation is significant with a coefficient of − 0.89 and no time lag. The result is reasonable, given that a deep mixed layer usually results from intense surface cooling and the resultant deepening further entrains cold water below the mixed layer.
The STMW is subducted and advected to the south of the formation region. We compare the decadal variations in the mixed layer in March in the formation region and those of the STMW in the S region. The yearly time series of the monthly-mean STMW thickness and temperature in the S region are plotted for each month in Fig. 3. The decadal variations are predominant with almost the same phase among the months, which are also similar to the variations in the mixed layer in the formation region. The lag correlation analysis reveals that the MLD (MLT) in March in the formation region is significantly correlated with the STMW thickness (temperature) for every month, with a maximum correlation in April of the next year (in November of the same year) with a coefficient of 0.85 (0.94) (figures not shown). The time lag suggests that the thickness (temperature) anomalies travel to the S region for 13 (8) months. These different travel times may be consistent with the finding that the STMW thickness changes behind the temperature in the S region, though the mechanism for the different travel times needs further investigation. These correlations support the conclusion that the decadal variations in the S region originate in the wintertime mixed layer south of the Kuroshio Extension.

Variations in the upper thermocline
Here, we examine how the decadal variations in the STMW thickness are related to those of the thermocline in the S region. For this purpose, the monthly means of the temperature profiles and STMW thickness are first calculated. Then, their year-to-year time series are low-pass filtered and detrended for each month. The variations in the temperature profile are regressed on those of the STMW thickness for each month from 1982 to 2016. The result is plotted along with the monthly climatologies of the temperature profiles, PV and MLD in Fig. 4a. The STMW appears at 200-300 m depths throughout the year, with a lower PV of less than 1.7 × 10 -10 m −1 s −1 from April to November. The regression is significantly negative in the upper thermocline above the STMW layer (> 19.5 °C), with large values in the seasonal thermocline from June to November. The seasonal thermocline forms in the upper 100 m depth with strong stratification from spring to fall, as shown in Fig. 4a. In contrast, the regression is overall positive in the main thermocline below the STMW layer (< 15.0 °C). This regression pattern indicates a decrease (increase) in temperature in the upper (main) thermocline in years of thick STMW, which is consistent with the analysis of JMA summertime observations at 137°E by Kobashi et al. (2021). The regression persists not only in summer but also year-round.
To examine the heaving of isotherms, we calculate the depth of the isotherm surfaces with a temperature increment of 0.5 °C using linear interpolation and then average it in the S region for each month. Figure 5 shows the regression of the isotherm depths on the STMW thickness, together with the climatologies of the depths. The regression is significantly negative (positive) above (below) the STMW layer (approximately 16-18 °C), indicating the shoaling (deepening) of the upper (main) thermocline in years of thick STMW. This result is consistent with the baroclinic adjustment of the thermocline proposed by Xie et al. (2011). The magnitude of the regression coefficients is almost the same in the upper thermocline above the 20 °C isotherm. Because the change in temperature due to the heaving, ΔT , at a depth of z 0 is related to the vertical temperature gradient T z and the displacement of isotherms ΔZ , that is, , the uniform heaving of the isotherms results in large changes in temperature in the seasonal thermocline because of the large temperature gradient (Fig. 4a).
The temperature changes associated with the heaving of isotherms are obvious in the composite temperature sections in Fig. 6. The composites are constructed for June using the monthly-mean temperature data with reference to the yearly time series of the monthly-mean STMW thickness in the S region (Fig. 7b). All the data are detrended before the analysis. One composite is made by averaging the data when the thickness anomalies exceed one standard deviation (thick STMW years;1984, 1986, and the other is made when the negative anomalies exceed one standard deviation (thin STMW years;1997-2000, 2002, 2009. In years of thick STMW, the isotherms are notably elevated above the STMW with negative temperature anomalies, while in years of thin STMW, the isotherms move downward and yield positive temperature anomalies. The temperature anomalies are overall significant above the STMW layer, except near the surface in years of thick STMW years. Below the STMW layer, the temperature anomalies are generally opposite to those above the STMW layer, which is consistent with the results from Fig. 4a.
The heaving of the isotherms can change the stratification. Figure 4b shows the regression of the vertical temperature gradients on the STMW thickness. At depths between 200 and 400 m, the regression is negative overall because a thick STMW weakens the stratification in the vicinity of the STMW layer. The regression is significantly positive and negative along the top and bottom depths of the mean seasonal thermocline, respectively, from July to October. The pair of regressions with opposite signs is consistent with the heaving of the seasonal thermocline. The uplift of the seasonal thermocline weakens the stratification at the lower part of the mean seasonal thermocline while enhancing the stratification at the upper part.

Variations in the mixed layer
The composite cross sections in Fig. 6 display the temperature anomalies extending up to the surface mixed layer. The regression in Fig. 4a also captures the changes in temperature near the surface. We calculate the regression of the MLT onto the STMW thickness and the explained variance for each month (Figs. 8a, c). The low-pass filter and detrend are applied to the yearly time series of the monthly mean for each month. The regression is significantly negative from Fig. 4 a Monthly regression coefficients of the temperature profiles on the STMW thickness in the S region, together with the monthly mean of the temperature profiles (contours), MLD (thick black curve) and potential vorticity (PV; gray contours). The regression coefficients are plotted only for significant areas at the 95% confidence limit. The PV contours denote 1.7 and 2.0 × 10 -10 m −1 s −1 , representing a thick STMW. b The same as in (a) but the regression coefficients of the vertical temperature gradient profiles. c The same as in (a) but the result from Free FORA-WNP30 (see the text) (color figure online)

Fig. 5
Monthly regression coefficients of the isotherm depths on the STMW thickness in the S region, together with the monthly mean isotherm depths (contours). The regression coefficients are plotted only for significant areas at the 95% confidence limit (color figure online) March to November except for September, with explained variance peaks of more than 60% in June and approximately 50% in October. The relationship between the MLT and STMW thickness is also evident in the time series in Fig. 7, with a significant correlation coefficient of − 0.80 in June and − 0.70 in October. The regression is computed at each grid point and mapped in Fig. 9. The negative regression is quite robust between 140 and 160°E in June, and the area almost exactly corresponds to that of the thick STMW in the climatology in Fig. 1b. In October, the regression becomes small but significant, especially to the west of 150°E. Note that the correlation between the STMW thickness and the MLT is present on decadal timescales. The MLT varies also on interannual timescales (Figs. 7a, c), which shows no Fig. 6 Composite cross sections of the temperature (contours in °C) and its anomalies (color) averaged between 143 and 155°E for (a) thick STMW years (1984, 1986, 2005, 2014 and 2015) and (b) thin STMW years (1997-2000, 2002, and 2009-2010) in June. These years are chosen based on the time series of the STMW thickness anomalies in the S region. Shade indicates areas where the temperature is significantly different from the mean climatology at the 95% confidence limit (color figure online) The negative regression signifies that the MLT anomalies have the same sign as the temperature anomalies of the STMW because the STMW thickness correlates negatively with the STMW temperature (Fig. 2). It should be noted, however, that the MLT anomalies are not formed by the outcropping of the STMW at the surface, namely, the reemergence of the STMW. As seen in Fig. 4a, the STMW always stays below the upper thermocline and does not outcrop at the surface in the S region. Instead, the heaving of the upper thermocline that is induced by the STMW is considered to be important for the formation of the MLT anomalies. From December to February and in September, the regression is not significant and has a low explained variance (Figs. 8a, c). For these months, the MLT variations could be also affected by other factors such as intense surface heat flux in winter and summer.
The STMW alters the stratification below the mixed layer (Fig. 4b), which can affect the development of the mixed layer. We calculate the monthly regression of the MLD on the STMW thickness and the explained variance (Figs. 8b, d). The regression is significantly negative from July to September, with an explained variance peak of more than 60% in August. This indicates that the mixed layer is shallow (deep) in years of thick (thin) STMW. This relationship, which has a significant correlation of -0.81, is obvious in the year-to-year time series in August, as shown in Fig. 10.
In August, the MLD is shallow and spatially uniform in the STMW region (Fig. 11a). The vertical temperature gradient below the mixed layer is large between 140 and 160°E (Fig. 11a) above the thick STMW in the climatology (Fig. 1b). The regression of the MLD on the STMW thickness is negative overall east of 140°E (Fig. 11b). The distribution is quite similar to that of the regression of the temperature gradients on the STMW thickness with the opposite signs (Fig. 11c). These results indicate that a thick (thin) STMW heaves the seasonal thermocline up (down), which enhances (weakens) the stratification at depths below the mixed layer and thus hinders (favors) the development of the mixed layer. The regression is large along the southern edge of the STMW area east of 140°E (Figs. 11b, c). The reason for this result is unclear, but the mixed layer could be vulnerable to STMW variations because of the relatively deep mixed layer there (Fig. 11a).

Diagnosis of the MLT variations
How does the STMW alter the MLT? To address this question, heat budget analysis is carried out for the mixed layer using the FORA-WNP30. The heat budget is written as: where T m is the MLT; Q is the net surface heat flux, with positive values denoting heat gain; q is the downward radiative flux at the base of the mixed layer; is the reference density of seawater; c p is the specific heat; h m is the MLD; is the sea surface height; is the horizontal velocity; w is the vertical velocity; ∇ H is the horizontal gradient operator; D H is the horizontal diffusion; and T inc is the temperature increment added by the data assimilation in the FORA-WNP30. The left-hand side denotes the MLT tendency. The first term on the right-hand side is the net surface heat flux, the second term is the horizontal advection, the third term is the vertical advection, the fourth term is the horizontal diffusion, and the fifth term is the increment. The sixth term, m , is residual and is considered to represent the sum of the vertical diffusion at the base of the mixed layer and the entrainment of the water below the mixed layer by the deepening mixed layer.
(1) Fig. 10 Yearly time series of (a) the MLD and (b) STMW thickness in August in the S region. Blue and red curves denote the low-pass filtered values. The correlation coefficient between the blue and red curves is denoted at the top of (a) (color figure online) Fig. 11 a August mean of the MLD (gray contours every 5 m) and vertical temperature gradients at 10 m below the base of the mixed layer (colors). Thick black contours indicate a monthly mean STMW thickness of 20 m for the guide of the STMW region. Regression coefficients of (b) the MLD and (c) vertical temperature gradients at 10 m below the base of the mixed layer on the STMW thickness in August, plotted in the STMW region with a monthly mean thickness of more than 20 m delineated by thick contours. The regression coefficients are plotted only for significant areas at the 95% confidence limit (color figure online) All the terms are first computed on a daily basis using the archived data of the ocean variables, heat fluxes and increments at each grid point. Note that the heat fluxes are also model outputs of the FORA-WNP30. The calculation uses the same code as in the FORA-WNP30, which is described in detail by Usui et al. (2017) and Tsujino et al. (2006Tsujino et al. ( , 2010. Then, the budget terms on the right-hand side are integrated each day from the same start date the year before from 1982 to 2016. These values correspond to the MLT tendency of the previous year, ΔT m , as expressed below: where Δt is the length of a year. These integrated daily values are then averaged for each month in the S region to produce the monthly time series. Using this monthly time series, we examine the budget of the year-to-year variations in the monthly-mean MLT to identify the process driving the MLT decadal variations for each month. The calculation uses the daily mean variables instead of variables at the model time step of the FORA-WNP30. Thus, the nonlinear terms may be different from those at the model time step in the strict sense. To check how the different time intervals of the data change the heat budget estimate, we carried out the same analysis using 3-day or 5-day mean variables computed from the daily data. On the decadal timescale, the results are almost identical to those from the daily data. Therefore, we consider that the average over such short periods may not change the estimate. Figure 12 shows the decadal variations in the tendency term and each budget term in June and October, when the MLT correlates highly with the STMW thickness (Fig. 8a). The variations in the terms are quite similar between June and October. The heat flux and increment terms are considerably large in magnitude in both months and are a few times larger than the tendency term. The horizontal advection and In the panels, NSF denotes net surface heat flux, HAD denotes horizontal advection, VAD denotes vertical advection, HDI denotes horizontal diffusion, INC denotes the increment, and RES denotes the residual that is the sum of the vertical diffusion and entrainment terms residual (entrainment and vertical diffusion) terms also exhibit relatively large variability. Figure 13 indicates the correlation and covariance ratio between the tendency term and each budget term in June and October. The covariance ratio is the covariance that is normalized by the variance in the actual temperature tendency on the left-hand side of Eq. (2) and describes the contribution of each budget term to the total temperature tendency (Tesdal and Abernathey 2021). Because the sum of all the terms is equal to the tendency term, the sum of the covariance ratio must equal one. Interestingly, all the terms show no significant correlation (Figs. 13a, b), while the covariance ratio is remarkably large in the increment term (Figs. 13c,d), which suggests that the increment introduced by data assimilation contributes significantly to the MLT variations.
To determine the impact of data assimilation, we utilize the Free FORA-WNP30 to calculate the regression of the temperature profiles on the STMW thickness in the same way as in Fig. 4a (Fig. 4c). In contrast to the FORA-WNP30, the STMW has a much lower PV throughout the year. A negative regression appears above the STMW layer, but it is absent in the seasonal thermocline. In the mixed layer, significant regression is seen from October to December, however, there is no significant regression in the seasonal thermocline. The feature is quite different from that shown in Fig. 4a. The data assimilation is crucial in reproducing the MLT anomalies associated with the STMW thickness in the FORA-WNP30.
Some of the budget terms show similar behavior to the increment term in Fig. 12, which implies that these terms may be related to the increment. The budget terms have errors when they are not reproduced completely by physical processes in the model. The increment compensates for the errors. Although the effects of the increment are not necessarily physically meaningful, the relationship between the increment and the other terms may suggest the local effects of the increment in the S region. Figure 14 shows their correlations for June and October. The correlation is largely negative for the heat flux and vertical advection terms and positive for the residual (vertical diffusion and/or entrainment) term. These are significant at the 95% confidence limit except for the vertical advection in June. These results suggest that the increment tends to reduce the variations in the heat flux and vertical advection, while it tends to enhance those of the vertical diffusion and/or entrainment. However, it is unclear how much each budget term is related to the increment. If the heat flux is mainly related to the increment, for example, the correlation suggests that the cooling or warming of the mixed layer due to the surface heat flux is exaggerated in the model and therefore is suppressed by the increment. If the entrainment is related, the cooling effect of the entrainment is weak in the model and thus is enhanced by the increment. Given that vertical diffusion and entrainment are processes that can convey temperature anomalies from the underlying upper thermocline, they could be important for the decadal MLT variations. In the S region, the Fig. 13 Monthly correlation coefficients between the MLT tendency term on the left-hand side in Eq. (1), and each term on the right-hand side in Eq. (1) for (a) June and (b) October. On the horizontal axis, NSF denotes net surface heat flux, HAD denotes horizontal advection, VAD denotes vertical advection, HDI denotes horizontal diffusion, INC denotes the increment, and RES denotes the residual that is the sum of the vertical diffusion and entrainment terms. c and d are the same as (a) and (b), respectively, but for the covariance ratio MLD starts deepening in June in the climatology (Fig. 4a). Therefore, the entrainment could also be possible even in June as well as October.
Note that the budget terms are related not only to the local increment but also to the increment at other times and places. The comparison between the budget balances in the FORA-WNP30 and the unconstrained Free FORA-WNP30 may give more insight into the effects of data assimilation, which will be addressed in future work.

Summary and discussion
We investigate decadal variations in the STMW and their influences on the upper thermocline and mixed layer using the FORA-WNP30. Figure 15 shows a schematic summary of the results. In the STMW formation region south of the Kuroshio Extension, the wintertime mixed layer becomes thick/cold and thin/warm on a decadal scale. These variations are subducted and advected to the south, possibly with different travel times between the thickness and temperature. Consistent with a previous study, the thick (thin) STMW makes the upper thermocline heave up (down), producing cold (warm) temperature anomalies at subsurface depths, with large anomalies at the depths of the seasonal thermocline from June to November.
Subsurface temperature anomalies emerge in the mixed layer from March to November, except in September. In the FORA-WNP30, because the formation of the MLT anomalies owes much to the increment introduced by data assimilation, its mechanism still remains an open question. The heat budget analysis of the mixed layer, however, suggests the importance of entrainment and/or vertical diffusion at the base of the mixed layer for conveying temperature anomalies from the upper thermocline to the mixed layer. The STMW also affects the MLD. A thick (thin) Fig. 14 Monthly correlation coefficients between the increment term and the other terms on the right-hand side in Eq. (1) for (a) June and (b) October. Black bars are significant at the 95% confidence limit. On the horizontal axis, NSF denotes net surface heat flux, HAD denotes horizontal advection, VAD denotes vertical advection, HDI denotes horizontal diffusion, and RES denotes the residual that is the sum of the vertical diffusion and entrainment terms Fig. 15 Schematic meridional temperature section illustrating the heaving of the upper thermocline due to the thick cold STMW that forms in the deep cold mixed layer south of the Kuroshio Extension (KE). a The uplift of the thermocline produces cold anomalies above the STMW that appear in the mixed layer from March to November except in September, while b it enhances the stratification below the mixed layer and shoals the mixed layer from July to September STMW shoals (deepens) the seasonal thermocline, which enhances (weakens) the stratification at depths below the mixed layer and thus hinders (favors) the development of the mixed layer from July to September in summer.
The MLT anomalies in the S region have the same sign as those of the wintertime mixed layer south of the Kuroshio Extension (Fig. 15). This is apparently consistent with the remote reemergence phenomenon proposed by Sugimoto and Hanawa (2007), where wintertime SST anomalies move at subsurface depths and then reemerge at the surface in a different location. Indeed, the MLT variations in June and October in the S region are correlated significantly with those south of the Kuroshio Extension in March of the previous year (Fig. 16). It should be noted, however, that the STMW stays below the upper thermocline and does not outcrop at the surface in the S region (Fig. 4a). Thus, the formation of the MLT anomalies is due not to the reemergence of the STMW but to the heaving of the upper thermocline. This differs from the typical reemergence phenomenon in which the water that memorizes winter SST anomalies is entrained into the mixed layer.
What processes cause the heaving of the upper thermocline? At the subsurface depths, the temperature change is primarily controlled by advection and diffusion: The left-hand side denotes the tendency of temperature T . The first term on the right-hand side is the divergence of radiative flux, the second term is the horizontal advection, the third term is the vertical advection, the fourth term is the horizontal diffusion, and the fifth term is the increment. The residual, r , represents the vertical diffusion. We diagnose the vertical averages of each term between 50 and 100 m depths  in the seasonal thermocline. Using the same procedure as for the mixed layer, we evaluate the contribution of each budget term to the decadal temperature tendency. The time series of each term in June are shown in Fig. 17, and their correlation and covariance ratio with the tendency term are presented in Fig. 18. The horizontal advection shows large variations that are similar to those of the tendency term, with a significant positive correlation and large covariance ratio, indicating the importance of the horizontal advection. The STMW is advected to the south from the formation region, which can heave up and down the upper thermocline. The horizontal diffusion also presents a significant correlation, though the magnitude and covariance ratio are pretty smaller than the horizontal advection. As in the mixed layer, the increment has large variations and covariance ratio. Further examination will be needed to clarify the mechanism.
Heaving of the isotherms also occurs in mesoscale eddies. In Sukigara et al.'s (2014) analysis of hydrographic observations in the STMW area, the uplift of isopycnals is found to be associated with the passage of a mesoscale cyclonic eddy. They suggest that the uplift of isopycnals supplies nutrients from the deep layer to the euphotic layer and energizes the photosynthesis of phytoplankton in the subsurface layers. Although the spatial and temporal scales are quite different between the mesoscale eddies and the STMW, one may expect that the STMW may also carry materials up and down by heaving isopycnals. Indeed, a recent study analyzing JMA repeat hydrographic observations at 137°E finds decadal variations in the dissolved inorganic carbon in the surface layer and shows that they are reasonably explained by the heaving of the thermocline (Ono et al. 2022, personal communication). The STMW may be important for the variability in not only physical but also biogeochemical properties in the surface layer.
SST variations associated with STMW thickness in Argo profiling float observations are reported by Oka et al. (submitted), who show that a recent large meander of the Kuroshio causes a drastic decrease in the STMW thickness south of Japan, which deepens the upper thermocline and increases the SST. These results are consistent with those of the present study. Because the STMW yields MLT anomalies over an extensive area of the subtropical ocean ( Fig. 9), it might have an impact on the atmosphere and climate. This should be further explored in future research. Fig. 18 a Correlation coefficients and b covariance ratio between the temperature tendency term on the left-hand side in Eq. (3), and each term on the right-hand side in Eq. (3) in 50-100 m depths for June. Black bars in (a) are significant at the 95% confidence limit. On the horizontal axis, DRF denotes divergence of radiative flux, HAD denotes horizontal advection, VAD denotes vertical advection, HDI denotes horizontal diffusion, VDI denotes vertical diffusion, and INC denotes the increment