1. Introduction
In this study, salt-finger (SF) double-diffusive convection (e.g., Stern 1960) in the western North Pacific region was examined. Double-diffusive convection in the ocean can occur when temperature or salinity stratification is unstable for molecular diffusion. Consider the case of an unstable salinity stratification in which salinity and temperature increase upward and the density stratification is stabilized by the temperature, and the warm and saline water that was originally in the upper layer, whose lower boundary was displaced downward. Because the molecular diffusivity of heat is approximately 100 times that of salinity, only heat from the upper layer in the downward displaced area is cooled from the surroundings, resulting in an increase in density and causing the water to descend. This convection efficiently transports salt vertically and is referred to as salt-finger double-diffusive convection. In this case, the high-salinity water moves downward with increasing density and the low-salinity water moves upward with decreasing density, and the originally unstable salt stratification is relaxed, and salinity tends to become vertically uniform, while the stratification due to temperature is maintained; thus, double-diffusive convection strengthens the density stratification. SF also play an important role in the vertical mixing of the ocean by transporting dissolved substances such as salinity and nutrients in the vertical direction and to contribute to biological production (Lewis et al. 1986; Hamilton et al. 1989).
Double-diffusive convection can be identified by the density ratio Rρ [=(αθz)/(βSz)], which is the ratio of the effect of temperature and salinity on the density gradient (density stratification), where α is the thermal expansion coefficient, β is the salinity contraction coefficient, θz is the vertical gradient of potential temperature, and Sz is the vertical gradient of salinity. When Rρ = 1, the vertical density gradient is zero. SF could occur for Rρ > 1 (Stern 1960), whereas SF is active with large unstable growth rate when 1 < Rρ < 2 (Schmitt 1981; St. Laurent and Schmitt 1999; Radko 2013) and the SF is not active when Rρ > 2 for which the growth rate is relatively low.
The global distribution of double diffusion (You 2002) indicates that there is active SF in the Atlantic Ocean near the thermocline that is due to the subduction of the high-salinity subtropical surface water. This high salinity is caused by excess evaporation over precipitation at the surface. Active SF also occurs on a vertical scale of several thousand meters in an area where relatively warm and saline North Atlantic Deep Water overlies cold and less-saline Antarctic Bottom Water. In the Pacific Ocean, active SF is reported to occur in the South Pacific and in the eastern North Pacific subtropical gyre; however, there is almost no active SF in the western North Pacific (You 2002) based on annual mean climatological data. The Rρ in the upper warm and saline water mass (Central Water) in the subtropical and tropical North Pacific is 3 < Rρ < 5 (Figueroa 1996). Shimada et al. (2007) reported that in the western North Pacific Rρ in the upper part of the salinity minimum of North Pacific Intermediate Water is mostly greater than 2, with a mode at Rρ ∼ 3.6 (Fig. 1 in Shimada et al. 2007) and the overall frequency of active SF is low, with active SF only found in some limited areas near Hokkaido, using WOCE hydrographic data.
Overall, it is widely accepted that the SF is much less active in the western North Pacific than in other oceans of the world (You 2002; Shimada et al. 2007). There are reports of active SF in the western North Pacific: microstructure measurements in the Tsugaru Warm Water (Inoue et al. 2007) and near the Kuroshio Extension (Nagai et al. 2015) just above the Oyashio low-salinity intrusion near Japan, and profiling float data analyses near the cores of Central Mode Water and Transitional Zone Mode Water in the Kuroshio–Oyashio Transition Area east of Japan that showed the SF could play a role in the transformation of the mode water masses (Saito et al. 2011).
Previous studies in the western North Pacific have collected data ranging from heavily smoothed annual mean climatological data (You 2002) to ship-based WOCE hydrographic high-quality one-time observations (Shimada et al. 2007), specialized ship-based observations (Inoue et al. 2007; Nagai et al. 2015) and Argo profiling float observations (Saito et al. 2011). Previous studies, other than Saito et al. (2011), did not provide information on temporal variability. Individual Argo profiling float data analysis (Saito et al. 2011) is useful for tracking the temporal change of a specific float data; however, it is not enough for understanding large-scale views and their long-term variations. In the present study, we attempted to determine the large-scale distribution of active SF and its seasonal and/or interannual variations by analyzing a gridded hydrographic dataset compiled from Argo float temperature, salinity, and pressure profiles that were uniformly sampled in both time and space in the upper ocean. In particular, the dataset covers wintertime, when ship-based observations are difficult to perform because of severe winter conditions.
In the next section, the data and detection methods for active SF are described. We assessed the validity of active SF detection using data with heavy horizontal smoothing and low-vertical resolution by comparing it with concurrent ship-based high-quality hydrographic data and showed that active SF is reasonably detected east of 150°E, whereas it is not in the area west of 150°E, where mesoscale-to-submesoscale ≤O(10 km) structures are dominant and are smoothed by large-scale ∼O(100 km) interpolation. In the results section, the following are demonstrated:
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Active SF appears most frequently in March along the latitude of 40°N around the Subarctic Boundary (SAB) in the western North Pacific and then decays until August and tends to disappear from the shallower and lower-density part of active SF.
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The distribution of active SF in March is consistent with the hypothesis that surface mixed layer water with the horizontal density ratio in the meridional direction 1 < RL [=(αθy)/(βSy)] < 2 is subducted and vertically superposed, resulting in an active SF with Rρ = 1–2.
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Active SF in March is distributed just below the surface mixed layer from the surface density +0.02σθ to +0.2σθ and in the density range of 26.1–26.4σθ.
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The mean density of the active SF in March had a decreasing trend in the period from 2001 to 2016, following the surface temperature increase (∼0.057°C yr−1) in the surface area with RL = 1–2.
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Interannual variations of the active SF in March are large, and the number of detection is relatively large in 2004–05, 2008, and 2012–13 and is less in 2002, 2006–07, 2009–11, and 2014–15. This variability is explained by both horizontal and vertical extents, with a significant positive correlation between the two (i.e., vertically thicker in years of wider horizontal extension), and the contribution from vertical extension is greater than that from horizontal extension.
2. Data and method
We used the temperature and salinity gridded dataset compiled from the data of temperature, salinity, and depth from Argo floats and other available sources [Grid Point Value of the Monthly Objective Analysis using the Argo data (MOAA GPV), version 1.0; Hosoda et al. 2008], which is published by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). This dataset covers an area of 70.5°N–60.5°S, 179.5°W–179.5°E, except for the marginal seas such as the Japan Sea, East and South China Sea, Sea of Okhotsk, and Mediterranean Sea, with grid intervals of 1° × 1° in the horizontal and 25 vertical levels: 10, 20, 30, 50, 75, 100, 125, 150, 200, and 250 dbar, 100-dbar intervals between 300 and 1500 dbar, and 1750 and 2000 dbar. We used monthly averaged temperature and salinity data for January 2001–December 2016.
The dataset was generated through two-dimensional optimal interpolation on each isobaric surface, using only profile data that had undergone quality control procedures (Hosoda et al. 2008). The uncorrelated distance at 40°N in the North Pacific is 10°–11° in longitude and 5°–7° in latitude, and the signal-to-noise ratio is 1–1.3, depending on depth (White 1995). The oceanic structure below the scale of mesoscale eddies from several tens of kilometers to several hundreds of kilometers is smoothed by interpolation of approximately 10° in the zonal direction and 6° in the meridional direction.
Because the vertical resolution of the 25 levels is not uniform, we linearly interpolated the water temperature and salinity data in the vertical direction at 5-dbar intervals to obtain the vertical gradients of potential temperature and salinity (θz, Sz) and the thermal expansion coefficient α and salinity contraction coefficient β before computing the density ratio Rρ = (αθz)/(βSz). For vertical interpolation, simple linear interpolation was employed because spline interpolations sometimes yield unrealistic profiles from profiles with complicated vertical profiles.
Following previous studies (e.g., Schmitt 1981; St. Laurent and Schmitt 1999; Radko 2013), we defined “active SF” to occur at 1 < Rρ < 2. If the density ratio of 1 < Rρ < 2 at a depth of 5-dbar interval was met, then active SF was considered to occur, and the number of occurrences at each horizontal grid was counted by summing the vertical grid numbers. The search for the active SF was limited to 10–300 dbar in the vertical direction because the vertical resolution of the data before interpolation was ≥100 dbar at depths of >300 dbar.
The degrees of freedom N was defined as the number of data divided by the product of 10.6 × 5.4 × (59/11), considering that the data were smoothed in the range of 10.6° in the zonal direction and 5.4° in the meridional direction (Hosoda et al. 2008), and that in the vertical direction, 59 levels at 5 dbar interval were obtained by interpolating 11 levels in the original data. The 95% confidence interval was estimated as approximately
We compare the data from the in situ hydrographic CTD observations along 40°N during the May 2016 cruise of the Japan Meteorological Agency R/V Keifu Maru (Figs. 1a,b) to assess the efficiency of the active SF detections using smoothed gridded data. Figure 1 shows the Turner angle Tu {=tan−1[(Rρ + 1)/( Rρ − 1)]; Ruddick 1983} vertical cross sections along 40°N between 140° and 165°E from the surface to 500 dbar with potential density contours, where the active SF with 72° < Tu < 90° (equivalent to 1 < Rρ < 2) are red shaded with darkening to Tu → 90° (Rρ → 1). In Fig. 1a, the density ratio Rρ at 5-dbar interval with half overlap was computed from the 10-dbar-mean vertical gradients of θz and Sz from 1 dbar interval temperature and salinity data, and then active SF was selected by the definition of 1 < Rρ < 2. The active SF distribution in Fig. 1b was evaluated from the lower vertical resolution data by picking up temperature and salinity data at pressure levels of 10, 20, 30, 50, 75, 100, 125, 150, 200, and 250 dbar; 100-dbar intervals between 300 and 1500 dbar; and 1750 and 2000 dbar and then interpolating the vertically sparse grid data to a 5-dbar interval by the same interpolation operated for the MOAA GPV gridded data. Figure 1c shows the Tu cross section from the MOAA GPV dataset with horizontal smoothing and vertical 5-dbar interpolation from the vertically sparse grid data.
Zonal vertical cross sections of Turner angle [red shades denote active SF of 72° < Tu < 90° (1 < Rρ < 2) with darkening to 90°, and blue shades denote diffusive convection of −90° < Tu < −72° with darkening to −90°] and potential density anomaly (contours) along 40°N latitude in May 2016, based on (a) the 1-dbar-vertical-resolution CTD observation data obtained in the R/V Keifu Maru KS1605 cruise, with the active SF detection where Rρ is evaluated every 5 dbar in 10-dbar bins with half overlap, (b) the data with reduced vertical resolution at the 25 vertical levels and then linearly interpolated at 5 dbar, used to evaluate Rρ, and (c) the dataset MOAA GPV, Ver. 1.0, at the 25 vertical levels, linearly interpolated to 5 dbar.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
Although the red shades become lighter from Figs. 1a–c indicating that the values of Rρ become larger, the detection of the active SF distribution from the MOAA GPV dataset was confirmed to be reasonable in the offshore area of 150°–165°E along 40°N (Table 1, third column). Table 1 shows the mean (for each longitude band in Table 1) vertical grid numbers of the active SF from each cast (Figs. 1a,b) and each horizontal grid (Fig. 1c). The cast-mean grid numbers are used to show the efficiency of active SF detection because the horizontal resolution of the CTD cast were not uniform. At longitude of 150°–165°E (Table 1, third column), the active SF detection (the cast-mean grid points) decreased by approximately 30% from 23.6 in the vertical high-resolution analysis (Fig. 1a) to 16.6 in the case of the vertically sparse data (Fig. 1b). The active SF detection decreased only by 15% from 16.6 in the case without horizontal smoothing (Fig. 1b) to 14.1 in the case of MOAA GPV with horizontal smoothing (Fig. 1c). Whereas in the vicinity of Japan at 140°–150°E (Table 1, second column), the horizontal smoothing in the MOAA GPV dataset drastically reduced the detection of the active SF by about 85% (Table 1, second column) from 14.4 in the case without smoothing (Fig. 1b) to 2.1 in the case of MOAA GPV with smoothing (Fig. 1c). Based on the evaluation above, active SF detection with the MOAA GPV dataset is useful for the offshore area east of 150°E; however, it is important to note that the active SF is not well detected in the area west of 150°E, where mesoscale structures such as eddies and intrusions are observed (Fig. 1a), and horizontal smoothing of the MOAA GPV dataset significantly reduces active SF detection. Note also that Rρ tends to be estimated larger in the MOAA GPV than in the high-resolution data.
Cast-mean grid numbers of the active SF detection evaluated from the three kinds of the data in Fig. 1 and for the three longitudinal bands of 140°–150°E, 150°–165°E, and 140°–165°E. The active SF were counted in the depths of 10–300 dbar.
3. Results
a. Distribution and variation of active SF in the western North Pacific
1) Global distribution of active SF
The monthly mean global horizontal distributions of the active SF in March and September are shown in Fig. 2, where the total number of occurrences of vertical grids satisfying the density ratio Rρ = 1–2 at depths of 10–300 dbar were counted at each monthly horizontal 1° grid during 2001–16. As previously reported by studies that used annual mean climatological data (e.g., You 2002), the active SF is remarkable in the Atlantic, South Pacific, and South Indian Oceans, as well as the subtropical eastern North Pacific, in both March and September. In the subtropical eastern North Pacific, active SF was present even in September (Fig. 2b), albeit at a lower rate than in March (Fig. 2a).
Horizontal distribution of the occurrence rate of active SF (occurrence number/total grid numbers in 10–300 dbar during 16 years) for a period from 2001 to 2016 in (a) March and (b) September. The color scale is adjusted to emphasize the seasonal variations in the western North Pacific.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
Focusing on the western North Pacific, as in the annual mean data (You 2002), there was almost no active SF in September (Fig. 2b). In March (Fig. 2a), there was an active SF distribution mainly along 40°N, east of Japan. The large difference between late winter in March and late summer in September suggests that there are significant seasonal variations.
2) Seasonal and interannual variations of active SF occurrence in the western North Pacific
Seasonal variations in the western North Pacific are evident in Fig. 3, which shows the monthly mean numbers of active SF in each month within the area of 140°E–180° and 30°–45°N for the 16-yr period from 2001 to 2016. The appearance of the active SF was the highest in March, significantly decreased from April to May, reached a minimum in August, and increased from January to March.
Monthly mean occurrence rate of active SF (occurrence number/total grid numbers in each year within 10–300 dbar and the area of 140°E–180°, 30°–45°N, 5-dbar vertical, and 1° × 1° horizontal grids) in the western North Pacific and standard deviation (error bars) for a 16-yr period (2001–16).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The interannual variation of the active SF grid numbers in March in the area of 140°E–180°, 37°–43°N was depicted in Fig. 4a, where we focused on the area limited to 40°N ± 3° because the active SF in the western North Pacific was mainly observed there (Fig. 4b). The minimum number of occurrences in 2009 (approximately 800) and the maximum in 2005 (approximately 2600) were observed, indicating a fourfold variability in the number of occurrences from year to year. When the horizontal distributions of occurrences in 2005 (Fig. 4b), the highest year, were compared with those in 2009 (Fig. 4c), the lowest year, it was seen that there was a significant change in occurrences in the region along 40°N.
(a) Year-to-year variation in the number of active SF occurrences in March in the area of 140°E–180°, 37°–43°N. Also shown is the horizontal distribution in (b) March 2005, the year with the highest number of occurrences, and (c) March 2009, the year with the lowest number of occurrences.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
3) Vertical distribution and structure of active SF in March
The correspondence between the active SF and the salinity-density zonal cross-sectional structure along 40°N in March 2006 is illustrated in Fig. 5a. The latitude of 40°N and the month of March shown in Fig. 5a were chosen because the occurrence of the active SF was highest in March and concentrated at around 40°N (Figs. 2a, 3, and 4a). In this case, we used the March 2016 section as an example, which roughly showed an average number of occurrences (Fig. 4a).
Vertical cross sections of the active SF (denoted by white boxes) distribution superposed over salinity (colors) with potential density (contours) in March 2016 for (a) a zonal section along 40°N and (b) a meridional section along 158°E. The red dashed curves denote the depths of 10-m density +0.02 (kg m−3). The blue dashed curves denote the depths of 10-m density +0.20 (kg m−3). SAB and SAF in the meridional cross section denote the locations of the Subarctic Boundary and the Subarctic Front, respectively, and the Transition Domain (TD) is bounded between SAF and SAB.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The active SF along 40°N was distributed in areas with upward salinity gradient west of 180°, especially between 150°E and 180°, which roughly corresponds to the formation region of Central Mode Water (Suga et al. 1997; Saito et al. 2011). In the vertical direction, the active SF was distributed in the potential density range of 26.1–26.4σθ. It is also noted that the active SF is seen between the red and blue dashed curves, where the red and blue denote the depths of 10-m density +0.02 kg m−3 and the depths of the 10-m density +0.2 kg m−3, respectively. This zone can be recognized as the area just below the mixed layer. The active SF was also observed in the water with a small vertical density gradient of 26.2–26.4σθ between 180° and 160°W longitude. This area corresponds to the SF active zone identified by Saito et al. (2011).
Active SF was examined in the meridional salinity-density vertical cross section along 158°E between 30° and 45°N in March 2016 (Fig. 5b). In this cross section, a large meridional gradient of potential density corresponding to the flow axis of the Kuroshio Extension was observed at approximately 34°N, and the Subarctic Boundary (Favorite et al. 1976), as indicated by the surface salinity of 34 psu, was located at approximately 40°N. Both the temperature and salinity in the 0–200 dbar layer decreased in the northward direction in the area north of the Kuroshio Extension, and the area between the SAB and Subarctic Front (SAF) indexed at 4°C at 100-m depth is called the Transition Domain (TD) (Favorite et al. 1976), which is characterized as a subarctic region where salinity decreases vertically toward the surface. The thermohaline structure in the TD differs from the area north of the SAF at around 43°N in Fig. 5b where the temperature minimum exists, with respect that TD has a subtropical-type temperature structure in which the temperature increases toward the surface (Yasuda 2003). The TD from the SAB to the SAF is an area in which a deep mixed layer forms during winter. The active SF was seen at 37°–41°N from the vicinity of the SAB to the north of the Kuroshio Extension, where salinity increases toward the sea surface and the mixed layer depth (red dashed curve in Fig. 5b) deepens toward the north, and the corresponding density is 25.8–26.4σθ at depth of 10 m. These active SF were mainly distributed in the region between the red and blue dashed curves representing +0.02σθ and +0.2σθ of density increase from the sea surface density, respectively.
The active SF was also observed near the current axis of the Kuroshio Extension (32°–34°N, density 25.1–25.7σθ, and depth of 100–300 dbar). It is known that Oyashio water penetrates into the intermediate layer of the saline Kuroshio Extension, forming a large salinity gradient in the upper part of North Pacific Intermediate Water, characterized by a salinity minimum (Yasuda et al. 1996; Kouketsu et al. 2005), and the active SF was examined by microstructure observation (Nagai et al. 2015). This intrusion of Oyashio water is on a scale of less than a few 10 km horizontally (Kouketsu et al. 2005), which may have been removed from the smoothed MOAA GPV data used in this study.
A recent study (van der Boog et al. 2021), which evaluated vertical diffusivity by detecting SF staircase structures in temperature–salinity vertical profile data observed by Argo floats, did not comment on the presence of active SF in the western North Pacific. By careful examination of their Fig. 2b, it is noticed that the salinity diffusivity was enhanced along 40°N, east of Japan. This enhanced salinity diffusion corresponds to the active SF observed in this study.
4) Active SF during decreasing months
Active SF, which appeared in March along 40°N from 140°E to 180° in the western North Pacific, rapidly decreased from March to June (Fig. 6), although the distribution along 40°N remained even in June around 155°–160° and 170°E and near the east coast of Japan (Fig. 6d). In the vicinity of Japan, where the Oyashio and Kuroshio confluence zones are located, Inoue et al. (2007) reported a structure where cold and fresh Oyashio water penetrated beneath warm and saline eddies and Tsugaru Warm Water. The area at 155° and 165°E is the northward pathway of warm and saline subtropical water (Isoguchi et al. 2006; Masujima and Yasuda 2009), which may have enhanced the superposition of saline subtropical water over northern fresh subarctic water, corresponding to eddy activity around these areas. In March, the active SF is also present in areas south of 40°N, from near the Kuroshio Extension (around 35°N) to the areas south of the Kuroshio Extension where Subtropical Mode Water is formed (Masuzawa 1969), whereas in June, the active SF has almost disappeared.
Horizontal distribution of active SF (vertical grid points accumulated during 2001–16 at each horizontal grid) for (a) March, (b) April, (c) May, and (d) June.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The decay of the active SF was evident in the zonal vertical cross sections along 40°N from March to June 2008 (Fig. 7). The active SF observed in March 2008 at depths of 100–300 dbar in 140°E–180° disappeared from the shallower and lower-density zones to deeper and denser parts and was almost completely absent in June. The active SF (1 < Rρ < 2), which formed just below the winter mixed layer in March and had a relatively high growth rate, could relax the unstable double-diffusive stratification with increasing density stratification, resulting in Rρ > 2 to eliminate the active SF. Enhanced turbulence in the shallow depths with relatively low density also might contribute to decrease in the SF. It is noted that the rapid disappearance of the active SF corresponds to the decay of Central Mode Water that is rapidly stratified after March (Saito et al. 2011).
Zonal sections along 40°N in 2008 for (a) March, (b) April, (c) May, and (d) June. The red dashed curves denote the depths of 10-m density +0.02σθ (kg m−3). The blue dashed curves denote the depths of 10-m density +0.20σθ (kg m−3).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The hydrographic features (Fig. 5a) suggest that the active SF was distributed in a specific density range. The change in the density of active SF in the areas of 140°E–180° and 35°–45°N during the decay period is depicted in Fig. 8a, which shows the histograms of the density of the active SF are shown from March, when the number of occurrences is the highest, to August, when the number is the lowest. Here, the mode of density of the active SF was 26.27σθ in March (mean ± 95% confidence interval: 26.18 ± 0.05σθ), 26.32σθ in April (mean 26.29 ± 0.04σθ), 26.43σθ in May (mean 26.30 ± 0.05σθ), 26.37σθ in June (mean 26.34 ± 0.06σθ), 26.41σθ in July (mean 26.35 ± 0.10σθ), and 26.41σθ in August (mean 26.33 ± 0.08σθ). The mean density increased while the number of occurrences decreased from March to July, corresponding to the disappearance of the shallow and low-density parts of the active SF as observed in the 40°N section (Fig. 7).
Histograms for the potential density anomaly of (a) the active SF (Rρ = 1–2) occurrence during the decay period from March to August and (b) the 10-m-depth horizontal density ratio RL = 1–2 occurrence in March. The occurrences were counted in the western North Pacific (140°E–180°, 35°–45°N).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
b. Hypothesis for active SF formation in March
1) Relation between Rρ at the base of winter mixed layer and surface horizontal density ratio RL
We here attempt to know how the active SF is formed in March along 40°N in the northwestern Pacific. It is known that winter surface mixed layer water is pumped down into the thermocline in the subtropical areas where downward Ekman pumping prevails and that the water characteristic of temperature, salinity, and potential density tends to be preserved along isopycnal surfaces in the pycnocline (e.g., Iselin 1939; Stommel 1979) under weak diapycnal diffusivity. This suggests that the vertical density ratio Rρ = (αθz)/(βSz) in the pycnocline could be related to the horizontal (meridional) density ratio RL = (αθy)/(βSy) in the late winter surface mixed layer in March.
The distribution of RL = 1–2 corresponds well to that of the active SF (Rρ = 1–2). Figure 9 illustrates the horizontal positional relationship among the active SF occurrence (color shade), the areas satisfying 1 < RL < 2 at a depth of 10 m (crosses), the SAB (denoted by the green curve), the SAF (denoted by the red curve), the TD between the SAB and SAF, and the deep mixed layer (>200 m denoted by dots) in March 2008.
Horizontal distribution of the active SF occurrence frequency (color shading) in the western to central North Pacific in March 2008. The SAB and SAF are indicated by the thick green and red curves, respectively. Crosses indicate regions of 1 < RL < 2, and dots indicate regions with a mixed layer depth > 200 m defined by the depth with 10-m density +0.125σθ (kg m−3).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The region satisfying 1 < RL < 2 (crosses in Fig. 9) corresponds to the area from the southern part of the TD to the south of the SAB (green curve) along the SAB. A large number (>10 in the color bar) of the active SF corresponded well to the region noted above, especially in the active SF region with dense occurrence (>20), which corresponded to the area where the deep (>200 m) mixed layer of Central Mode Water and Transitional Mode Water (Saito et al. 2011) were distributed (dots). It is noted that the dense active SF tend to be distributed 1°–2° south of the area of 1 < RL < 2 (crosses).
It is also pointed out that this meridionally narrow and zonally elongated distribution of the horizontal density ratio 1 < RL < 2 along the latitude of 40°N and the SAB in the western North Pacific (crosses in Fig. 9) well corresponds to the zonal distribution of 1.3 < RL < 2.4 along 40°N [horizontal Turner angle Tu(RL) = 67.5°–82.5°] shown in the global map of Tu(RL) in the month of maximum mixed layer depth (Fig. 7b of Johnson et al. 2012).
We next examine the mean density with the horizontal density ratio of RL = 1–2. It is noticed that the potential density of the March surface RL = 1–2 shows a mode at around 26.2σθ in the western North Pacific Ocean (140°E–180°, 35°–45°N) (Fig. 8b) that is similar to the mode density (the mode at 26.27σθ) with Rρ = 1–2 in March (Fig. 8a). This supports the idea that the surface mixed layer water with RL = 1–2 is related to subsurface water with Rρ = 1–2.
Furthermore, the March-averaged potential densities along 40°N in each year with 1 < Rρ < 2 and 1 < RL < 2 in the area of 140°E–180° and 37°–43°N were variable during 2001–16 as shown in Fig. 10, whereas there is a linear relationship [correlation coefficient R = 0.72, significance P < 0.01, the regression of the mean potential density anomaly σθ(1 < Rρ < 2) = 0.55 × mean-σθ(1 < RL < 2) + 11.76] between the March-averaged potential densities with 1 < Rρ < 2 and 1 < RL < 2. This supports the idea that the surface RL was linked with subsurface Rρ on a year-to-year basis. The average density of the active SF (1 < Rρ < 2) is slightly smaller than the average density in the area (1 < RL < 2). Although this lighter density of the active SF might be caused by the entrainment of lighter water during subduction, this issue is a subject for future studies.
Scatterplots of March mean densities in each year in the area of 140°E–180° and 37°–43°N satisfying horizontal density ratio 1 < RL < 2 vs the mean density of the active SF with the vertical density ratio 1 < Rρ < 2. The error bars represent 95% confidence intervals.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
For wider global subtropical oceans, Shimada (2007) compared the mode of winter (January–March) surface Turner angle of RL [Tu(RL)] with the mode of Tu(Rρ) at depth of surface density +0.1σθ in each horizontal 10° × 10° box with the surface temperature of 7°–19°C (Fig. 5.8 in Shimada 2007), and explained the mode Rρ ∼ 3.6 in the Central Water in the subtropical North Pacific (Shimada et al. 2007) by the winter surface RL (Fig. 5.5 in Shimada 2007).
By using the data in the present study, the relation between Tu(Rρ) and Tu(RL) in March is examined in the subtropical North Pacific (140°E–120°W, 20°–45°N), where Tu(RL) at depth of 10 m as surface mixed layer horizontal density ratio and Tu(Rρ) at the mixed layer base, which is here defined as the depth at which the potential density is 10-m density + 0.02σθ. The scatterplot in the SF range of 45° < Tu(Rρ) < 90° (Fig. 11a) shows a dense distribution of dots along the line of Tu(Rρ) ∼ Tu(RL) and a significant positive correlation between Tu(Rρ) and Tu(RL) {R = 0.20, P < 0.01, N = 15 220, and degrees of freedom = 266 [=N/(10.6 × 5.4)] considering smoothing lengths} and thus between the mixed layer RL and Rρ at its base, whereas the data are largely scattered and there are scarce data in the range 72° < [Tu(RL), Tu(Rρ)] < 90° even for the data in the target area along 40°N (140°E–180°, 37°–43°N) (red dots in Fig. 11a).
Scatterplots between the mixed layer horizontal Turner angle Tu(RL) and the vertical Turner angle Tu(Rρ) at its base in the whole North Pacific subtropical area (140°E–120°W, 20°–45°N) in the range 45° < Tu < 90° during 2001–16: (a) Mixed layer base is set at depth of 10-m density +0.02σθ. (b) Nearest Rρ → +1 is searched at 1° south of RL and vertically at depth of 10-m density from +0.02σθ. to +0.2σθ. Red dots denote the data along 40°N in the western North Pacific (140°E–180°, 37–43°N); 72° < Tu(Rρ) < 90° indicates the active SF (1 < Rρ < 2).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
When the search of Rρ is changed to the horizontal grid 1° south of each RL grid at which nearest Rρ → +1 is selected in the vertical extent of 10-m density from +0.02 to 0.2σθ, considering that the dense active SF tend to be distributed 1°–2° south of the area of 1 < RL < 2 (Fig. 9) and that the active SF appeared in the density range (as in Fig. 5) where surface mixed layer possibly temporarily deepens or shoals in the late winter of March. The scatterplot (Fig. 11b) shows that the dense distribution of dots along the line of Tu(Rρ) ∼ Tu(RL) extends to 72° < [Tu(RL), Tu(Rρ)] < 90° involving the data in the target area along 40°N (140°E–180°, 37°–43°N) (red dots in Fig. 11b). The positive correlation between Tu(Rρ) and Tu(RL) is significant (R = 0.21, P < 10−4, N = 23 554, and degrees of freedom = 411).
2) Hypothesis for the active SF formation
The correspondences between the thick Rρ = 1–2 distribution and the hydrographic structures (RL = 1–2, SAB, and deep mixed layer) (Fig. 9) as well as between the density modes of Rρ = 1–2 (Fig. 8a) and RL = 1–2 (Fig. 8b) and between the mean densities of surface mixed layer RL = 1–2 and its base Rρ = 1–2 in each year (Fig. 10) and the scatterplot between RL and Rρ in the subtropical North Pacific (Fig. 11b) support a hypothesis that the surface mixed layer water with RL = 1–2 sinks (subducts) beneath saline water with nearly conserving its potential density, forming a water mass of active SF that satisfies Rρ = 1–2 by vertical overlapping. This hypothesis is schematically shown in Fig. 12b.
Hypothesis of the active SF formation in March along the SAB at around the latitude of 40°N: (a) Zoom-in of the meridional salinity–density vertical cross section at 158°E (Fig. 5b), and (b) schematic representation of along-isopycnal subduction from surface mixed layer with the meridional density ratio of 1 < RL < 2 and vertically superposed with conserving potential density, resulting in vertical density ratio of 1 < Rρ < 2. This could be possible in the area where the mixed layer deepens northward. In (a), color shades denote salinity, black curves denote isopycnal (isopotential density) contours, numerals denote potential density anomaly in σθ, and white boxes denote the active SF. In (b), blue curves denote isopycnal contours and the red dashed curve denotes mixed layer base. In (a) and (b), the green double arrows indicate the latitudes of 1 < RL < 2. The inclined sky-blue bar in (b) represents mixed layer slumping (lighter water overrides heavier water) of the density front (see section 4a for details).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The structures of the density and surface mixed layer of this hypothesis (Fig. 12b) are consistent with the salinity and density structures along 158°E (Fig. 12a, which is a zoom-in of Fig. 5b). The surface mixed layer deepens in the northward direction (the red dashed curves in Figs. 12a,b) near the SAB and the southern part of the TD with 1 < RL < 2 (green arrows near the surface in Figs. 12a,b) connected to the sloping isopycnals at the bottom of the mixed layer (26.1–26.4σθ contours in Fig. 12a and the blue curves in Fig. 12b). The sloping isopycnals suggest eastward geostrophic flow. The reason why the area of 1 < RL < 2 is formed along 40°N and SAB is beyond the focus of the present study, and it is discussed in section 4a on the basis of previous studies and speculation.
c. Interannual variations of active SF in March
1) Trend in the decreasing density, warming and shoaling of the march active SF during 2001–16
Focusing on the month of March, when the active SF occurrences are the highest, which suggests the formation of active SF, we examined the interannual variation in the mean density of the active SF (1 < Rρ < 2) areas (solid line in Fig. 13a), where a decreasing trend is found in the mean density from 2001 to 2016 (density decrease ∼0.2 kg m−3), with a rate of 0.11 kg m−3 over the 10-yr period.
Interannual variations in the (a) mean potential density, (b) mean temperature of the active SF (1 < Rρ < 2; solid lines) and of the horizontal density ratio of 1 < RL < 2 (dashed lines), and (c) mean depth (dbar) of the active SF in the western North Pacific within the area of 140°E–180° and 37°–43°N in March. Error bars represent the 95% confidence intervals of the mean density for each year. There are trends in the period from 2001 to 2016 in the (a) decreasing mean density [in (a)], warming of the active SF and RL = 1–2 [in (b)], and shoaling of the active SF [in (c)].
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
This decreasing density trend well corresponded to the warming trend of the active SF (solid line in Fig. 13b). The warming reached about 2°C during 2001–16, with a rate of about 1°C over the 10-yr period. Salinity of the active SF did not show well-defined trend (not shown). It is also noted that the mean depth of the active SF showed a shoaling trend (depth decrease of ∼20 m during 2001–16) with large interannual variability (Fig. 13c).
2) Trend in the decreasing density and warming of winter mixed layer 1 < RL < 2
We may explain the trends in decreasing density and warming of the active SF (1 < Rρ < 2) in March by the density decrease and warming at surface in the area with the horizontal density ratio 1 < RL < 2, if the hypothesis for the active SF formation along 40°N in March is valid. Conversely, the relationship supports the hypothesis that these trends of the active SF in March is related to the density decrease and warming in the area of 1 < RL < 2.
The interannual variation of the mean potential density of 1 < RL < 2 (dashed line in Fig. 13a) shows clear decreasing trend during 2001–16 (density decrease ∼0.2 kg m−3), with a rate of 0.1 kg m−3 over the 10-yr period. The decreasing rate of 1 < RL < 2 is similar to the one of 1 < Rρ < 2.
The temperature T10 at a depth of 10 m averaged in the region of 1 < RL < 2 (dashed line in Fig. 13b) showed a clear warming trend during 2001–16 and was negatively correlated with the mean density (correlation coefficient r = −0.86; r2 = 0.74). This warming trend in the winter surface mixed layer within 1 < RL < 2 could explain the trends in density decrease and warming of the active SF (Figs. 12a,b). The temperature at 10 m in March in the region satisfying 1 < RL < 2 was well approximated as T10(°C) ≈ 0.057 × (AD year − 2000) + 8.412. The mean salinity at 10 dbar in the region of 1 < RL < 2 did not show trendlike features but interannually varied, as the mean and standard deviation were 34.04 ± 0.04 psu (not shown).
The horizontal distribution of the correlation coefficients between the mean T10 in the region satisfying 1 < RL < 2 in March and March T10 at each location in the North Pacific is illustrated in Fig. 14 for the period of 2001–16. The region of significant correlation (correlation coefficient R > 0.497, P < 0.05) extended near the area at approximately 40°N latitude and 150°–170°E in longitude that roughly coincided with the region satisfying 1 < RL < 2.
Distribution of correlation coefficients between the 10-m-depth temperature averaged over the area satisfying 1 < RL < 2 in March and the 10-m temperature at each location from 2001 to 2016. The contours indicate a correlation coefficient R = 0.497, indicating that the correlation is significant at greater than 95% confidence.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
The horizontal distribution of the March T10 trend (°C yr−1) from 2001 to 2016 in the North Pacific region is shown in Fig. 15. The average rate of increase in T10 in the region satisfying 1 < RL < 2 is 0.057°C yr−1 (Fig. 13b), with a similar rate of increase seen in the area at approximately 40°N in the longitude of 140°–170°E. The warming trend in this region was particularly high in the North Pacific. This warming trend in the surface mixed layer is thought to have affected the decrease in density in the SF formation area. This fact that the density of the SF active region is decreasing is the first to show that global warming is affecting salt finger double-diffusion as far as the authors notice.
The 10-m-depth temperature T10 trend (°C yr−1) in March from 2001 to 2016 in the North Pacific. The thick black contours denote the trend of 0.057°C yr−1.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
3) Factors contributing to the interannual occurrence variation of active SF
Here, we discuss the reason for the year-to-year variation in total active SF occurrence (detected number of active SF grids) in March (Fig. 4a). The occurrence was composed of the horizontal extent multiplied by the vertical extent. The first question is which (horizontal or vertical) extent is important for the year-to-year occurrence variation.
It has been suggested that the active SF area in March is horizontally distributed along 40°N latitude from the area near the Subarctic Boundary (SAB) to its northern TD, where the horizontal density ratio 1 < RL [=(αθy)/(βSy)] < 2 and the mixed layer deepens northward (Figs. 5b, 9, and 12). In the vertical direction, it is often present in the 26.1–26.4σθ from a 10-m-depth density of +0.02σθ to a depth of +0.2σθ.
We counted the number of grids satisfying all the three horizontal and the one vertical conditions: 1) from 1°N to 3°S of SAB, 2) RL = 1–2, and 3) northward deepening of the mixed layer depth, and 4) 10-m-depth density from +0.02σθ depth to +0.2σθ depth. The total number of grids satisfying all the four conditions corresponded well with the interannual variation in the total number of active SF detections in March (Fig. 16). The correlation coefficient is 0.74 at the 99% significance level, which is approximated by the regression SF occurrences = 0.6244 × (number of grids satisfying the conditions) − 264.53. This indicates that the variation in the number of SF occurrences in March can be explained by the variation in horizontal and vertical conditions.
Total number of SF occurrences in March within the area of 140°E–180° and 35°–45°N (solid line), and the interannual variation in the number of grids satisfying the three horizontal and one vertical conditions (dashed line).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0244.1
4. Discussion
a. Possible formation mechanism of RL = 1–2 along the SAB in the western North Pacific
The SAB was identified as the zonal salinity front along 40°N in the western and central North Pacific (Favorite et al. 1976). Roden (1975, 1977) found that the SAB (“subarctic front” in his papers) is density compensated (but with temperature and salinity gradient), implying RL ∼ 1, and discussed the frontogenesis of the SAB. Yuan and Talley (1996) described the subarctic frontal zone and also identified the SAB as density-compensated (RL ∼ 1) temperature and salinity front. Masujima and Yasuda (2009) described the water-mass formation by the convergence of northward saline subtropical water as geostrophic current and near-surface southward low-salinity Ekman drift in the Transition Domain in the western and central North Pacific.
For a zonal salinity front with large meridional gradient assuming ∂/∂x = ∂/∂z = 0 in the salinity advection equation [∂S/∂t = −υ(∂S/∂y)] in a vertically uniform mixed layer,
Ferrari and Young (1997) showed that strong winter convection following the slumping (lighter water overrides heavier water) of density front in winter mixed layer forms density-compensated (RL ∼ 1) temperature and salinity front, and this process is equivalently expressed as horizontal mixing whose diffusivity is nonlinear function of the density gradient (Young 1994; Chin and Young 1995; Ferrari and Young 1997). The slumping is schematically depicted in Fig. 12b as the inclined blue bar. Rudnick and Ferrari (1999) observed such RL ∼ 1 fronts in the length scales of 10 m–100 km. The mixed layer slumping process under winter convection is similar to submesoscale mixed layer instability and was examined (e.g., Fox-Kemper et al. 2008; McWilliams 2016). This mixed layer (slumping) instability along the SAB where northward saline subtropical water (as geostrophic current) and near-surface southward low-salinity Ekman drift converge (for ∂τx/∂y > 0 and υG + υEK = 0) could generate density-compensated SAB with RL ∼ 1–2. This qualitative view of the density-compensated SAB needs further quantitative studies with respect of the SAB frontogenesis and submesoscale mixed layer instability.
b. Validity of the hypothesis on the relation between surface RL and subsurface Rρ (active SF formation) in the global subtropical oceans
This study supports the hypothesis that “vertical layering of water masses with the horizontal density ratio in the winter surface mixed layer in the late winter of March forms the active SF region with the vertical density ratio,” which could explain the formation of the SF active region along the SAB in March in the western North Pacific as well as large Rρ (>2) in the subtropical North Pacific (Fig. 11). The idea on the relationship between RL and Rρ was originally introduced by Stommel (1993) and Stommel and Young (1993) where the vertical density ratio Rρ (∼2) in the Atlantic and Indian Oceans can be explained by RL. Shimada (2007) and K. Shimada (2023, personal communication) showed relations between Rρ and RL in the global subtropical oceans.
We here discuss the possibility of the active SF formation (Rρ = 1–2) from winter surface mixed layer RL = 1–2 in the global subtropical oceans as in the Atlantic, the south Indian Ocean, the South Pacific and the eastern North Pacific. We notice a striking correspondence between the active SF (Rρ = 1–2) frequency distribution (Fig. 2) and the distribution of Turner angle Tu(RL) = 67.5°–90° (1 < RL < 2.4) (Fig. 7b in Johnson et al. 2012), except that the active SF (Fig. 2) extends toward lower latitude than the area of Tu(RL) = 67.5°–90°. This extension could be explained by the equatorward subtropical circulation, which transports the active SF water along isopycnal surfaces, although further quantitative studies are necessary to validate this speculation.
These studies support the hypothesis that winter surface RL distribution determines Rρ of the subducted water in the subtropical area. The reason why SF is less active in the western North Pacific than in the Atlantic, the south Indian Ocean and the South Pacific could be attributed to the much less area with RL = 1–2 in the western North Pacific than in the other subtropical oceans (Fig. 7b in Johnson et al. 2012). The difference in the areas with RL = 1–2 in each ocean might be related to the basin-scale salinity. The lower salinity in the North Pacific than in the other oceans might lead to the lower salinity gradient in the meridional direction. In addition, in the North Atlantic where northward heat transport prevails following the meridional overturning circulation, meridional temperature gradient is less than in the North Pacific. Both the lower temperature gradient and the higher salinity gradient might make RL less in the North Atlantic. We need further quantitative studies to validate this speculation.
c. Impact of active SF and decreasing density and warming trends of the active SF and RL = 1–2 on ecosystem and material circulation
It is known that the area along 40°N in the western North Pacific is where nutrient and dissolved inorganic carbon concentrations largely decrease from winter to summer and the decrease takes the horizontal maximum along 40°N (Yasunaka et al. 2014), indicating high biological production drawdowns nutrients and carbon. Since the active SF along 40°N and SAB could enhance nutrient vertical diffusivity (e.g., Hamilton et al. 1989), the nutrient supply to the ecosystem and fixing of carbon dioxide could be strengthened along 40°N. Future studies on the nutrient supply and biological productivity associated with the enhanced vertical diffusion of salinity and nutrients by SF are expected.
The warming and decreasing density trends in the active SF and in the areas of RL = 1–2 (Figs. 13a,b) was found to be accompanied by the shoaling of the active SF depth (Fig. 13c). These shoaling and warming trends might activate biological productivity along 40°N and SAB if the enhancement of vertical diffusion of nutrients by the active SF occurs at shallower depths and warmer water that enhances species of warmer living phytoplankton. Conversely, these same trends might inactivate biological productivity if colder-water species dominate.
The distribution of SST trend in March (Fig. 15) shows the warming (cooling) south (north) of 40°N in the longitude of 150°–165°E, indicating the enhancement of SST gradient. Considering that there was no obvious trend in the surface salinity (not shown), this increasing SST gradient might lead to the increase of RL and the decrease of the active SF. Whereas, the density-compensation mechanism of RL → 1 along the SAB (e.g., Ferrari and Young 1997; Rudnick and Ferrari 1999) might relax this RL increase; it is indeed the decreasing occurrence trend of active SF is not obvious due to the dominance of interannual variability (Fig. 4a). On the other hand, there is a sign of slight decreasing trend (the occurrence decreased from ∼2000 in 2001 to ∼1500 in 2016 in Fig. 4a), implying the discourage of the biological productivity. We need further studies on the change of the SAB and the active SF and its impact on the biological productivity.
5. Summary
The large-scale distribution and variation of active salt finger (SF) in the western North Pacific were examined by detecting the active SF with the vertical density ratio Rρ = (αθz)/(βSz) = 1–2 at depths of 10–300 m based on a monthly gridded hydrographic dataset (MOAA GPV) in the period from 2001 to 2016. First, the validity of active SF detection using the data with heavy horizontal smoothing and low vertical resolution was evaluated by comparing it with concurrent ship-based high-quality hydrographic data, which revealed that the active SF along 40°N was reasonably detected at 150°–165°E, but not west of 150°E, where mesoscale ∼O(10)-km structures were dominant and the active SFs were smoothed out by large-scale ∼O(100)-km interpolation.
Although SF has been previously recognized as inactive in the western North Pacific by using annual-mean hydrographic data, the present study demonstrated that the active SF is distributed in March along the latitude of 40°N in the western North Pacific around the Subarctic Boundary (SAB) and in the southern part of the Transition Domain, where the winter surface mixed layer deepens northward and corresponds to the formation site of Central Mode Water at depths, just below the winter mixed layer down to the density +0.2σθ of surface density and mainly in the density range of 26.1–26.4σθ. This active SF along 40°N underwent remarkable seasonal variation and decayed rapidly from March to August from the shallower and less dense parts of the active SF with increasing mean density.
The mixed layer, thermohaline, and density structures of the active SF in March are consistent with the hypothesis that a surface mixed layer with a horizontal density ratio in the meridional direction 1 < RL [=(αθy)/(βSy)] < 2 is subducted and vertically superposed, resulting in an active SF with 1 < Rρ < 2. The fact that the mean density of the active SF in March is well correlated with that of the surface 1 < RL < 2 and that the mean density of the active SF showed a decreasing trend from 2001 to 2016 following the surface temperature increasing trend (∼0.057°C yr−1) in the area with 1 < RL < 2, further supports this hypothesis.
Interannual variations in the detection of the active SF in March were large, and it was relatively large in years 2004–05, 2008, 2012, and 2013 and less in 2002, 2006, 2007, 2009–11, and 2014–15. This variability is explained by both horizontal and vertical extensions with a significant positive correlation between the two (i.e., vertically thicker in years of wider horizontal extension), and the contribution from vertical extension is greater than that from horizontal extension. This suggests that the formation of the active SF in the western North Pacific is linked to the thickness variability of Central Mode Water. The year-to-year variations of the active SF in March in the area of 37°–43°N and 140°E–180° can be reproduced by the four conditions: 1) from 1°N to 3°S of SAB, 2) RL = 1–2, and 3) northward deepening of the mixed layer depth, and 4) the 10-m-depth density from +0.02σθ depth to +0.2σθ depth.
The active SF might contribute to biological production in the western North Pacific through enhanced vertical nutrient diffusivity and nutrient supply to biological production. The warming and shoaling trends of the active SF could influence on ecosystem. To further quantify the impact and make clear the mechanisms and variations, further observational and modeling studies are required.
Acknowledgments.
The authors thank Prof. Jiro Yoshida and Dr. Keishi Shimada for introducing the studies on double-diffusive convection and valuable discussion. This study was supported by KAKEN JP20H05598, JP20H04965, JP21H04921, JP21H05056, JP22H04486, and JP22H05205.
Data availability statement.
The temperature/salinity/pressure gridded data are available online (https://www.jamstec.go.jp/argo_research/dataset/moaagpv/index_dataset.html).
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