Modification of North Pacific Intermediate Water around ...svr4.terrapub.co.jp/journals/JO/pdf/5902/59020211.pdf · North Pacific Intermediate Water (NPIW) is defined as broadly spreading

211

Journal of Oceanography, Vol. 59, pp. 211 to 224, 2003

Keywords:⋅ North PacificIntermediateWater,

⋅ Mixed WaterRegion,

⋅ mixing,⋅ neutral surfaces,⋅ cabbeling,⋅ double diffusiveconvection.

* Corresponding author. E-mail: [email protected]

Copyright © The Oceanographic Society of Japan.

Modification of North Pacific Intermediate Water aroundMixed Water Region

RYUICHIRO INOUE1*, JIRO YOSHIDA1, YUTAKA HIROE2, KOUSEI KOMATSU2,KIYOSHI KAWASAKI2 and ICHIRO YASUDA3

1Department of Ocean Sciences, Tokyo University of Fisheries, Konan, Minato-ku, Tokyo 108-8477, Japan2National Research Institute of Fisheries Science, Fukuura, Kanazawa-ku, Yokohama, Kanagawa 236-8648, Japan3Department of Earth and Planetary Physics, Graduate School of Science, University of Tokyo, Yayoi, Bunkyo-ku, Tokyo 113-0033, Japan

(Received 18 February 2002; in revised form 13 September 2002; accepted 26 September 2002)

The mixing processes in the Mixed Water Region (MWR) that lead to changes in theproperties of North Pacific Intermediate Water (NPIW) have been studied using ob-servational data sets obtained in May–June 1998. Neutral surfaces, the equation ofwater mass conversion rate on neutral surfaces and the equation of vertical velocityacross neutral surfaces have been used to distinguish dominant processes by assum-ing the horizontal scale to be the streamer scale (under 100 km). The possibility ofdouble diffusive convection is also discussed in relation to the density ratio. Theseresults may be summarized as follows: (1) the difference between the potential den-sity surface and the neutral surface may rise to –0.04 kg/m3 around the source waterof NPIW; (2) horizontal diffusion causes strong modifications of the source water ofNPIW; (3) the density range within which strong modification of the source water ofNPIW occurs becomes dense from the northern part of MWR near the Oyashio Frontto the southern part near the Kuroshio Front, and to the eastern part. Our modelingof these processes shows that cabbeling has effects on the density increment of thesource water of NPIW in the northern and southern part of MWR. Double diffusiveconvection has effects on the density increment of the source water of NPIW, mainlyin the northern part of MWR. The possible density increment due to cabbeling inthese areas is estimated to be 0.01~0.03 kg/m3. The possible density increment due todouble diffusive convection is 0.01~0.03 kg/m3. The total density increment due tocabbeling and double diffusive convection amounts to 0.06 kg/m3.

face does not reach this density in the North Pacific.The density of the NPIW must increase due to some

mixing processes occurring below the sea surface. Talley(1993) and Talley et al. (1995) suggested that the salinityminimum in NPIW is originated from the Oyashio wintermixed layer, which has a density of around 26.50–26.65σθand a salinity of 33.30~33.40PSU. This water intrudesbeneath the Kuroshio water in the northern part of theMixed Water Region (MWR), the area between theOyashio and the Kuroshio. This water is then eroded bythe upper layer and increases i ts salinity (to33.80~34.00PSU) and density (to 26.80σθ) through ver-tical mixing processes to form new NPIW in MWR. Onthe other hand, Yasuda (1997) suggested that the salinityminimum in NPIW has its origin in the Okhotsk Sea Mode

1. IntroductionNorth Pacific Intermediate Water (NPIW) is defined

as broadly spreading low salinity water (33.80~34.10PSU)around the mid depth (300~800 m) of the North Pacific,and is considered to originate in the subpolar region (e.g.,Sverdrup et al., 1942). This water intrudes into the sub-tropical gyre as a cross gyre flow and spreads into themid depth of the North Pacific. Reid (1965) pointed outthat the salinity minimum could be traced on a 26.80σθsurface; he also demonstrated that the outcropping sur-

212 R. Inoue et al.

Water, characterized its low salinity (33.50~33.60PSU)and low potential vorticity around 26.70~26.90σθ. Thiswater is formed by the release of brine during the forma-tion of winter ice in the northern part of the Okhotsk Sea,coupled with the vertical mixing there and near the KurilIslands. This water intrudes into MWR and then mixesisopycnally with the Kuroshio water near the KuroshioExtension (the southern part of MWR) to become saltier(33.80~34.00PSU) and become new NPIW. Previous in-vestigations have differed in their analyses and opinionsas to the source of the salinity minimum, the amount ofdensity increment, modification processes and the areawhere strong modification occurs.

However, the key to understanding the main sourceof the salinity minimum in NPIW is to identify the mix-ing processes and mixing areas, and to estimate the den-sity increment of the source water of NPIW around MWR.The reader should note that MWR has a complicated struc-ture (see, e.g., figure 1 in Yasuda et al., 1996). The north-ern part of MWR contains the Oyashio and the OyashioFront. The southern part of MWR contains the KuroshioExtension and the Kuroshio Front. The locations of thesefronts are 3°~5° from each other. Many streamers andwarm core rings can be seen in MWR. These meso-scalefeatures may contribute to the modification of NPIW. Onthis assumption, therefore, we have examined the modi-fication of NPIW in relation to the detailed oceanic struc-tures.

This study is as follows: Section 2 explains the ob-servation data sets. Section 3 presents our analytical meth-ods and possible mixing processes. Section 4 describeshydrographic features and possible mixing processes thatmay modify NPIW in MWR. The possible density incre-ment of NPIW due to these processes is discussed in Sec-tion 5; conclusions are presented in Section 6.

2. Observation and DataWe have used CTD and RMS bottle sampled data

obtained by R/V Soyo-maru (National Research Instituteof Fisheries Science) during its course from 18 May to12 June 1998. This survey was planed to clarify thehydrographic structure of NPIW, to estimate mass trans-port between the Oyashio and the Kuroshio, and to eluci-date dynamic features of the Oyashio intrusion and ex-change process across the Kuroshio Extension. The dataused in this study (Fig. 1) are a part of all observationscarried out during the cruise. Data from Sea-bird 911 PlusCTD have been used for observations of temperature andsalinity. CTD salinity data have been calibrated againstbottle sampled salinity data. Overall residual rms errorsare within 0.002PSU. The accuracy of temperature andpressure sensors is within 0.002°C and 1 dbar (Yasuda etal., 2001).

3. Analysis Methods

3.1 Neutral surfacesIsopycnal analysis has been used to trace the salin-

ity minimum of NPIW. However, potential density fixesreference pressure and neglects the thermobaric effect inthe equation of state. Therefore, water parcel does notnecessarily move along potential density surfaces with-out being affected by the buoyancy force. On the otherhand, neutral surfaces (McDougall, 1987a) explicitly in-clude the thermobaric effect in the equation of state. Inthis context, You et al. (2000) used neutral surfaces as areference frame for the study of NPIW and found that theneutral surface followed the salinity minimum surfacebetter than potential density surface. Neutral surfaces arealso applied in this study.

A neutral surface is defined as

α θ θ β θS P S P Sn n, , , , .( )∇ = ( )∇ ( )1

Here α is the thermal expansion coefficient, β is thehaline contraction coefficient and ∇ n is horizontal gradi-ent on a neutral surface.

Neutral surfaces are defined by the method ofMcDougall (1987a) rather than that of Jackett andMcDougall (1997) in this study for convenience in com-paring differences between the neutral surface and thepotential density surface. The relations between two CTD

Fig. 1. Observation points used this study. These points are apart of observation conducted by R/V Soyo-maru in 1998.St. 113–St. 124 is named as Section 5, St. 124–St. 139 asSection 6. St. 147–St. 155 as Line1, St. 156–St. 164 asLine2, and St. 165–St. 173 as Line3, Line1~Line3 are calledas Kuroshio Extensive survey. Station intervals are about37.0 km for Section 5, about 37.2 km for Section 6, about31.5 km for Line1~Line3, respectively.

Modification of North Pacific Intermediate Water around Mixed Water Region 213

casts determine neutral surfaces. We use potential den-sity at St. 147 (the eastern most station along Line1) as areference density. The difference between two surfaces(σθ–σn) is calculated to clarify the thermobaric effect onNPIW. Here σθ is a potential density calculated on a con-stant neutral surface, σn is a neutral surface calculatedfrom St. 147 by Eq. (1).

3.2 Possible candidate for density increment of NPIWWe describe possible processes that can induce down-

ward density fluxes to increase the density of NPIW,cabbeling, double diffusive convection andthermobaricity.

Cabbeling occurs due to the nonlinear dependenceof the thermal expansion coefficient on temperature inthe equation of state (e.g., Foster, 1972). When two wa-ter masses on a neutral surface, having different tempera-ture and salinity, mix completely, this new water massbecomes heavier. This effect becomes large at low pres-sure and temperature.

Double diffusive convection is driven by the differ-ence between molecular diffusivities in salt and heat.When salty, hot water overlies fresh, cold water, a saltfinger occurs. Both salt and heat are transported down-ward. However, the downward density flux due to salt isgreater than the upward density flux due to heat, and anet downward density flux is then induced. When thestratification of heat and salt is in the opposite sense, adiffusive convection occurs. In this case, both salt andheat are transported upward, but the downward densityflux due to heat is greater than the upward density fluxdue to salt, and a net downward density flux is then gen-erated. Both types of double diffusive convection resultin a lower, heavier layer. The source water of NPIW in-trudes under the Kuroshio water in MWR, the salt fingershould cause the source water of NPIW to be saltier andheavier.

Thermobaricity occurs due to the nonlinear depend-ence of the thermal expansion coefficient on pressure inthe equation of state. However, this effect is often ne-glected by using potential density (see Subsection 3.1).Thermobaricity should have effects on the modificationof NPIW. When a water parcel is mixed and moves alonga neutral surface, the dependence of the thermal expan-sion coefficient on pressure changes, and then this waterparcel has the possibility to become either heavier orlighter.

3.3 Detection of possible mixing processesTo clarify the effectiveness of each mixing process,

we use the equations of water mass conversion rates andvertical velocities derived by McDougall (1987b).

The equations of water mass conversion rate for heatand salt are defined as

∂∂

+ − ∇( ) ⋅ ∇ = ∇ + ∂∂

+ ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

+ ∂∂

∇ ⋅ ∇ ∂∂

− ∂

−

−

−

θ θ θ θ βθ

θ θ αθ

αβ

α αβ

β

θ θ α αβ

tV K K DgN

z

d S

d

KgNz S S

KgNz

PP

nn n n

n

n n

2 23 2

2

2 22

2

2

2

ββ∂

( )P

, 2

and

∂∂

+ − ∇( ) ⋅ ∇ = ∇ + ∂∂

+ ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

+ ∂∂

∇ ⋅ ∇ ∂∂

− ∂

−

−

−

S

tV K S K S DgN

z

d S

d

KgNS

z S S

KgNS

zP

P

nn n n

n

n n

2 23 2

2

2 22

2

2

2

θ αθ

θ αθ

αβ

α αβ

β

θ α αβ

ββ∂

( )P

. 3

Here, g is the gravitational acceleration (m/s2), N2 isthe buoyancy frequency (1/s), D is the vertical diffusiv-ity (m2/s), K is the horizontal diffusivity (m2/s), and Vn isthe horizontal advective velocity along a neutral surface(m/s). ∂θ/∂z is the vertical potential temperature gradi-ent, ∂S/∂z is the vertical salinity gradient. The verticalaxis z is positive upward. These equations represent po-tential temperature and salinity modification rates due toeach process on a neutral surface. We replace ∇ n with thedirection of observation line alone in this study, due tolimitations of observation points. However, we believethat is sufficient to compare the magnitude of the twomodification processes. On the right-hand side of theseequations, the first term is the water mass conversion ratedue to horizontal diffusion, the second one represents theconversion rate due to turbulence, the third one due tocabbeling, and the forth one due to thermobaricity, re-spectively.

The vertical velocity equation is defined as

Area (horizontal mixing scale) Horizontal diffusivity(m2/sec)

Section 5 (∆X = 74.0 km) 310.7

Section 6 (∆X = 74.4 km) 312.9

Line1–Line3 (∆X = 63.0 km) 250.7

Table 1. Horizontal scale and horizontal diffusivity for eacharea used in this study.

214 R. Inoue et al.

eD

zgN D

z

S

z

KS S

K PP P

e

n

e

n n

e

− ∂∂

= ∂∂

− ∂∂

− ∇ ∂∂

+ ∂∂

− ∂∂

− ∇ ⋅ ∇ ∂∂

−∂

( )

−

( )

( )

( )

22

2

2

2

22

22

4

α θ β

θ αθ

αβ

α αβ

β

θ α αβ

αβ

turb

cabb

therm

.

Here e is the total vertical velocity (m/s) across aneutral surface. On the right-hand side of this equation,eturb, ecabb and etherm are vertical velocity due to turbu-lence, cabbeling and thermobaricity, respectively. Thesalinity and temperature data for insertion into these equa-tions could be obtained from CTD casts. The vertical dif-fusivity (D), horizontal diffusivity (K) and their typicalmixing scales remain to be determined. Vertical scale andvertical diffusivity are taken to be ∆Z = 10 m and D =10–5 m2/s (e.g., Gregg, 1989). Streamers and eddies fromthe Kuroshio Extension and the Oyashio could drive hori-zontal mixing in MWR. These horizontal scales could beunder 100 km. We approximate this scale (∆X) by the dis-tance between three observation points, and then hori-zontal diffusivity is obtained from the relation given byOkubo (1971). We use constant diffusivities for each areato simplify these equations. Table 1 shows the horizontalscales and horizontal diffusivities used in this study. Ver-tical velocities by different diffusivities are calculated andcompared in Subsection 5.1.

The possibility of double diffusive convection is in-vestigated in terms of the density ratio, which is definedas

Rz

S

zρ α θ β≡ ∂∂

∂∂

( ). 5

Vertical gradients are calculated from CTD casts with10 m least squares fitting. When Rρ approaches unity, boththe salt finger and diffusive convection become vigorous(Schmitt, 1998). The occurrence frequency of double dif-fusive convection in 26.00~27.00σn is used to grasp thearea dependency for the potential occurrence of doublediffusive convection.

4. Results

4.1 Hydrographic featuresWe present vertical cross-sections of potential tem-

perature, salinity and difference between potential den-sity surfaces and neutral surfaces.

Section 5 (Figs. 2(a) and (b)) includes the OyashioFront between St. 117 and St. 118. The cold fresh water(below 5.00°C and 33.70PSU) is encircled by the warmsaline water (above 7.00°C and 33.90PSU) to the southof this front. The cold and warm waters were considered

Fig. 2. Vertical cross sections of potential temperature (a), sa-linity (b) and difference between neutral surface and po-tential density surface (c) along Section 5. The vertical axisis the neutral surface. The horizontal axis is distance fromSt. 124, the southernmost station along Section 5. Contourinterval is 1.0°C, 0.1PSU and 0.01 kg/m3, respectively. In-verted triangles are observation stations.


to be a cold fresh core ring detached from the Oyashioand a warm streamer from the Kuroshio Extension, re-spectively (Yasuda et al., 2001). Thus, this feature sug-gests that horizontal mixing must occur between warmstreamer and cold fresh core ring. This cold fresh corering originates from the Oyashio winter mixed layer(Yasuda et al., 2001). Line1 in the Kuroshio Extensivesurvey (Figs. 3(a) and (b)) includes the Kuroshio Frontbetween St. 150 and St. 151. There is a salinity minimum(below 6.00°C and 33.80PSU) around 26.50~26.70σn andlow salinity water (below 6.00°C and 33.80PSU) around

26.30~26.90σn. These waters are adjacent to the KuroshioExtension water (above 8.00°C and 34.20PSU). This fea-ture suggests that horizontal mixing occurs between theKuroshio Extension and the salinity minimum water. Itshould be noted that the warm saline water and the coldfresh water along Line1 are warmer and saltier than thesealong Section 5. Along Section 6 (Figs. 4(a) and (b)), thesalinity minimum (33.70~33.90PSU) has distributedaround 26.70~26.80σn suggesting that mixing betweenthe Kuroshio and Oyashio waters has gradually formednew NPIW.

Fig. 3. As in Fig. 2, but along Line1. The horizontal axis isdistance from St. 155, the westernmost station along Line1.

Fig. 4. As in Fig. 2, but along Section 6. The horizontal axis isdistance from St. 139, the southernmost station along Sec-tion 6.

216 R. Inoue et al.

The difference between two surfaces (σθ–σn) alongSection 5 (Fig. 2(c)) becomes –0.04~–0.03 kg/m3 in thenorth of the Oyashio Front. Since St. 147 has been se-lected as a reference density to calculate neutral surfaces,this feature indicates that a water parcel that advects alongthe neutral surface from St. 147 on 26.80σθ becomes26.76σθ in the Oyashio region. Therefore, the potentialdensity at the Oyashio region is heavier than that in theKuroshio region. The difference becomes –0.02 kg/m3

around the salinity minimum in the cold fresh core ring,and it becomes –0.03~–0.02 kg/m3 below the salinityminimum. The difference along Line1 (Fig. 3(c)) becomes–0.03~–0.01 kg/m3 around the salinity minimum. On theother hand, the difference in the Kuroshio water becomes+0.01~+0.03 kg/m3. The difference along Section 6 (Fig.4(c)) becomes –0.03~–0.02 kg/m3 around the salinityminimum. These results suggest that the thermobaric ef-fect exerts a significant influence on the source water ofNPIW and varies from place to place. The lower the tem-perature becomes, or the higher the pressure, the largerthe thermobaric effect becomes. These results also sug-gest that the thermobaric effect may be important whencalculating the mixing ratio on potential density surfaces,as used in discussions of the formation of NPIW.

4.2 Mixing processes for density increment and modifi-cation of NPIWWe present the results of calculating the water mass

conversion rates, the vertical velocities and the occurrencefrequencies of density ratio.

First of all, we focus on the water mass conversionrates due to the horizontal and vertical diffusion in Eqs.(2) and (3). The density range in which the strong hori-zontal diffusion occurs changes for each area (Fig. 5(a)).In Section 5 and in Line1~Line3, the water mass conver-sion rate becomes large, such as below 26.40σn above26.80σn. The water mass conversion rate becomes largearound 26.80σn in Section 6. The water mass conversionrate due to the vertical diffusion is smaller by about oneorder of the magnitude (Fig. 5(b)). These distributionssuggest that strong modifications of the source water ofNPIW should occur due to horizontal diffusion in MWR,and the density range in which strong modification couldoccur becomes dense from the northern part of MWR toits southern and eastern part.

We next compare the vertical velocities in Eq. (4) toreveal the relative importance of each process. The verti-cal velocity due to cabbeling becomes large around26.55σn (Fig. 6(a)) in Section 5 and around 26.55σn andabove 26.80σn (Fig. 6(b)) in Line1~Line3. The verticalvelocity due to turbulence becomes relatively large around26.55σn in Line1~Line3. In Section 6, it becomes largeat all densities; on the other hand, the vertical velocitydue to cabbeling becomes small (Fig. 6(c)). These distri-

butions suggest that cabbeling, which is caused by hori-zontal diffusion, has effects on the density increment ofthe source water of NPIW near the Oyashio and KuroshioFronts. And the density range in which a strong verticalvelocity could occur becomes dense, similarly to the wa-ter mass modification.

Finally, the occurrence frequency of the density ra-tio, calculated from Eq. (5), between 26.0~27.0σn is com-pared to investigate the importance of double diffusiveconvection for each area. Peaks are around Rρ 1.3 and Rρ0.5 in Section 5 (Fig. 7(a)), and at Rρ 1.5, Rρ 4.4 and Rρ0.7 in Line1~Line3 (Fig. 7(b)). However, its magnitudeat Rρ 0.7 becomes smaller. The peak at Rρ 1.3~1.5 and Rρ0.5~0.7 disappears, but the peak at Rρ 3.0~5.0 becomeslarge in Section 6 (Fig. 7(c)). These distributions suggestthat, in the northern part of MWR, the potential tempera-ture and salinity structures are favorable for the onset ofa strong salt finger. This result coincides with the con-

Fig. 5. Averages of absolute value of water mass conversionrates for salinity (PSU/s) due to horizontal diffusion (a) andvertical diffusion (b) in Eq. (3). Thin solid line is for Sec-tion 5, thick solid lines is for Line1~Line3, thin dashed lineis for Section 6. The horizontal axis is the neutral surface.


clusions of previous studies (Miyake et al., 1995;Nagasaka et al., 1999). On the other hand, in the south-ern and eastern part of MWR, the potential temperatureand salinity structures gradually become unfavorable forthe onset of strong double diffusive convection.

The above-mentioned results should be responsiblefor the formation of a salinity minimum of NPIW. Thesource water of NPIW is gradually modified by horizon-

tal diffusion with the Kuroshio water from a lighter layerto a denser layer and loses its strong anomaly. A salinityminimum then appears around 26.80σn. During this proc-ess, cabbeling and double diffusive convection exertstrong effects on the density increment of the source wa-ter of NPIW.

Fig. 6. Averages of absolute vertical velocities (m/s) given byeach component of Eq. (4) in Section 5 (a), in Line1~Line3(b), in Section 6 (c). Dashed line is vertical velocity due tocabbeling, thick solid line is that due to turbulence, thinsolid line is that due to thermobaricity. The horizontal axisis the neutral surface.

Fig. 7. Distributions of occurrence frequencies of density ratio(Rρ) between 26.0~27.0σn in Section 5 (a), Line1~Line3(b), Section 6 (c). The horizontal axis is the density ratio.The vertical axis is the occurrence frequency. 0 < Rρ < 1;diffusive convection regime, 1 < Rρ < ∞; salt finger regime,and other values; doubly stable regime.

218 R. Inoue et al.

5. Discussion

5.1 CabbelingWe discuss the effect of the cabbeling on the density

increment of the source water of NPIW.

The vertical velocity due to cabbeling becomes largebetween the warm streamer and the cold fresh core ringaround 26.55σn (Fig. 8(a)) in Section 5. It becomes largebetween the salinity minimum water and the KuroshioExtension around 26.50~26.60σn and 26.70~26.80σn (Fig.8(b)) in Line1. Horizontal mixing could occur in theseoceanic structures (see Subsection 4.1). In Section 6, thevertical velocity is smaller than in other areas (Fig. 8(c)).In estimating the cabbeling effect, there is an uncertaintyin horizontal diffusivities. In order to understand the rela-tive importance of cabbeling, we compare absolute meanvalues of the vertical velocities due to cabbeling and tur-bulence around these structures (Section 5 from St. 120

Horizontal diffusivity

4.82 48.17 310.70 481.70

Vertical diffusivity10–6 1.0 10.0 64.5 100.010–5 0.1 1.0 6.45 10.010–4 0.01 0.1 0.65 1.0

Fig. 8. Vertical cross sections of vertical velocity due tocabbeling (m/s) and salinity (PSU) along Section 5 (a),Line1~Line3 (b), and Section 6 (c), respectively. The verti-cal and horizontal axes are as in Fig. 2. Contour interval ofsalinity is 0.1PSU. Vertical velocity due to cabbeling ishatched below –10–6 m/s. Inverted triangles are observa-tion stations.

Table 2. Comparison between vertical velocity due to cabbelingand that due to turbulence with changing diffusivity in Sec-tion 5 and Line1. This shows ratio of cabbeling velocity toturbulence velocity. When the ratio is greater than 1.0,cabbeling velocity overcomes turbulence velocity. Horizon-tal diffusivities show this threshold value (ratio = 1.0)against changing vertical diffusivity from 10–6, 10–5, 10–4

m2/s.

Section 5 (26.50~26.60σn)

Line1 upper layer (26.50~26.60σn)

Line1 lower layer (26.70~26.80σn)


8.95 89.54 250.70 895.40



5.56 55.59 250.70 555.90



to St. 122 with 26.50~26.60σn, Line1 from St. 152 to St.154 with 26.50~26.60σn and Line1 from St. 149 to St.151 with 26.70~26.80σn). The vertical velocity due tocabbeling seems to be dominant in Section 5 (Table 2). It

also seems to be dominant in the lighter and denser layerin Line1. However, the vertical velocity due to turbulencebecomes relatively large in the lighter layer.

Table 3. Possible density increment due to cabbeling on neutral surfaces (from Eq. (9)) and on potential density surfaces (assum-ing mixed equal volume).

Neutral surface Density increment Potential density Density increment

26.50 0.00 26.50 0.0026.51 0.00 26.51 0.0126.52 0.00 26.52 0.0126.53 0.01 26.53 0.0226.54 0.01 26.54 0.0226.55 0.02 26.55 0.0126.56 0.01 26.56 0.0126.57 0.01 26.57 0.0126.58 0.01 26.58 0.0126.59 0.01 26.59 0.0126.60 0.03 26.60 0.01


26.50 0.02 26.50 0.0326.51 0.01 26.51 0.0326.52 0.01 26.52 0.0326.53 0.01 26.53 0.0326.54 0.00 26.54 0.0326.55 0.00 26.55 0.0326.56 0.00 26.56 0.0226.57 0.00 26.57 0.0226.58 0.00 26.58 0.0226.59 0.00 26.59 0.0226.60 0.00 26.60 0.02


26.70 0.01 26.70 0.0026.71 0.01 26.71 0.0126.72 0.01 26.72 0.0126.73 0.02 26.73 0.0226.74 0.02 26.74 0.0226.75 0.02 26.75 0.0126.76 0.02 26.76 0.0126.77 0.01 26.77 0.0126.78 0.01 26.78 0.0126.79 0.00 26.79 0.0126.80 0.00 26.80 0.01

Line1 (26.70~26.80 kg/m3)

Section 5 (26.50~26.60 kg/m3)

Line1 (26.50~26.60 kg/m3)

220 R. Inoue et al.

The density increment due to cabbeling is estimated.The density change rate due to cabbeling on a neutralsurface is defined as

1 1

6

ρρ α θ β

ρρ α θ β∂

∂= − ∂

∂+ ∂

∂≈ = − +

( )t t

S

t t t

S

tcab cab cab

∆∆

∆∆

∆∆

.

Here, the subscript cab indicates the density changecaused by cabbeling. (∂θ/∂t)cab and (∂S/∂t)cab are deter-mined by the cabbeling term in the equation of water massconversion rate in Eqs. (2) and (3), and are

∂∂

= ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

( )−θ θ θ α

θαβ

α αβ

βt

KgNz S Scab

n2 2

2

22 7,

∂∂

= ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

( )−S

tKgN

S

z S Scabn

2 22

22 8θ αθ

αβ

α αβ

β.

Equations (7) and (8) can be substituted into Eq. (6).In estimating ∆ρ, ∆t is unknown. If we assume that hori-zontal diffusion mixes the water mass completely, anddefine mixing time as ∆t = ∆ S /K∇ n

2S, here ∆ S is onehalf of the salinity difference between two stations; wecan define ∆ρ as

∆

∆

ρ ρ α θ θ αθ

αβ

α αβ

β

β θ αθ

αβ

α αβ

β

= − ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

+ ∂∂

∇ ∂∂

+ ∂∂

− ∂∂

×

∇

( )

−

−

gNz S S

gNS

z S S

S

S

n

nn

2 22

2

2 22

2 2

2

2

9

.

It should be noted that ∆ρ does not depend on hori-zontal diffusivity. In these equations, all variables couldbe obtained from CTD casts. We also estimate the den-sity increment due to cabbeling under the assumption thattwo water parcels having the same potential density butdifferent potential temperature and salinity mix equally.The maximum density increment is almost the same onboth surfaces and becomes 0.01~0.03 kg/m3 in both partsof MWR (Table 3).

5.2 Double diffusive convectionWe discuss the effect of double diffusive convection

on density increment in the northern part of MWR. It isnoted that the potential density is used to estimate den-sity increment, because the relation between two CTDcasts determines the neutral surface.

As discussed in Subsection 4.2, the oceanic struc-ture is favorable for a strong salt finger in Section 5. TheKuroshio water (warm and salty) lies above the cold corering (cold and fresh) in St. 120 (Fig. 9). This station has a

Fig. 9. Vertical profiles of density ratio (Rρ), salinity (PSU), potential temperature (°C) and potential density (kg/m3) at St. 120.The vertical axis is pressure (db). 0 < Rρ < 1; diffusive regime. 1 < Rρ < 5; salt finger regime. Other values; doubly stableregime.


salinity minimum around 26.53σθ at 180 db. The densityratio is close to 1 around this salinity minimum. A saltfinger can occur above this salinity minimum and diffu-sive convection can occur below it. We estimate the den-sity increment of this salinity minimum due to doublediffusive convection using the flux laws given by Hebert(1988) and Kelley (1990) in the case 1 and simple nu-merical model by Schmitt (1981) and Zhang et al. (1998)in the case 2, assuming no horizontal mixing and noadvection.

In the case 1, we discretize the salt and heat balanceequations as (Fig. 10),

∂∂

= ∂∂

∂∂

= − ∂∂

( ) ≈ = − −( )

∂∂

= ∂∂

∂∂

= − ∂∂

( ) ≈ = − −( )∂∂

= − ∂∂

+ ∂∂

S

t zK

S

z zF

S

t hF F

t zK

z zF

t hF F

t t

S

t

S S S S

T T T T

∆∆

∆∆

1

2

1

2

1

1 2

1 2

,

,θ θ θ

ρρ α θ β ≈≈ = − +

= − +( )

( )

1

10

ρρ α θ β

ρ ρ α θ β

∆∆

∆∆

∆∆

∆ ∆ ∆

t t

S

t

S

,

.

Here, KS is vertical eddy diffusivity for salt and KTis that for heat due to double diffusive convection. FT1,FS1 and γ1 are the heat and salt flux due to a salt fingerand the flux buoyancy ratio of a salt finger, respectively.These are determined by the flux law (Hebert, 1988),

F F C R

F C g k S

R

T S

S T

1 1 1 1 1 1 11 91

1 1 11 3

14 3

1 1

0 04 0 327

0 35 1 05 2 16 1

11

= ( ) = +

= ( ) ( )= − −( )[ ]{ }

( )

−γ β α

β

γ

ρ

ρ

/ , . . ,

,

. exp . exp . .

.

/ /∆

FT2, FS2 and γ2 are the heat and salt flux due to diffu-sive convection and the flux buoyancy ratio of diffusiveconvection, respectively. These are determined by the fluxlaw (Kelley, 1990),

F Cg k

T CR

F F

R R

R

TT

S T

2 22

1 3

24 3

220 72

2 22

22

221

21 3 2

21 3 2

0 00324 8

1 4 1

1 14 1

=

( ) =

=

=+ −( )

+ −( )

−

− −

−

αν

γ αβ

γ

ρ

ρ ρ

ρ

//

.

/

/

, . exp.

,

,

..

∆

( )12

These fluxes are calculated by using potential tem-perature and salinity at 100 db (defined as above the sa-linity minimum where a salt finger can occur, S =33.78PSU and θ = 6.77°C), 180 db (salinity minimum,S = 33.43PSU and θ = 4.14°C) and 260 db (defined asbelow the salinity minimum where diffusive convectioncan occur, S = 33.61PSU and θ = 4.39°C) at St. 120. Thevalues used here are summarized in Table 4. Densitychange due to double diffusive convection becomes 0.01kg/m3 with α = 1.08 × 10–4 (°C–1), β = 7.73 × 10–4

(PSU–1), ρ = 1026.53 (kg/m3) at the salinity minimum.Salinity becomes 33.65PSU. It should be noted that theeffect of double diffusive convection is determined byinitial anomaly in this estimation.

In the case 2, we use an ad-hoc model proposed bySchmitt (1981), stating that eddy diffusivity by doublediffusive convection is a function of the density ratio andchanges in each time step:

∂∂

= ∂∂ ( ) ∂

∂

∂∂

= ∂∂ ( ) ∂

∂

( )

θ θρ

ρ

t zK R

z

S

t zK R

S

z

T

S

,

.

13

KT and KS are vertical diffusivities for salt and tem-perature and defined as follows (Zhang et al., 1998);

Fig. 10. Schematic view of vertical heat and salt fluxes in wa-ter column by double diffusive convection assuming onedimension balance. The vertical axis is pressure (db). Thehorizontal axes are salinity (PSU) and potential tempera-ture (°C), respectively. Thin lines are vertical profiles ofsalinity and potential temperature, respectively. Parametersused here are summarized in Table 4.

222 R. Inoue et al.

Table 4. Parameters used in Fig. 10 and Eqs. (10), (11) and (12).

K K R R R K

R k k

K K R R K

T C

n

T S

S C

n

= +( )

+

( )= +( )

+

∗ ∞

∗ ∞

γ ρ ρ

ρ

ρ

1

1

/

/ ,

/

1 < < , salt finger

K C R k K R R

k k R

K R K K K

T a T a

S T

S T

= + = ×

( )= −( ) +

∞ −

∞ ∞

21 3 9 1 1

2

0 25 10/ ., .

,

ρ

ρ

ργ

/ < < 1, diffusive convection

K K KT S= = ( ){ ( )∞ other, doubly stable . 14

kS is molecular diffusivity of salt and is 1.5 × 10–9

m2/s. K* is 10–4 m2/s, K∞ is 3 × 10–5 m2/s, RC is 1.6, n is 6and γ is buoyancy flux ratio for a salt finger, γ = 0.7. C2and γ2 are given by Eq. (12). We integrate these equa-tions using the finite difference method, taking the verti-

cal scale ∆z as 20 m, which is an appropriate scale forthis parameterization, and time step ∆t as 60 sec. No fluxis assumed at both boundaries. The density and salinityof the salinity minimum becomes 0.03 kg/m3 heavier and0.08PSU saltier after 180 days (Fig. 11). After 180 days,the density flux due to turbulence dominates over thatdue to double diffusive convection in this model. In thesetwo cases, possible density increments due to double dif-fusive convection are obtained 0.01~0.03 kg/m3. Thus,we find that the density increment due to cabbeling anddouble diffusive convection amounts to 0.06 kg/m3.

Recently, Talley and Yun (2001) stated that the wa-ter in the Oyashio winter mixed layer could become anew NPIW salinity minimum due to cabbeling and dou-ble diffusive convection. They calculated that the den-sity increment amounts to 0.15 kg/m3. Their value is largerthan the one found in our study. One reason for this isthat they calculated the possible density increment due tocabbeling and double diffusive convection using the endmembers of two source waters, and they neglected thedetailed oceanic structures in MWR considered in thisstudy.


6. ConclusionsThe dominant modification processes, areas and den-

sity increment for the source water of North Pacific In-termediate Water (NPIW) have been analyzed, consider-ing the detailed oceanic structures in Mixed Water Re-gion (MWR). Neutral surfaces, the water mass modifica-tion rates on neutral surfaces, the vertical velocities acrossneutral surfaces and the occurrence frequency of densityratio have been used in this study. Conclusions are sum-marized as follows:

1) The difference between the potential densitysurface and the neutral surface becomes up to –0.04kg/m3 around the source water of NPIW. This suggeststhat the thermobaric effect is important when calculatingthe mixing ratio between the Kuroshio and Oyashio wa-ters.

2) The water mass modification rates indicate thatstrong modifications of the source water of NPIW shouldoccur due to horizontal diffusion in MWR. The densityrange in which strong modification could occur becomesdense for each region. In the northern and southern partof MWR, the strong modification occurs above 26.80σn.Finally, a salinity minimum appears around 26.80σnaround the eastern part of MWR.

3) The distribution of the vertical velocities showsthat cabbeling, which is caused by horizontal diffusion,affects the density increment of the source water of NPIWnear the Oyashio and Kuroshio Fronts. The density rangein which strong vertical velocity could occur becomesdense, the same as the water mass modification. This sug-gests that, during strong modifications of the source wa-

ter of NPIW by horizontal diffusion, cabbeling has strongeffects on the density increment of the source water ofNPIW.

4) The occurrence frequency of density ratio showsan activity of a salt finger shifts from strong to weak anda peak at weak diffusive convection shift from exists tonon exists in the area from the northern part of MWR toits eastern part. This result suggests that the density ofthe source water of NPIW increases due to a salt fingermainly around the northern part of MWR.

5) Considering detailed oceanic structures inMWR, the density increment of the source water of NPIWdue to cabbeling and double diffusive convection is esti-mated as 0.01~0.03 kg/m3 by cabbeling and 0.01~0.03kg/m3 by double diffusive convection. The total densityincrement amounts to 0.06 kg/m3 which is smaller thanthe value obtained by Talley and Yun (2001).

Finally, there remain uncertainties that need to bestudied in the future: the difference between the potentialdensity surface and the neutral surface should be investi-gated further. The effects of warm core rings, which areregarded as one of the key sources for formation of NPIW,have not been analyzed in this study. Other observationdata sets need to be analyzed. We estimate total densityincrement by cabbeling and double diffusive convectionseparately, neglecting the nonlinear interaction of theseprocesses. When cabbeling and double diffusive convec-tion occur at the same time, the salt and heat balancewould be changed and density increment also would bechanged (e.g., Schmitt, 1991). Therefore, theoretical workand more microstructure measurements are needed inMWR.

AcknowledgementsThe authors wish to thank Drs. M. Matsuyama, H.

Nagashima, H. Yamzaki, and Y. Kitade at Tokyo Univer-sity of Fisheries for their discussions and valuable com-ments. The authors also thank the captain and crew of theR/V Soyo-maru for supporting the observation. Commentsfrom two anonymous reviewers were very helpful andimproved this manuscript.

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Modification of North Pacific Intermediate Water around ...svr4.terrapub.co.jp/journals/JO/pdf/5902/59020211.pdf · North Pacific Intermediate Water (NPIW) is defined as broadly spreading