Progress in Oceanography 202 (2022) 102756

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Progress in Oceanography
journal homepage: www.elsevier.com/locate/pocean

Nutrient streams in the North Pacific
Yu Long a, b, Xinyu Guo a, c, *, Xiao-Hua Zhu a, b, d, Zhiyuan Li eaState Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China
Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, 519082, ChinacCenter for Marine Environmental Study, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, JapandSchool of Oceanography, Shanghai Jiao Tong University, Shanghai, 200030, Chinae
Key Laboratory for Technology in Rural Water Management of Zhejiang, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, Chinab

A R T I C L E I N F O

A B S T R A C T

Keywords:
Nutrient stream
North Pacific
Nutrient transport
World Ocean Circulation Experiment
Inverse method

The nutrient streams in the North Pacific were examined by analyzing the results derived from the inverse
calculation of the World Ocean Circulation Experiment (WOCE)-revisit cruise data. The Kuroshio, Alaskan
Stream, and Oyashio drive the most intensive nutrient transport within the basin. The upper portion of thenutrient stream (lighter than 26.2 kg/m3) contains mode waters and recirculates within the subtropical gyre,
while the intermediate portion (26.2–27.15 kg/m3) relates to North Pacific Intermediate Water (NPIW) andcontributes most to nutrient transport in the nutrient stream. The nutrient concentration in the nutrient streamincreases in the subtropical gyre along the Kuroshio and Kuroshio Extensions but decreases in the subarctic gyrefrom the Alaskan Stream to the Oyashio region. This increase or decrease in nutrient concentration from the
upstream region to the downstream region mainly results from lateral water exchange, although it also partly
depends on biogeochemical processes and vertical diffusion. Specifically, the lateral exchange of the nutrient
stream in the subarctic gyre with water from lower latitudes decreases the nitrate concentration of the Alaskan
Stream and that with water from the Okhotsk Sea decreases the nitrate concentration of the Oyashio. For verticalnitrate transport, our estimation shows that the ventilation processes of subduction and induction are compa­
rable to the sum of vertical advection and diffusion. This implies that nutrient transport related to the ventilationof the North Pacific is in a dynamic balance on an annual cycle and should be quantified in future work.

1. Introduction
The ocean circulation in the North Pacific features two gyres, which
are the clockwise subtropical gyre that includes the Kuroshio and its
extension, the North Pacific Current, the California Current and theNorth Equatorial Current, and the anticlockwise subarctic gyre, which
includes the Alaskan gyre and the Western Subarctic Gyre. The twogyres encounter the Kuroshio Extension region, where warm, saline, andnutrient-depleted subtropical waters are mixed with cold, fresh, andnutrient-rich subarctic water and where mode water, for example,
Subtropical Mode Water and Central Mode Water, and North PacificIntermediate Water (NPIW) form. Ocean currents transport (export)
nutrients within (between) gyres, supporting local and basin-scale pri­mary productivity.
The importance of large-scale nutrient transport has been addressedin many studies. Pelegri and Csanady (1991) and Pelegrí et al. (1996)

examined nutrient transport by the Gulf Stream and proposed that the
Gulf Stream provides nutrients to the subpolar North Atlantic Ocean andthat both vertical and lateral processes are important to the supply ofnutrients along the stream. Sarmiento et al. (2004) revealed the signif­
icant role of high-latitude nutrient export in supporting primary pro­ductivity in low-latitude regions and suggested that NPIW formation
was responsible for 70% of the silicic acid supply to diatom production.
Letscher et al. (2016) demonstrated that lateral transport accounts for
24–36% of the nitrogen and 44–67% of the phosphorus supply in gyremargins. Their study confirmed again that lateral processes were asimportant as vertical processes to local primary production and theyagreed with the conclusion given by Lozier et al. (2011) that the inter­annual variability in oceanic productivity depends not only on wind andbuoyancy forcing but also on subsurface advective nutrient supply to thesurface rather than on local stratification.
Generally, the western boundary currents have the most intensive* Corresponding author at: State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources,
Hangzhou 310012, China.
E-mail address: guoxinyu@sci.ehime-u.ac.jp (X. Guo).
https://doi.org/10.1016/j.pocean.2022.102756
Received 7 July 2021; Received in revised form 24 January 2022; Accepted 8 February 2022
Available online 16 February 2022
0079-6611/© 2022 Elsevier Ltd. All rights reserved.

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Fig. 1. Location of hydrographic data (white dots) and mean sea level (color shading) of the North Pacific. Red characters in the globe denote the main currents: 1.
Alaskan Stream, 2. East Kamchatka Current, 3. Oyashio, 4. Kuroshio, 5. Kuroshio recirculation, and 6. Ryukyu Current. Red dots overlapping the white dots denotethe subsections used to represent the nutrient stream. Red characters represent the name of subsections. Blue characters at the endpoint of the sections represent theirnames and correspond to their ExpoCode at the lower left. White characters denote the number of the box.

nutrient transport. The downward decreased velocity of the boundary
currents, together with increased nutrient concentration, result in thesubsurface maximum nutrient flux. As suggested by Pelegri and Csanady(1991), the Gulf Stream forms a nutrient stream acting as a giant conduit
underneath the sea surface, transporting nutrients from low-latitude tohigh-latitude regions. The nutrient sources of the Gulf Stream are theMode Waters from the Southern Ocean and the tropics (Williams et al.,2006; Palter and Lozier 2008). Both area-weighted (section-averaged
nutrient concentration with each data point having a weight defined by
the product of the distance between two hydrographic stations and thelayer thickness represented by the data) and transport-weighted(nutrient transport divided by the volume transport through the same
section) nutrient concentrations increase along the nutrient stream,
which is caused mainly by lateral water exchange rather than by dia­pycnal mixing (Palter and Lozier, 2008; Williams et al., 2011). Forty
percent of the transport of the Gulf Stream nutrient stream is inducted
into the mixed layer in the downstream area, which supplies nutrients toisopycnals cropping out in the subpolar gyre, while the rest recirculates
locally (Williams et al., 2006). Recently, Pelegrí et al. (2019) reviewed
the progress of the Gulf Stream nutrient stream in the Atlantic, from thenutrient-bearing stratum (Csanady, 1990) to the role of the nutrient
stream in the Earth system.
In the North Pacific, Chen et al. (1994) first revealed the multicore
structure in the subsurface maximum of Kuroshio nutrient flux east of
Taiwan. Guo et al. (2012, 2013) and Long et al. (2018) examined themean state and long-term variations in the Kuroshio nutrient stream
from the East China Sea (ECS) to the area south of Japan. Their findings
indicated that the subsurface nutrient flux maximum of the Kuroshio is
at a depth of 400 m; the Kuroshio nutrient stream south of Japan rep­resents the confluence of the ECS Kuroshio (~170 kmolN/s), the Ryukyu
current (~350 kmolN/s), and the Kuroshio recirculation south of Japan(~700 kmolN/s); and the variation in nutrient concentration along theKuroshio is mainly due to lateral water exchange, especially in the deep
layers. Additionally, Long et al. (2019) reported that the equatorward
nitrate transport of the Oyashio reaches approximately 350 kmolN/s,
and it exports 24 kmolN/s to the subtropical gyre along with the for­mation of NPIW. Nishioka et al. (2013) demonstrated that intensive

mixing along the Kuril Island chain is responsible for iron export fromthe Okhotsk Sea to NPIW. Although the significance of the nutrient
stream has been addressed, the spatial pattern of nutrient transport in
the North Pacific remains unclear.
On a basin scale, Ganachaud and Wunsch (2002) used the inversebox model to calculate the velocity across transoceanic sections andestimated the transport of silicate, nitrate, phosphorus, and oxygen.
They found that meridional nitrate transport is approximately 10
kmolN/s southward in the North Pacific (Section P3 in their Fig. 3,
approximately 24◦ N) and approximately 270 kmolN/s northward in theSouth Pacific (Section P21 in their Fig. 3, approximately 17◦ S). The
nutrient transport of the Indonesian throughflow (ITF) is approximately
260 kmolN/s (Ayers et al., 2014). The nutrient budget within theenclosed area bounded by Sections P3 and P21 and the ITF is almost
balanced. These results may lead to the conclusion that direct transportof nutrients occurs from the South Pacific to the ITF. However, Gordon
et al. (1994) suggested that a sizable proportion of ITF originates in the
North Pacific. Therefore, the plausible explanation is that the northward
nutrient transport almost equals the southward transport at Section P3
and that both could be large and may have different origins. If so, in­formation about the spatial patterns of nutrient transport, as well as thenutrient streams in the North Pacific, is crucial to determine the nutrient
export of the North Pacific at 24◦ N.
Advection also plays an important role in the nutrient supply be­
tween the thermocline and mixed layer through the ventilation process,i.e., subduction and induction. By definition (Qiu and Huang, 1995),
subduction occurs mainly in the subtropical gyre, where the seawater inthe mixed layer enters the permanent thermocline, and induction occurs
in the subpolar gyres, where the seawater flows from the permanent
thermocline to the mixed layer. Pelegrí et al. (1996, 2006) and Williams
et al. (2006) demonstrated the nutrient transport of the Gulf Stream andthat their induction into the mixed layer plays an important role inmaintaining primary production in the North Atlantic Ocean. On theother hand, the mode water formation connects closely to subduction(Suga et al., 2008), which depends closely on the dynamic status of theKuroshio and Kuroshio Extension (Qiu and Chen, 2006). Palter et al.
(2005) suggested that the formation of mode water in the North Atlantic
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Fig. 2. Spatial pattern of volume transport. (a) Ekman component, (b) sea surface-26.2 kg/m3, (c) 26.2–27.15 kg/m3, (d) 27.15–27.6 kg/m3, and (e) 27.6–27.9 kg/
m3. Numbers denote the volume transport of the adjacent section (Sv). Positive values denote northward or eastward directions. Red bars represent the volumetransport per unit width (Sv/km, the volume transport over a station pair divided by the distance between the station pair). Western part of P2 and P3 represents theKuroshio and that of P1 represents the Oyashio. The northern part of Sections P14 and P16 represents the Alaskan Stream.

subtropical region might induce spatial and temporal variability in thesubsurface nutrient reservoir and may affect primary productivity in its
downstream region.
Nishioka et al. (2020) recently suggested that the subpolar marginalseas supply nutrients to the North Pacific through the formation andadvection of intermediate water and proposed the concept of the sub­arctic intermediate nutrient pool. It includes the intermediate layers of
the subarctic North Pacific and its marginal seas. Although the Okhotsk
Sea exports iron to the North Pacific, its role in the transport of mac­ronutrients, such as nitrate, remains unclear. Here, the role of the Bering
Sea in nutrient concentration variation along the subarctic gyre was also
investigated as another candidate of the subarctic intermediate nutrient
pool. As a natural hypothesis, the water exchange between these mar­
ginal seas and the North Pacific should change the nutrient concentra­tion along the nutrient stream.
In addition to nutrient transport, the variation in nutrient concen­
trations along the nutrient streams is also a compelling aspect. Williams
et al. (2011) suggested that diapycnal mixing, biological consumption
and regeneration, and lateral water exchange are the main mechanisms
responsible for this variation. Diapycnal mixing provides an upward
nutrient flux from nutrient-rich deep water to nutrient-depleted surface
water and can cause an increase in surface nutrient concentration along
the stream path. Biological consumption and regeneration are the sinkand source terms for the surface layer and deep layer, respectively, andcan cause a decrease in nutrient concentration along the stream path in
the surface layer and an increase in nutrient concentration along thestream path in the deep layer. Lateral water exchange results in both
positive and negative variations in the nutrient concentration along thestream path, depending on the nutrient concentration in the adjacentwater involved in this process.
This study is structured as follows: the data and methods are briefly
described in the next section, and the spatial patterns of volumetransport and nutrient transport within several isopycnal layers areshown in Section 3. The subtropical nutrient stream and subarctic
nutrient stream are presented in Sections 4 and 5, respectively. The
vertical nutrient transport due to vertical advection, vertical diffusion,and ventilation processes are examined in Section 6, and concluding
remarks are provided in Section 7.
2. Data and methods
The hydrographic data used in this study geographically encom­
passed most of the North Pacific and were observed by World Ocean
Circulation Experiment (WOCE)-revisit cruises during 2004–2007(Fig. 1). The conductivity–temperature–depth (CTD) data for the full
depth, with a vertical resolution of 1 or 2 dbar, together with nitrate,
silicate, and phosphate concentrations of up to 36 levels, were used in
the box model analysis. The data are available on the CCHDO (CLIVAR
and Carbon Hydrographic Data Office) website. Hydrographic data fromthe Japan Meteorological Agency (JMA) and Japan Agency for MarineEarth Science and Technology (JAMSTEC) were also used to show thenitrate concentrations in the Okhotsk Sea and Bering Sea, respectively.
The absolute geostrophic velocity at each section was calculatedusing the inverse method (Wunsch, 1978) (details are presented in the
Appendix). After the absolute geostrophic velocity was determined, thenitrate flux was calculated by multiplying it by the nitrate concentra­tion, and nitrate transport was obtained by integrating the nitrate flux
over the section. The focus of this study was the nutrient stream, which
is mainly determined by the upper layer circulation, and therefore, thisanalysis was limited to the results in the upper 2000 m. Nitrate flux waschosen to represent the nutrient streams. Phosphate flux and silicate flux
have a similar spatial distribution to nitrate flux, and their transport canbe approximately obtained by the Redfield ratio and nitrate transport.
Because the cruises were carried out in different months, the data3

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Fig. 3. Spatial pattern of nitrate transport. (a) Ekman component, (b) sea surface-26.2 kg/m3, (c) 26.2–27.15 kg/m3, (d) 27.15–27.6 kg/m3, and (e) 27.6–27.9 kg/
m3. Numbers denote the nutrient transport of the adjacent section (kmol/s). Positive values denote northward or eastward directions. Red bars represent the nutrienttransport per unit width (mol/s/km, the nitrate transport through a station pair divided by the distance between a station pair). Western part of P2 and P3 represents
the Kuroshio and that of P1 represents the Oyashio. The northern part of Sections P14 and P16 represents the Alaskan Stream.

include not only spatial variation but also temporal variations, espe­
cially in the upper layer (first and second layers in our inverse model).
Due to this factor, our analysis of the nitrate concentration along thestream was limited to the layers from the third layer. The regeneration
process, which converts organic nitrogen to nitrate, was analyzed. The
regenerated nitrate concentration (Creg) was estimated from theapparent oxygen utilization (AOU, the difference between the saturation
oxygen concentration calculated from in situ temperature and salinity
and the observed dissolved oxygen concentration from the same sample)
by assuming Creg = − AOU/R, where the Redfield ratio R was taken as
O2:N = − 170:16 (Sarmiento and Gruber, 2006). The regeneration rate is
the ratio of regenerated nitrate concentration to the measured nitrateconcentration and is related to the duration since the latest ventilation of
the observed water mass.

to 2000 m (Fig. 2e)).
The Ekman components of volume transport at Sections P1, P2, andP3 generally decrease from south to north (Fig. 2a), while nitratetransport increases from south to north (Fig. 3a) because of the north­ward increase in the surface nitrate concentration. Transport in thesurface layer appears mostly in the subtropical gyre (Fig. 2b). For thesection corresponding to the Kuroshio (western-most part of P2), thetransport in the surface layer explains 63% of the total volume transport(Fig. 2b, the volume transport of the surface layer divides that of theupper 2000 m, that is, 36.9 Sv/(36.9 + 12.1 + 8.5 + 1) Sv)), and 23% of
the nitrate transport (Fig. 3b, the nitrate transport of the surface layer
divides that of the upper 2000 m, 211.7 kmolN/s/(211.7 + 304 + 351.9+ 42.9) kmolN/s) in the upper 2000 m. The lower ratio of the nitratetransport is because the nitrate concentration is lower in this layer thanin the other layers.
The intermediate layer where the NPIW exists is ventilated directlyin the subarctic gyre but indirectly in the subtropical gyre through NPIW
formation (Talley et al., 1995). The values in this layer explain
approximately 21% (32%) of the volume transport (Fig. 2c) and 33%(27%) of the nitrate transport (Fig. 3c) in the upper 2000 m (numbers
prior to the parentheses represent the Kuroshio in the western part ofSection P2; the numbers in the parentheses represent the Oyashio in thewestern part of Section P1). When considering the layer thickness, its
nitrate transport is the most intensive among all layers (Fig. 3). The flow
pattern shows that the western portion of Section P01 (Fig. 2c), i.e., theOyashio, is the only advective pathway for subarctic water exported tothe subtropical gyre. It has an approximately 4 Sv volume transport,
which is consistent with that given by Talley et al. (1995). Nitratetransport is approximately 130 kmolN/s (Fig. 3c), which agrees with thevalue estimated from different datasets (Long et al., 2019). Apart fromthe Oyashio, the volume transport in the eastern part of Section P1 isnorthward, indicating a poleward transport of the lower nutrient con­centration seawater from the subtropical gyre.

3. Spatial pattern of nutrient transport
The large-scale flow pattern derived from the inverse method is
generally consistent with the understanding of the upper layer circula­tion in the North Pacific. The box model encompassed the northern halfof the subtropical gyre and the entire subarctic gyre. The boundary
currents, that is, the Kuroshio, Oyashio, and Alaskan Stream, can berecognized by the large volume transport per unit width at the bound­aries of the basin (Fig. 2).
According to the typical distribution of the water mass, the volumetransports within four isopycnal layers were presented. These included
the surface layer where the central water and mode water exist (seasurface–26.2 kg/m3 with a typical thickness of 400 m in the subtropicalgyre and 50–100 m in the subarctic gyre (Fig. 2b)), the intermediate
layer where the NPIW exists (26.2–27.15 kg/m3 with a typical thicknessof 350–400 m (Fig. 2c)), the deep layer (27.15–27.6 kg/m3 from thebottom of NPIW to a depth of approximately 1000 m (Fig. 2d)), and thebottom layer (27.6–27.9 kg/m3 from a depth of approximately 1000 m
4

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Fig. 4. Velocity and nitrate flux along the Kuroshio. (a), (b), and (c) show the velocity of the Kuroshio in the ECS (at Section P03), south of Japan (at Section P02),
and the Kuroshio Extension (at Section P10). Red contours denote the nitrate concentration (mmol/m3). (d), (e), and (f) represent the nitrate flux for the KECS, KSJ,
and KKE, respectively. Red contours denote the neutral density surface (kg/m3). The black dashed line denotes a contour of 7 mmol/m2/s for nitrate flux. Positive andnegative values indicate eastward and westward directions, respectively.
Table 1
Volume transport (Vt), nitrate transport (Nt), transport weighted nitrate concentration (Ct) and area weighted nitrate concentration (Ca) within seven isopycnal layers
for the section in the ECS (at section P03), south of Japan (at section P02), and the Kuroshio Extension (at section P10). The numbers in the first column are the index of
isopycnal layers, ‘T’ means total water column, and red and blue characters denote increasing and decreasing of nitrate concentration along the stream path. The lower
boundary of the layers is 26.2, 26.8, 27.15, 27.35, 27.6, 27.8, and 27.9 kg/m3. Positive (negative) values indicate northward (southward) or eastward (westward).
Vt (Sv)

T
1
2
3
4
5
6
7

Nt (kmol/s)

Ct (mmol/m3 )Ca (mmol/m3 )

KECS

KSJ

KKE

KECS

KSJ

KKE

KECS

KSJ

KKE

KECS

KSJ

KKE

30
23.00
4.22
1.41
0.37
1.00
N/A
N/A

78.19
49.14
8.97
5.54
2.79
5.02
4.71
2.02

81.13
42.24
11.11
7.71
4.59
6.31
5.93
3.24

315.88125.90100.14
45.62
14.02
39.29
N/A
N/A

1215.95
262.26205.13182.11108.55208.88201.1684.75

1578.06
246.94246.98259.49184.44274.03268.73146.00

N/A
5.47
23.72
32.46
37.72
39.31
N/A
N/A

N/A
5.34
22.86
32.90
38.89
41.59
42.68
42.05

N/A
5.85
22.24
33.66
40.17
43.41
45.34
45.05

N/A
5.33
23.75
31.89
35.90
39.03
N/A
N/A

N/A
5.94
22.82
32.35
37.71
40.29
41.24
40.54

N/A
5.67
22.13
32.84
39.21
42.39
43.90
43.43

The deep layer (Figs. 2d and 3d) and the bottom layer (Figs. 2e and3e) show reductions in volume transport and nitrate transport. Theselayers are deep portions of the nutrient stream, accounting for oneseventh of the volume transport and more than half of the nitratetransport within the entire water column, which results from the highnutrient concentration of the deep water. These layers export nutrientsto the intermediate layer through vertical advection and vertical diffu­
sion and are too deep to directly influence local primary productivity.
The nutrient stream is defined by the large values of volume trans­
port and nitrate transport per unit width in the boundary current region,
particularly in the intermediate layer (Fig. 3). Following this definition,sections across the Kuroshio in the subtropical gyre and those across the
Oyashio and Alaskan Streams in the subarctic gyre were chosen to
represent the nutrient streams in the North Pacific.

4. Subtropical nutrient streams
The subtropical nutrient stream is associated with the Kuroshio. The
width of the Kuroshio increases in the downstream direction (Fig. 4a–c)
from the ECS (KECS, Section P03, Fig. 1) to the area south of Japan (KSJ,
Section P02) and further to the Kuroshio Extension (KKE, Section P10).
This is mainly attributed to the presence of the Kuroshio recirculation
gyre (negative values in Fig. 4b, c) that joins the Kuroshio and becomes apart of the eastward current in the Kuroshio. Consequently, the eastward
volume transport varies from 30.0 (KECS) to 78.2 (KSJ) to 81.1 Sv (KKE)(Table 1). The vertical structure of nitrate concentration changes little
among the three sections, and the nutricline, for example, the contour of
15 mmolN/m3, is located at a depth of approximately 300–800 m(Fig. 4a–c).
The nitrate flux is intensified from the KECS to KKE (Fig. 4d–f). For
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Fig. 5. (a), (b), and (c) represent the ratio of regenerated nitrate concentration to nitrate concentration of the Kuroshio in the ECS (at Section P03), south of Japan (atSection P02), and the Kuroshio Extension (at Section P10). Red contours denote the neutral density surface (kg/m3). The top layer is blank due to the large un­certainties. (d), (e), and (f) represent the temperature-salinity diagram, and color shading denotes the nitrate flux for the KECS, KSJ, and KKE, respectively. Potential
density contours 26.13, 26.67, 26.98, 27.16, 27.39, 27.56, and 27.65 in (d–f) correspond to neutral densities of 26.2, 26.8, 27.15, 27.35, 27.6, 27.8, and 27.9,
respectively.

example, the subsurface maximum core (defined by the contour of 7
mmolN/m2/s in Fig. 4d–f) varies in size, depth (350–600 m for theKECS, 400–700 m for the KSJ, and 300–800 m for the KKE), and density
range (26.2–26.8 kg/m3 for the KECS, 26.2–27.15 kg/m3 for the KSJ,
and 26.2–27.15 kg/m3 for the KKE). The nitrate flux subsurface cores of
the KECS, KSJ, and KKE are generally located within the NPIW range(26.2–27.15 kg/m3), implying that the nutrient stream is closely related
to NPIW. In addition, nitrate transport varies from 315.9 (KECS) to1216.0 (KSJ) to 1578.0 (KKE) kmolN/s. The nitrate transport of the
KECS and KSJ is close to the values reported by Guo et al. (2013), whilethat of the KKE is the first to be reported.
Notably, from the KSJ to KKE, the volume transport increases byapproximately 3 Sv, while the nitrate transport increases by approxi­
mately 360 kmolN/s. The volume transport difference between the KSJ
and KKE in each layer (Table 1) shows that there is a decrease of
approximately 7 Sv in the surface layer and an increase of approximately
10 Sv within layers 2–7. Consequently, nitrate transport decreases by 15
kmolN/s in the surface layer but increases by 389 kmolN/s in layers 2–7.
Therefore, the large nitrate transport increase from the KSJ to KKE re­sults from the lateral water exchange that exports nutrient-poor water inthe surface layer but imports nutrient-rich water in the subsurface anddeep layers.
Both the area-weighted and transport-weighted nitrate concentra­
tions increase along the Kuroshio in deep layers 3–7 (Table 1). The ni­
trate concentration variation along the Kuroshio from the KECS to KSJ
was examined and was concluded to be caused primarily by lateralwater exchange (Guo et al., 2013; Long et al., 2018); therefore, the main
focus here was on the KKE section. Following Williams et al. (2011), therole of regeneration, diapycnal mixing, and lateral water exchange inchanging the nitrate concentration along the Kuroshio nutrient stream
was examined.
Fig. 5 shows the regeneration rate of nitrate (Fig. 5a–c) and the T-S

relationship (Fig. 5d–f). For the Kuroshio from the KECS to KSJ, theregeneration rate of nitrate (Fig. 5a, b) and the T-S relationship (Fig. 5d,e) change little. For the Kuroshio from the KSJ to KKE, the regeneration
rate (Fig. 5b, c) decreases in the intermediate layer but slightly increases
in the deep layer. Combined with the increased nitrate concentrationfrom the KSJ to KKE, it is suggested that the water mass involved inlateral water exchange has a low regeneration rate and a high nitrateconcentration. Since the newly ventilated water has a low regeneration
rate but a high nitrate concentration, the decreases in regeneration ratefrom the KSJ to KKE should be caused by lateral water exchange with
newly ventilated water. The zigzag T-S relationship (Fig. 5f) in the in­termediate layer in the KKE confirms the intense water mixing in thesalinity minimum layer and its close relationship with NPIW formation(Talley et al., 1995); that is, the Kuroshio and Oyashio mix in the mixed
water region and export the newly ventilated water from the subarctic
gyre to the subtropical gyre.
For layers 4–7, according to Slawyk and Raimbault (1995), the ni­
trate released from dissolved organic nitrogen is at a rate of
0.0048–0.012 mmolN/m3/day. If a water mass flows along the Kur­oshio, it takes ~60 days from the KSJ to KKE (distance between the KSJ
and KKE is ~1500 km, and the mean velocity of the Kuroshio in theintermediate layer is ~0.3 m/s). The product of the release rate and theduration of a water parcel flowing from the KSJ to KKE suggests thatregeneration increases the nitrate concentration by a range of 0.3–0.7
mmolN/m3. For vertical diffusive nitrate transport, assuming a mean
upward nitrate flux of 10-6 mmolN/m2/s (Kaneko et al., 2013), multi­
plying the duration of a water parcel flowing from the KSJ to KKE anddividing by the typical layer thickness of the intermediate layer (400 m),
vertical diffusion increases the nitrate concentration by an order of 0.01
mmolN/m3. Because net effective diffusion is the sum of the nitrateexport through the upper interface and import through the lower
interface, it should be less than 0.01 mmolN/m3. The observed nitrate6

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Fig. 6. Velocity and nitrate flux along the subarctic gyre. (a), (b), and (c) represent the eastern portion of the Alaskan Stream (at Section P16), the western portion of
the Alaskan Stream (at Section P14), and the Oyashio (at Section P01). Red contours denote the nitrate concentration (mmol/m3). (d), (e), and (f) represent thenitrate flux. Red contours denote the neutral density surface (kg/m3) for the ASE, ASW, and OYA. Positive and negative values indicate eastward and westward
directions, respectively.
Table 2
Volume transport (Vt), nitrate transport (Nt), transport weighted nitrate concentration (Ct) and area weighted nitrate concentration (Ca) of the Oyashio (at sectionP10), the Alaskan stream (West, at section P14), and the Alaskan stream (East, at section P16). Blue character denotes that the nitrate concentration decrease along theflow path. The lower boundary of the layers is 26.8, 27.15, 27.35, 27.6, 27.8, and 27.9 kg/m3. Positive (negative) values indicate northward (southward) or eastward(westward).
Vt (Sv)

T
1–2
3
4
5
6
7

Nt (kmol/s)

Ct (mmol/m3 )Ca (mmol/m3 )

ASE

ASW

OYA

ASE

ASW

OYA

ASE

ASW

OYA

ASE

ASW

OYA

¡20.02− 5.11− 3.65− 3.33− 3.91− 2.78− 1.25¡19.05− 5.90− 3.75− 2.57− 3.07− 2.35− 1.42¡14.36− 2.00− 3.31− 2.97− 2.79− 2.41− 0.88¡788.12− 104.89− 156.05− 154.79− 183.60− 131.15− 57.63¡782.61− 183.52− 158.62− 120.47− 144.89− 110.43− 64.69¡577.62− 47.32− 125.31− 128.92− 126.72− 109.71− 39.63

N/A
20.53
42.72
46.50
47.01
47.24
46.28

N/A
31.11
42.35
46.81
47.17
47.09
45.65

N/A
23.67
37.84
43.43
45.40
45.52
44.94

N/A
21.07
41.61
45.09
45.57
45.63
44.61

N/A
30.33
41.03
44.68
45.39
45.15
44.03

N/A
23.35
37.33
42.39
44.12
44.05
43.34

concentration increases from the KJS to KKE by 1.5, 2.1, 2.66, and 2.89
mmolN/m3 for layers 4–7, respectively, and therefore, regeneration anddiffusion are likely to be minor causes for the increase in nitrate con­centration along the Kuroshio.
Although the diffusive nitrate flux contributes little to the increased
nitrate concentration along the Kuroshio, it is important to the nitratebudget in the surface layer over the entire Kuroshio region. For example,
with an assumption that a diffusive nitrate flux of 10− 6 mmolN/m2 /soccurs over an area 2000 km long and 200 km wide, the upward
diffusive nitrate supply is ~13 × 1012 molN/y.

Arc (Stabeno et al., 2005) and flows into the North Pacific through the
Kamchatka Strait as the East Kamchatka Current. The East Kamchatka
Current flows southward along the Kuril Island chain to the southeast of
Hokkaido and is named the Oyashio. During the long journey, intense
mixing along the island chain and water exchange with other water
masses modifies the physical and biogeochemical properties of theocean currents in the subarctic gyre.
In terms of the sectional velocity, there is a single surface maximum
in the ASE (Fig. 6a). For the ASW (Fig. 6b), the eastward flow (Fig. 6b) isin the island wake and is treated together with the two adjacent west­
ward flows when calculating volume and nitrate transport. The Oyashio(Fig. 6c) has four alternative flows with two northeastward and two
southwestward flows. The left-most negative (southwestward) flow inthe section is chosen to represent the Oyashio (Fig. 6c). The surface
velocities of the ASE, ASW, and OYA are less than 0.4 m/s and decrease
to a depth of 2000 m with the same sign. This structure results in largetransport through the entire water column. The net volume transports
over the upper 2000 m are 20.2, 19.1, and 14.4 Sv (Table 2) westward

5. Subarctic nutrient streams
The subarctic nutrient streams (Fig. 6) consist of the Alaskan Stream(ASE denotes the eastern section of the Alaskan Stream at Section P16,
and ASW denotes the western section at P14, Fig. 1) and Oyashio (OYA
at Section P1, Fig. 1). The Alaskan Stream flows along the Aleutian Is­
land chain, enters the Bering Sea through several passes in the Aleutian7

Y. Long et al.

Progress in Oceanography 202 (2022) 102756

Fig. 7. (a), (b), and (c) represent the ratio of regenerated nitrate concentration to nitrate concentration of the eastern portion of the Alaskan Stream (at Section P16),
the western portion of the Alaskan Stream (at Section P14), and the Oyashio. Red contours denote the neutral density surface (kg/m3). The top layer is blank due tothe large uncertainties. (d), (e), and (f) represent the temperature-salinity diagram, and color shading denotes the nitrate flux for the ASE, ASW, and OYA,
respectively. Potential density contours 26.13, 26.67, 26.98, 27.16, 27.39, 27.56, and 27.65 in (d–f) correspond to neutral densities of 26.2, 26.8, 27.15, 27.35, 27.6,
27.8, and 27.9, respectively.

for the ASE, ASW, and OYA, respectively. The nitrate concentration
reaches almost 15 mmolN/m3 on the sea surface and increases to 40
mmolN/m3 at a depth of 400 m. Therefore, the nutricline is stronger andshallower here than in the subtropical gyre.
The value of the nitrate flux subsurface maximum in three sections
along the subarctic stream path (Fig. 6d–f) is comparable to that of theKuroshio but is located at a shallower depth (200–300 m), showing thehigh possibility of carrying nutrients directly into the mixed layer. The
nitrate transports for the ASE, ASW, and OYA are − 788.1, − 782.6, and− 577.6 kmolN/s, respectively. The volume transport and nitrate trans­
port between the ASE and ASW change little, while that from the ASW to
OYA decreases. In contrast to the Kuroshio, there is no downstream
intensification in volume transport and nitrate transport.
The nitrate concentration slightly decreases from the ASE to ASW(Table 2) in layers 3–7, and the reduction is evident from the ASW to OYA.
Regeneration tends to increase the nitrate concentration along thenutrient stream, and therefore, it is not the candidate responsible for the
reduced nitrate concentration. However, although there is strong tidal
mixing along the Kuril and Aleutian island chains, the uniform reduction
over several layers requires a net loss of nitrate in each individual layer;that is, the nitrate export at the upper interface is larger than the import at
the lower interface (diffusive nitrate flux is upward according to the ni­
trate concentration gradient). Assuming an upper (lower) interface thathas a large (small) diffusive nitrate flux of 10− 5 (10− 6) mmolN/m2/s(Kaneko et al., 2013), a typical horizontal velocity of 0.3 (0.2) m/s, a layer
thickness of 300 m, and a distance between two sections of 2000 km, thenitrate concentration reduction reaches approximately 0.2 mmol/m3(10− 5 mmolN/m2 /s × 2000 kmÃ⋅0.3 m/sÃ⋅300 m− 10− 6 mmolN/m2 /s × 2000 kmÃ⋅0.2 m/sÃ⋅300 m). This value is significantly smaller than
the actual reduction (~1–2 mmol/m3); therefore, we exclude the possi­
bility of regeneration and vertical diffusion. The lateral water exchange isleft and will be examined in detail.
To determine what occurs from the ASE to OYA, the change in watermass using a T-S diagram is presented (Fig. 7). The T-S relationship(Fig. 7d–f) shows that from the ASE to ASW, the water mass propertychanges little, while from the ASW to OYA, the core of the nutrient
stream, where the subsurface maximum of nitrate flux is located, be­comes cooler. The isopycnal range of the subsurface nutrient flux
maximum (Fig. 6d–f) scarcely changes along the nutrient stream, andtherefore, this subsurface cooling simply implies the existence of lateralwater exchange with cold water. Therefore, when considering the
reduction in nitrate concentration along the subarctic gyre, the candi­date involved in the lateral exchange process should have low temper­
atures and/or low nitrate concentrations.
From the ASE to ASW, there is net northward transport through thesouthern boundary of the box (Box 10 in Fig. 1) (Fig. 2). The seawater isfrom lower latitudes and therefore has a lower nitrate concentration. It
merges into the westward Alaskan Stream and flows out of the box
through its western boundary. The lateral water exchange with the low
nitrate concentration seawater from the south is the cause of the
reduction of nitrate concentration from the ASE to ASW. Moreover,layers 4–6 of the ASE and ASW are deeper than 500 m (Fig. 6d–f), while
the passes in the Aleutian Island chain (northern boundary of Box 10)
are shallower than 500 m, and water exchange with the southern area istherefore the only cause in these layers.
From the ASW to OYA, the situation is complicated because theBering Sea and Okhotsk Sea can both affect the nitrate concentration
along the stream path. The ASW section is located in the upstream region
where the water exchange between the Alaskan Stream and Bering Sea
occurs, and the OYA section is in the downstream region where waterexchange between the East Kamchatka Current and Okhotsk Sea occurs.
Roden (1995) demonstrated that the nutrient concentration (silicate,nitrate, and phosphate) of deep water is higher in the Bering Sea than in
the North Pacific. Therefore, water exchange with or water input fromthe Bering Sea increases the nitrate concentration along the stream path.
Andreev et al. (2010) demonstrated that the Okhotsk Sea receives 1.0 ×
8

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Progress in Oceanography 202 (2022) 102756

Fig. 8. Nitrate concentration as a function of neutral density and longitude/latitude at several sections in the Bering Sea and in the East Kamchatka Current. Locationof the sections (a)–(f) is given in (g). The color scales in (a)–(f) are different from those in (g).

1012 dissolved inorganic nitrogen, 4.0 × 1010 dissolved inorganic
phosphorus, and 4.0 × 1012 dissolved inorganic carbon annually fromthe North Pacific. Their estimation was apparently based on a waterexchange of 3–5 Sv and the nutrient concentration difference between
the Okhotsk Sea and North Pacific, that is, the effective transport.
Nishioka et al. (2020) reported that the upward nitrate transport aroundthe Kuril Island chain was 0.19 × 1012 molN/y, while that around the
Aleutian Island chain was 0.09 × 1012 molN/y. The upward nitratetransport was smaller than the nitrate export from the North Pacific to
the Okhotsk Sea. The hydrographic profiles in the Okhotsk Sea, obtained
from the Japan Meteorological Agency (JMA), and the Bering Sea, ob­tained from JAMSTEC, were used to explain the nitrate concentration
variation from the ASW to OYA.
Although the Bering Sea is considered to be a nutrient source,
particularly for silica, to the North Pacific, its nutrient export is rarely
discussed because of the lack of data. Therefore, the MR080500 and
MR040400 cruises from JAMSTEC were chosen to illustrate the spatial
variation in the nutrient concentration from the Bering Sea to the North
Pacific. The nitrate concentration in the Bering Sea, especially in the
Aleutian Basin (Line a, Fig. 8), is higher than that in the downstream
region of the East Kamchatka Current (Line d, Fig. 8). The upper layershows an undulated contour of nitrate concentration along the section(Fig. 8f), which is depressed in the Kamchatka Strait (Fig. 8b) and
uplifted in its downstream region (Fig. 8c–d). In a density layer of 26.8kg/m3, the nitrate concentration in the Bering Sea exceeds that in the
North Pacific by ~4 mmolN/m3 (Fig. 8g). Because the volume transportof the East Kamchatka Current is ~10 Sv (Panteleev et al., 2006), theeffective nitrate transport (Ayers et al., 2014) from the Bering Sea to theNorth Pacific should be on the order of 1.3 × 1012 molN/y. This value iscomparable to the nitrate transport from the North Pacific to the
Okhotsk Sea (Andreev et al., 2010) and is larger than the upward nitratetransport around the island chains.
The North Pacific has a higher nitrate concentration than the
Okhotsk Sea in the same isopycnal layer, particularly in the intermediate
layer (26.13–26.98 kg/m3, Fig. 9b, c). The nitrate concentration, as afunction of depth (Fig. 9e) or potential density (Fig. 9g), shows that
there is a reduced nitrate concentration from north to south in the North
Pacific. The nitrate concentration is higher in a latitude band of 48–50◦ N
in the North Pacific (Fig. 9e) than in the Okhotsk Sea in the upper 1000m (Fig. 9d) and is similar to that in the Okhotsk Sea when reaching alatitude band of 41–42◦ N. Because the Oyashio water on the Pacific side
moves from high latitudes to low latitudes, the reduction in nitrateconcentration during its movement from 48–50◦ N to 41–42◦ N indicatesthe possibility that Okhotsk Sea water with a low nitrate concentration ismixed with Oyashio water.
The nutrient stream in the subarctic gyre has comparable nutrienttransport as that in the subtropical gyre but has a shallower subsurface
maximum. Its nitrate concentration decreases along the stream path.
Although other mechanisms, such as vertical mixing and biogeochem­
ical processes, may affect the nitrate concentration, this reduction ismainly due to lateral water exchange. The Bering Sea and Okhotsk Sea
act as sources and sinks, respectively, for nutrients carried by thenutrient stream in the subarctic gyre.
6. Other nutrient transfers
The vertical nitrate transfer derived from the inverse method consistsof two components: vertical advection and vertical diffusion. Although
the vertical velocity derived from the inverse calculation may beaffected by the initial imbalance (net transport integrated along thesections that encloses a box) within each layer of the box, the value ofvertical volume transport still meets our general knowledge on the order9Y. Long et al.

Progress in Oceanography 202 (2022) 102756

Fig. 9. Comparison of nitrate concentrations between the Okhotsk Sea and North Pacific. (a) Locations of the hydrographic casts. Crosses and dots indicate thehydrographic casts in the Okhotsk Sea and North Pacific. The left and right panels are for the Okhotsk Sea (b, d, f) and North Pacific (c, e, g), respectively. (b) and (c)are the T-S diagrams with color showing nitrate concentration. (d) and (e) are the nitrate concentration as a function of depth with color showing latitude. (f) and (g)show the nitrate concentration as a function of neutral density, with color showing latitude. Potential density contours 26.13, 26.67, 26.98, 27.16, 27.39, 27.56, and27.65 in (b, c) correspond to neutral densities of 26.2, 26.8, 27.15, 27.35, 27.6, 27.8, and 27.9, respectively.

of magnitude, as does nitrate transport. According to the results pre­sented here (Table 3) (further details provided in the Appendix), thevertical diffusive nitrate transport is positive at the lower interface oflayers 1–5 due to the positive vertical gradient of nitrate concentration(Fig. 4) and negative at the lower interface of layers 6–7 due to thenegative vertical gradient of nitrate concentration (Fig. 6).
Vertical nitrate transport provides information on the nutrient
budget in the North Pacific. Nishioka et al. (2020) suggested that ver­tical diffusion supplies nitrate from the subarctic intermediate nutrient
pool to the upper layer at a rate of 0.1–10 × 1012 molN/y. They further
mentioned that nitrate transport from the deep layer to the intermediate
layer is unclear. Using the inverse calculation, a general estimation ofthese two nitrate transports can be given. First, nitrate import from theBering Sea (1 × 1012 molN/y, this study), nitrate export to the Okhotsk
Sea (1 × 1012 molN/y, Andreev and Pavlova, 2010), and nitrate export
to the subtropical gyre through NPIW formation (0.76 × 1012 molN/y,Long et al., 2019) suggest a net nitrate export of 0.76 × 1012 molN/y.
Second, the subarctic intermediate nutrient pool is within a potential
density range of 26.6–27.5 kg/m3, which corresponds to a neutral
density range of 26.7–27.7 kg/m3. Taking a neutral density of 26.8 kg/
m3 and 27.6 kg/m3 as an approximation of the subarctic intermediate
nutrient pool and using the northern half of Boxes 6, 7, and 8 (sum ofhalf of the vertical nitrate transport in Boxes 6, 7, and 8) and all of Boxes
9, 10, and 11 (sum of the vertical nitrate transport in Boxes 9, 10, and11) to represent the area of the subarctic intermediate nutrient pool, thenitrate transport from the intermediate layer to the upper layer is 1.31 ×
1012 molN/y (Table 3) (=(24.8 + 10.24 + 12.08)/2 + 2–16.29 + 32.37
kmolN/s), and from the deep layer to the intermediate layer it is 0.27 ×
1012 molN/y (Table 3) (=(− 17.98 + 2.89–5.77)/2 + 1.64 + 23.66–6.39
kmolN/m3). The vertical nitrate transport derived from the inverse
calculation of this study gives a deficit of 1.04 × 1012 molN/y (=1.31 ×
1012 – 0.27 × 1012 molN/y). Third, Nishioka et al. (2020) estimated thatnitrate export from the surface to depth was 1.79–2.76 × 1012 molN/y.
Hence, the nitrate export from the bottom of the intermediate layer tothe depth should be within a range of 0–0.96 × 1012 molN/y (1.79–2.76
× 1012–1.04 × 1012–0.76 × 1012 molN/y).
Subduction and induction processes can transport nutrients between
the mixed layer and permanent thermocline. These processes provide
routes for the exchange between the nutrient-depleted surface layer andnutrient-rich subsurface layer. Williams et al. (2006) demonstrated that
the Gulf Stream nutrient stream contributes 40% to the nitrate transport
provided by the induction process. This value is still unknown in the
North Pacific. Referring to the subduction amount given by Qiu andHuang (1995), nutrient transport by this process can be approximately
estimated. The volume transport induced by subduction and induction
are 32.5 and 7.8 Sv, respectively, in terms of annual mean (Qiu andHuang, 1995). The nitrate concentration in the subduction water can be
5 mmol/m3 (this value is from the first layer in Table 1, to represent thesurface layer of the subtropical gyre), while that in induction water is 21
mmol/m3 (this value is from the first layer in Table 2, to represent the10

Y. Long et al.

Progress in Oceanography 202 (2022) 102756

Table 3
Vertical advective (w), diffusive (d) and vertical (v, sum of w and d) nitrate transport (kmolN/s) within each box. The locations of the boxes are shown in Fig. 1. Positive
values indicate upward.
BOX1

BOX2

BOX3

BOX4

BOX5

BOX6

BOX7

BOX8

BOX9

BOX10

BOX11

26.20

w
d
v

− 9.817.39− 2.42− 19.49
4.60− 14.89

18.88
7.58
26.46

− 0.19
10.14
9.95

8.42
8.63
17.05

29.57
21.01
50.58

− 6.418.08
1.68− 4.72
16.63
11.91

N/A
N/A
N/A

N/A
N/A
N/A

N/A
N/A
N/A

26.80

w
d
v

7.70
8.03
15.73

− 15.58
9.57− 6.00− 0.039.50
9.47− 4.958.03
3.08− 12.85
6.95− 5.90

13.06
11.75
24.80

− 1.44
11.68
10.24

3.02
9.06
12.08

− 10.67
12.67
2.00− 29.37
13.08− 16.29

1.80
30.57
32.37

27.15

w
d
v

18.23
4.06
22.29

− 19.49
5.01− 14.48− 16.32
4.68− 11.64− 4.492.65− 1.84− 22.05
3.30− 18.75

8.28
2.97
11.25

− 4.444.17− 0.27

4.09
2.83
6.92

5.86
1.74
7.60

− 18.43
1.77− 16.67− 9.803.32− 6.48

27.35

w
d
v

− 13.85
1.79− 12.06− 13.35
1.74− 11.60− 28.55
1.06− 27.50− 5.240.77− 4.48− 12.85
1.49− 11.37

4.08
0.92
5.00

− 1.991.26− 0.72

0.80
0.86
1.66

− 0.27
0.38
0.11

4.39
0.44
4.83

− 24.20
0.27− 23.93

27.60

w
d
v

8.89
0.14
9.03

6.51
0.08
6.59

− 48.49− 0.16− 48.65

15.47− 0.13
15.34

11.95
0.29
12.24

− 18.130.16− 17.98

2.81
0.07
2.89

− 5.77
0.00− 5.77

1.49
0.15
1.64

23.58
0.08
23.66

− 6.35− 0.04− 6.39

27.80

w
d
v

2.29
− 0.341.95

31.93− 0.3131.62− 31.69− 0.28− 31.9815.22− 0.27
14.95− 6.93− 0.23− 7.16− 20.89− 0.19− 21.08− 1.63− 0.27− 1.90− 8.94− 0.29− 9.231.89− 0.291.60

4.52− 0.194.34− 0.08− 0.28− 0.36

27.90

w
d
v

− 0.22− 0.34− 0.5735.92− 0.4235.50− 4.28− 0.31− 4.59− 8.57− 0.31− 8.88− 13.42− 0.35− 13.76− 13.60− 0.40− 14.00− 6.85− 0.34− 7.19− 3.32− 0.37− 3.680.03− 0.35− 0.32− 13.62− 0.32− 13.94

10.84− 0.3810.45

surface layer of the subarctic gyre). Their net effect can be defined as theventilation process that contributes approximately 163 kmolN/s (=5.17
× 1012 molN/y, from the mixed layer to the permanent thermocline) and164 kmolN/s (=5.17 × 1012 molN/y, from permanent thermocline tomixed layer), respectively. These values are almost twice that of thevertical nitrate transport derived from the inverse calculation at thelower interface of the top layer (26.2 kg/m3, 100 kmolN/s or 3.15 ×
1012 molN/y, upward, 84 kmolN/s for vertical diffusion and 16 kmolN/s
for vertical advection) (Table 3, Row 4), although only half of the sub­tropical gyre was included in this calculation. Consequently, subduction
and induction processes play an essential role in the nitrate budget in theupper layer of the North Pacific.

vertical diffusion play a minor role in the change in nitrate concentra­tion along the stream path.
The contribution of vertical nitrate transport to the subarctic inter­mediate nutrient pool was estimated. The ventilation processes, inwhich the subduction that carries nutrients from the mixed layer to thepermanent thermocline in the subtropical gyre (5.17 × 1012 molN/y)
and induction that carries nutrients from the permanent thermocline tothe mixed layer in the subarctic gyre (5.17 × 1012 molN/y) are com­parable to the sum of dianeutral and diffusive nutrient transport (3.15 ×
1012 molN/y). The results of this study confirm that vertical nitratetransport is important at the basin scale and that lateral water exchangewith adjacent seawater is responsible for the change in nitrate transportand nitrate concentration along the nutrient streams in the North Pa­
cific. This analysis is based on the steady state and lacks temporal in­formation; therefore, the ventilation processes should be quantified
using a physical-biogeochemical coupled model in future work.

7. Concluding remarks
By applying the inverse method, the absolute geostrophic velocity
normal to the WOCE-revisit sections was calculated. The nitrate flux wasdetermined by multiplying the velocity and nitrate concentration andwas integrated over the section to obtain the nitrate transport. The
spatial pattern of the volume transport and nitrate transport per unit
width was presented for four isopycnal layers. The spatial patternshowed that the upper portion of the nutrient transport was related tothe mode waters and recirculation in the subtropical gyre, while theintermediate portion was closely related to the distribution of the NPIW
and had the most intensive nutrient transport.
The nutrient streams of the Kuroshio, the Alaskan Stream, andOyashio drive the most intensive nutrient transport within the basin.
Both the volume transport and nitrate transport of the Kuroshio areincreased downstream, which is due to the Kuroshio recirculation gyre.
The nitrate concentration in the same isopycnal layers increases along
the Kuroshio path. This variation from the area south of Japan to the
Kuroshio Extension is due to the confluence of the high nitrate con­centration water from the north.
For the subarctic gyre, there is no downstream intensification in thevolume and nitrate transport from the Alaskan Stream to the Oyashio.
The nitrate concentration decreases within most layers along the sub­arctic gyre. The lateral water exchange with the relatively low latitude
area and the Okhotsk Sea decreases the nitrate concentration along thenutrient stream in the subarctic gyre. The biogeochemical processes andDeclaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgments
This study was supported by the National Natural Science Founda­tion of China (42106035, 41920104006), Scientific Research Fund of
Second Institute of Oceanography, MNR (grants JB2105 and JZ2001),
the China Postdoctoral Science Foundation (grant 2020M681969), theInnovation Group Project of the Southern Marine Science and Engi­
neering Guang dong Laboratory, Zhuhai (No. 311020004), and the
grants from the Ministry of Education, Culture, Sports, Science andTechnology, Japan (MEXT) to a project on Joint Usage/Research Cen­
ter— Leading Academia in Marine and Environmental research (LaMer).
X. Guo thanks support by JSPS KAKENHI (grant numbers 20H01972)
and by the Environment Research and Technology Development FundJPMEERF20205005 of the Environmental Restoration and Conservation
Agency of Japan. The data used in this study were from CCHDO (https://cchdo.ucsd.edu/), CCMP (http://www.remss.com/measureme11

Y. Long et al.

Progress in Oceanography 202 (2022) 102756

nts/ccmp/), ECMWF (https://www.ecmwf.int/) and WOA (https://www.nodc.noaa.gov/OC5/woa13/). The authors appreciate the scien­tists and crews who deploy the WOCE-revisit cruise. The authors

appreciate Dr. J.L. Pelegrí and another anonymous reviewer and Dr.
Shin-ichi Ito for their supportive comments on the original manuscript.

Appendix
The WOCE data from 2004 to 2007 were used in the inverse calculation. Generally, the available hydrographic data encompass the period from1985 to the present. This period was chosen to reduce temporal aliasing error due to decadal oceanic variations in the North Pacific (e.g., Pacific
Decadal Oscillation, North Pacific Gyre Oscillation, and Kuroshio Extension Decadal Oscillation). In addition, the stations were carefully chosen to
avoid large transient variations at the hydrographic line intersections, as suggested by Macdonald et al. (2009). This is because if part of the eddy was
sampled at the endpoints of the section, this may induce an error to the baroclinic structure (it is dependent on water depth) in the initial imbalance ofproperty within the box. Although the vertical velocity and diffusion may be affected by this initial error, the reference velocity is not sensitive.
Apart from the WOCE data, other datasets were also used in the inverse calculation. The Ekman transport was calculated from the CCMP windproduct (0.25◦ × 0.25◦ ) (2004–2007), and sea surface freshwater flux (evaporation-precipitation) was calculated from the European Center for
Medium-Range Weather Forecasts (ECMWF) ERA-interim reanalysis data (0.25◦ × 0.25◦ ) (2004–2007). The density, salinity, and concentrations ofsilicate and nitrate for calculating the Ekman mass, silicate transport and neutral density surface were determined using WOA13 (World Ocean Atlas,2013) version 2 data.
The inverse box model (Wunsch, 1978) assumes conservation of mass, salt, P* (170P + O), heat, and silicate in each individual layer separated by aneutral density surface of 26.2, 26.8, 27.15, 27.35, 27.6, 27.8, 27.9, 27.95, 28, 28.05, 28.09, 28.1, and 28.11 kg/m3 for boxes south of Section P1,
while of 26.8, 27.15, 27.35, 27.6, 27.8, 27.9, 27.95, 28, 28.05, 28.09, 28.1, and 28.11 kg/m3 for the remaining boxes to avoid outcropping in the box.
Their selection follows the definition of the vertical boundary of the water mass (Macdonald et al., 2009; Ganachaud and Wunsch, 2002) or the entire
water column (Table A1). By using the thermal wind relation, the geostrophic velocity referring to the 28.05 kg/m3 neutral density layer (at a depth ofapproximately 3000 m) is calculated.
The general form of the equation is:
)
) ∑ ∑
(
(
∑∑∑L
∑∑∑
∂CbL
∂CbL
ami vRmi Cmij − wU αU Cb U + wL αL Cb L + κZU αUEmVEK mi Csurf mi + FW ≈ −amij vGmij Cmij .
(A1)+ κZL αL
−
j=U
∂Z
∂Z
m
m
m
i
i
i
j
The bold characters are the unknowns. VR denotes the velocity at the reference level, w denotes the vertical velocity, κz denotes the eddy
diffusivity, Em is the Ekman component correction factor, and FW is the fresh water flux.
C represents concentrations at each 1 dbar level (2 dbar interval data were linearly interpolated to a 1 dbar interval). Subscripts i, j, and m denotethe indices of the station pairs, indices of one level within each layer, and each side (usually the subsection) of the box, respectively. Specifically, C is ρ
for mass, α represents the interface areas and is calculated from the World Ocean Atlas, a represents the distance of each station pair, Cb represents
concentrations at the boundary of each interface as derived from the in situ sectional data, and U and L denote the upper and lower boundaries of thelayer, respectively. VEK is the Ekman volume transport and is calculated from the CCMP wind product and the WOA surface density, Csurf is theconcentration (ρ and nutrient concentration) at the sea surface and is derived from the WOA data, and VG denotes the baroclinic velocity calculated by
the thermal wind relation.
For the terms on the left-hand side, the first term denotes the relative transport, the second and third terms denote the vertical transport throughthe upper and lower interface of an individual layer, the fourth and fifth terms denote the vertical diffusion through the upper and lower interfaces ofan individual layer, and the sixth and seventh terms denote the Ekman transport and fresh water transport, respectively. The right-hand side represents
the initial imbalance of the properties.
The Guass-Markov estimator was used to solve the underdetermined problem (because the amount of velocity within station pairs usually exceedsthat of constraints, the number of unknowns exceeds the number of equations). All conservation equations were weighted according to their a priori
uncertainties. Compared to the tapered-weighted least squares, this solves the part of the solution that is not resolved by the constraints. The first guessof the solution, or the a priori information, is as follows: 0.2 m/s, 0.05 m/s, and 0.02 m/s for the depth of a station pair shallower than 500 m, from 500
to 1000 m and deeper than 1000 m, respectively; 1 × 10− 6 m/s and 10− 4 m2 /s for dianeutral velocity and eddy diffusivity, respectively; and thecoefficient of variation (standard deviation/mean, during 2004–2007) of Ekman transport at each subsection for Ekman correction, EP (sum of
evaporation (upward, negative) and total precipitation (downward, positive)), in each box for the EP correction. A priori noise is set as 0.5 × 109 kg/s
for mass in each individual layer that is not in contact with the sea surface and 1 × 109 kg/s for the surface layer and the entire water column. For thesalinity anomaly, PO (170 phosphate + oxygen) anomaly, and heat anomaly, a priori is set to be the standard deviation of the corresponding variablein each layer multiplied by 4 × 109 . The a priori for silicate is set as 52 × 109 .
According to the interpretation of the inverse results, this represents the mean state of the large-scale circulation during 2004–2007. Four out of
Table A1
Size of matrix of each term in the inverse problem as defined by Equation (A1). Abbreviations: SP for station pairs, IL for individual layers, Bo for boxes, SuB for
subsections, and N/A for not applicable. The property transport of the water column means the integration over full water depth, the lower layers means the layers that
do not contact the sea surface.
Mass
Mass for water column
Salt anomaly for lower layers
Salt for water column
PO anomaly for lower layers
Heat anomaly for lower layers
Silicate for water column

Relative transport

Dianeutral transport

Diffusion

Ekman correction

E-P correction

151 IL × 674 SP
11 Bo × 674 SP
140 IL × 674 SP
11 Bo × 674 SP
140 IL × 674 SP
140 IL × 674 SP
11 Bo × 674 SP

151 IL × 140 IL
11 Bo × 140 IL
140 IL × 140 IL
11 Bo × 140 IL
140 IL × 140 IL
140 IL × 140 IL
11 Bo × 140 IL

N/A
N/A
140 IL × 140 IL
11 Bo × 140 IL
140 IL × 140 IL
140 IL × 140 IL
11 Bo × 140 IL

151 IL × 20 SuB
11 Bo × 20 SuB
N/A
11 Bo × 20 SuB
N/A
N/A
11 Bo × 20 SuB

151 IL × 11 Bo
11 Bo × 11 Bo
N/A
N/A
N/A
N/A
N/A

12

Y. Long et al.

Progress in Oceanography 202 (2022) 102756

604 (less than 1%) solutions exceed the a priori mentioned above, indicating that the results are well constrained by the a priori. The spatial pattern ofdeep flow, net volume, heat, and mass transport over transoceanic sections such as P1, P2, and P3 were validated by comparison with those reported in
Mcdonald et al. (2009), Roemmich and McCallister (1989), and Ganachaud and Wunsch (2002).

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