Journal of Oceanography, Vol. 56, pp. 361 to 377, 2000
Study of Water Motion at the Dissolved Oxygen Minimum
Layer and Local Oxygen Consumption Rate from the
Lagrangian Viewpoint
NORIHISA IMASATO 1*, TAIYO K OBAYASHI 2 and S HINZOU FUJIO 3
1
Faculty of Information Science and Technology, Aichi Prefectural University,
Kumahari, Ibaragahazama 1522-3, Nagakute-cho, Aichi 480-1198, Japan
2
Center for Climate System Research, University of Tokyo,
Komaba 4-6-1, Meguro-ku, Tokyo 153-8904, Japan
3
Ocean Research Institute, University of Tokyo,
Minamidai 1-15-1, Nakano-ku, Tokyo 164-8639, Japan
(Received 25 June 1999; in revised form 11 November 1999; accepted 14 November 1999)
By using the Euler-Lagrangian method, we examine water movements within the layer
of minimum oxygen concentration and estimate local oxygen consumption rates for
15 regions of the global ocean. To do this, a number of labeled particles (which represent water parcels) are deployed at the center of a grid with 15 depth levels and tracked
backward in time for 50 years in a three-dimensional velocity field. We assume that a
particle picks up oxygen when it encounters the point of maximum oxygen concentration along the 50 years segment of its path. We introduce a contribution rate from
waters distributed throughout the global ocean to the oxygen concentration of a local
layer under consideration. Water parcels which are assumed to pick up oxygen within
the oxygen minimum layer of an oceanic region under consideration make a very
small contribution to the overall oxygen concentration of this layer. In addition, these
parcels move out of the layer and water parcels from the upper layers take their
place. The averaged Lagrangian local oxygen consumption rate is 0.033 ml/l/yr for
the depth of the oxygen minimum layer, 0.20 ml/l/yr at 100 m depth (euphotic layer),
0.043 ml/l/yr for layers from 150 m to 800 m depth and 0.012 ml/l/yr for deep layers
from 800 m to 3000 m. The present Lagrangian numerical experiment produces a
maximum difference between observed and calculated concentrations of oxygen and,
therefore, a maximum oxygen consumption rate. Although the present method has an
ambiguity as to how oxygen is picked up, we nevertheless were able to identify regions in which the water parcels pick up oxygen of maximum concentration. We found
that the South Equatorial Current (SEC) transports oxygen of higher concentration
to the middle latitude regions of both the North Atlantic and the North Pacific across
the equator.
Keywords:
⋅ Oxygen minimum
layer,
⋅ Lagrangian oxygen
consumption rate,
⋅ contribution rate to
oxygen concentration,
⋅ labeled particle
tracking.
This vertical profile of dissolved oxygen has been
explained by a classical vertical one dimensional
advective-diffusion model in which two sources of the
oxygen are taken into account. One source is from the
deep layers, and the other is from the surface layer. The
abyssal circulation transports oxygen from the North Atlantic and the Antarctic Sea to deep layers of the Indian
and the Pacific via the Antarctic Circumpolar Current
(ACC) region and then upwelling transports oxygen toward the sea surface. This transport produces a vertical
profile of oxygen concentration decreasing gradually from
the bottom toward the sea surface. On the other hand, for
1. Introduction
Dissolved oxygen in the ocean is a useful tracer for
tracking the movement of water-types and water-masses,
especially those in deep and bottom waters. Dissolved
oxygen is saturated in the euphotic layer, and its concentration decreases toward the main thermocline where a
minimum concentration layer often appears. At greater
depths the concentration increases once more.
* Corresponding author. E-mail: [email protected]
Copyright © The Oceanographic Society of Japan.
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the upper layer (from the sea surface to the main
thermocline), oxygen is transported toward the
thermocline due to vertical eddy diffusion (convection),
and at the same time is consumed by biochemical processes. Since horizontal water motion is very weak near
the thermocline, convection and diffusion must play an
important role in the transport of oxygen. As a result of
these processes, an “oxygen minimum” layer is formed
at mid-depths within the ocean.
The oxygen minimum layer near the eastern boundary of the North Atlantic was thought to be the result of
an increase in consumption due to upwelling along the
eastern boundary (Menzel and Ryther, 1968). However,
Luyten et al. (1983) showed that ventilation produces an
oxygen maximum layer in the North Atlantic and that an
oxygen minimum layer is produced in the eastern shadow
zone (unventilated zone) due to a decrease in oxygen replenishment because of poor ventilation. They also
showed that the Intermediate Water transports low salinity and high oxygen concentration water from the surface
or near surface layer to the middle layer. This water is
characterized by a salinity minimum. Figures 3 and 4 in
Reid (1965) show that the salinity minimum water in the
South Pacific is associated with high oxygen concentration. On the other hand, in the North Pacific, the oxygen
maximum lies above the core of the salinity minimum
and the oxygen minimum lies below it.
According to observations (e.g., Levitus, 1982), however, in the southern oceans the oxygen minimum layer
appears below the main thermocline. This fact suggests
that any water motion other than vertical diffusion or ventilation can contribute to the formation of an oxygen minimum layer. As Menzel and Ryther (1968) showed, oxygen concentration is augmented by water parcels which
have been transported horizontally from distant oceanic
regions, so that the true distribution of dissolved oxygen
must be produced by three dimensional water movements
including horizontal circulation, upwelling and sinking.
The traditional method of examining material transport is to solve the equations for a system of advection
and diffusion. As the processes of advection and diffusion are irreversible, this method provides a poor understanding of where a water parcel in a given oceanic region comes from and the route it subsequently takes. On
the other hand, the Euler-Lagrangian method, in which
many labeled particles can be tracked forward or backward in time, is ideally suited to this purpose. The method
has been applied by investigators at Kyoto University to
a number of problems in physical oceanography including tidal exchange through a narrow strait (Imasato et al.,
1980; Awaji et al., 1980), deep water movement (Fujio
and Imasato, 1991; Fujio et al., 1992b), and the Indonesian Through Flow (Miyama et al., 1995). Here, we use
the Euler-Lagrangian method to address the following
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N. Imasato et al.
critical questions in our understanding of the oxygen minimum layer: “What is the relation between the three dimensional velocity field and the oxygen minimum layer?”,
“What are the origins and fates of water parcels in the
oxygen minimum layer?”, and “How much oxygen is
transported by these water parcels and what proportion is
consumed?”.
2. Method and Data
The equations used to calculate the velocity field are
the same as those of Fujio and Imasato (1997). The global ocean is divided into 2° × 2° boxes horizontally and
15 layers vertically to make prognostic calculations of
the three dimensional velocity field. The horizontal and
vertical eddy viscosities are taken to be 8 × 108 and 102
cm2 s–1, respectively, and the horizontal and vertical eddy
diffusivities are taken to be 2 × 107 and 0.3 cm2 s–1, respectively. The annual mean water temperature and salinity fields are given as an initial condition from the
Levitus (1982) data set and the annual mean wind-stress
as a surface boundary condition from the Hellerman and
Rosenstein (1983) data set. The heat and freshwater fluxes
through the sea surface are simulated by restoring the
density field at the sea surface to the Levitus’ data. Starting from the initial condition of a motionless ocean, numerical integration is continued for 946.8 years to reach
a steady state.
A total of 10 5 particles are deployed horizontally at
the center of each level of the 2° × 2° box. They are spread
vertically at depths of 25 m, 100 m, 250 m, 500 m, 800
m, 1100 m, 1500 m and subsequently to bottom with an
interval of 500 m. Using the steady state velocity field,
these labeled particles are tracked for 50 years with a time
step of 0.25 years in the backward time direction. It would
also be possible to deploy many particles uniformly in
the euphotic layer only and to track these particles forward for many years (>3000 years). However, this latter
method will produce a large accumulation of error in particle tracking. Hence, in this paper we choose backward
tracking over the shorter period of 50 years to study the
formation process of the oxygen minimum layer and relating water movements, and to evaluate the local oxygen consumption rate.
Tracking is performed according to the method of
Fujio and Imasato (1991) by solving Eq. (1) numerically
in the backward time direction.
dX/dt = U(X),
(1)
X0 = X(0),
where U is three dimensional velocity, and X and X0 are
the positions of a labeled particle at time t and at the initial time (t = 0), respectively.
Fig. 1. Illustration of the process by which a labeled particle picks up oxygen.
The dissolved oxygen concentrations encountered on
the path of each labeled particle are derived from Levitus
(1982). Figure 1 illustrates where particles pick up oxygen. In this figure, the symbol 䊉 denotes the terminal
position (t = 0) of a particle, whereas symbol 䊏 denotes
the position where the particle picks up oxygen and the
symbol • gives the position at every 0.5 year interval.
All particles in the left panel of Fig. 1, for example,
which were outside the euphotic layer for over 50 years,
must pick up oxygen at the maximum concentration (the
symbol 䊏) encountered over the 50 year path. Now, consider a particle in the right-hand panel of Fig. 1, which
has been in the euphotic layer before arriving at its terminal position. We assume that this particle picks up oxygen at a recent position 䊏 in the euphotic layer: i.e., particle A picks up oxygen at A1 (0.5 year earlier) before
arriving at the terminal position, and also particles B and
C acquire oxygen at B1 and C1, respectively. Each particle is assumed to maintain its oxygen concentration up to
the terminal position so that oxygen is conserved and is
not consumed over the particle’s path out of the euphotic
layer. However, in most cases, the instantaneous oxygen
concentration of a particle will be different from that observed at its terminal position. This difference will give
both the local oxygen consumption rate averaged over
the path of a particle and the maximum oxygen consumption along its path, which is most likely due to demande
from biochemical processes.
3. Results and Analysis
3.1 Velocity field
Firstly, in order to strengthen our understanding of
water parcel movements, we briefly describe the characteristics of the velocity field at the three depth levels of
100 m, 500 m and 1100 m (Fig. 2) in all regions. The
velocity field at the 100 m level represents that for a lower
region of the euphotic layer, whereas the 500 m and 1100
m data represent those of the oxygen minimum layers
(Table 1). The prognostically calculated velocity field is
the same as velocity field (referred to as the experiment
1) calculated by Fujio et al. (1992a).
The Pacific Ocean:
The current off the north of New Guinea flows
weakly eastward at the 100 m level, but it changes to a
strong westward current at the 500 m and 1100 m levels.
Velocity vectors within the Indonesian Through Flow at
100 m and 500 m suggest that waters originate from the
Pacific North Equatorial Current (NEC). On the other
hand, water flowing on the 1100 m level originates from
the westward current off the north of New Guinea because the Pacific NEC is very weak at that depth.
The Equatorial Undercurrent (EUC) at the 100 m
level is very weak. For the 500 m level, the EUC (eastward current) appears at 140°E to 150°W, and the current
axis is located at 2°S to 4°S. On the other hand, a well
defined westward current appears at 130°W to 90°W. At
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
363
Table 1. Depths of the main thermocline and the range of oxygen minimum.
Region
Depth (m)
Depth of main thermocline
Depth of oxygen minimum layer
The Atlantic Ocean
A
B
C
D
E
F
350~950
600~1100
350~800
300~700
300~650
400~750
250~900 (500)
200~1100 (800)
200~1000 (650)
200~1000 (450)
200~1200 (500)
1000~2000 (1000)*
The Pacific Ocean
G
H
I
J
K
350~700
400~800
350~700
400~750
350~950
700~1500 (1100)*
750~1600 (800)
200~750 (500)
1100~2000 (1500)*
1300~2200 (1800)*
The Indian Ocean
L
M
N
300~1350
400~750
500~1100
400~1100 (800)
900~1600 (1100)*
1200~2200 (1750)*
The ACC Region
O
600~1750
600~1750 (1100)
*Region in which oxygen minimum layer appears at a level deeper than the main thermocline.
The numbers in parentheses show depths of the oxygen minimum layer.
Fig. 2. Distribution of horizontal velocity. (A): 100 m level, (B): 500 m level, and (C): 1100 m level.
the 1100 m level, the westward current at 180° to 100°W
becomes obscure. Stronger eastward current flows along
30°S and from 160°E to 175°E on the 100 m and 500 m
levels and clockwise circulation in the Ross Sea becomes
obscure.
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N. Imasato et al.
The Indian Ocean:
For the 100 m level, the Indonesian Through Flow is
connected to the Indian South Equatorial Current (SEC)
flowing between 10°S and 20°S. The Mozambique Current is strong but the southward current off the east coast
Fig. 2. (continued).
of Madagascar is weak.
For the 500 m level, the SEC water originates from
the south of Australia rather than the Indonesian Through
Flow and flows between 15°S and 25°S. For the 1100 m
level, the SEC flows between 20°S and 30°S, and the
north-westward current off west and south Australia becomes strong, although the current at the 100 m level in
this region flows very weakly south-eastward (i.e., the
flows are in the opposite direction to each other). Therefore, water in the euphotic layer of the equatorial current
region in the Indian Ocean originates from the Pacific
and water in the middle layer originates from the ACC
via the south of Australia.
Both the Mozambique Current and the southward
current off the east coast of Madagascar are very strong
in both the 500 m and 1100 m levels. The southward current at the 1100 m level off Somalia is not well defined.
The Atlantic Ocean:
The North Brazil Current (NBC) on the 100 m level
in the present model is weak, but in contrast, that on the
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
365
Fig. 3. Definition of oceanic regions based on primary productivity levels (Zeitzschel, 1973).
Fig. 4. Vertical profile of OLEV. Attached letters denote the name of the region. (A): The Atlantic, (B): The Pacific and (C): The
Indian and Southern Ocean.
1100 m level strong. For the 100 m level, the EUC and
the southward current off Brazil (Brazil Current) from
20°S to 35°S are strong. For all three levels, the Weddel
Circulation expands widely, and therefore the ACC becomes strong after passing through the Drake Passage.
3.2 Vertical profile of observed and calculated oxygen
concentrations
Figure 3 shows oceanic regions defined on the basis
of the distribution in primary productivity (Zeitzschel,
1973). Figure 4 shows the vertical profile of the observed
annual mean concentration of oxygen, OLEV. The oxygen
data used here are derived from the Levitus (1982) data
set, and OLEV is averaged for each level over an oceanic
region. Panels A, B and C show profiles for the regions
of the Atlantic, the Pacific and the Indian and the South366
N. Imasato et al.
ern Oceans, respectively. The “Southern Ocean” means
the ACC region and the Antarctic Seas, and is denoted as
region O in this paper. Table 1 shows the relation between
the depths of the main thermocline and the oxygen minimum layer. For many oceanic regions, the oxygen minimum layer appears around the depth of the main
thermocline. However, for regions in the southern hemisphere such as F, J, K, M and N, the oxygen minimum
layer appears under the main thermocline. For region O,
the vertical gradient in water temperature is very weak,
and the main thermocline and the oxygen minimum layer
expand over a wide range between 600 m to 1750 m. For
region G in the North Pacific, the oxygen minimum layer
appears between 700 m to 1500 m under the main
thermocline (350 m to 700 m).
Figure 5 shows the vertical profiles of oxygen dif-
Fig. 5. Vertical profile of ∆O2. Attached letters denote the name of the region. (A): The Atlantic, (B): The Pacific and (C): The
Indian and Southern Ocean.
Table 2. Horizontal and vertical locations at which a particle picks up oxygen. Vertical position is shown by relative depth.
ference, ∆O2, between the calculated and observed concentrations (∆O2 = OTR – OLEV), where O TR is the oxygen
concentration averaged over the particles on each depth
level of an oceanic region. Panels A, B and C show the
profiles for the oceanic regions of the Atlantic, the Pacific and the Indian and the Southern Oceans, respectively.
The main characteristics of these profiles are as follows;
1) For regions D and I, where upwelling is dominant, a maximum value appears at the same depth as that
of the oxygen minimum layer (300 m to 400 m).
2) For regions B, C, E, G, H, L, M and O, maximum difference and oxygen minimum layers appear at
depths between 500 m to 1000 m.
3) For region A, where the North Atlantic Deep and
Bottom Waters are produced, the vertical change of the
observed oxygen concentration OLEV and the difference
∆O2 is very small over the depth range from the surface
to the bottom.
4) For regions F, J, K and N in the southern hemisphere, both layers appear at depths between 1500 m to
2000 m.
3.3 Origin of oxygen transported by water parcels at the
oxygen minimum layer
Figure 6 shows the distribution of horizontal positions at which labeled particles flowing into the oxygen
minimum layer (hereafter ZMIN layer) pick up oxygen. In
this figure, the relative depth of a particle and the relative value of oxygen concentration are shown by using
six symbols (Table 2). Symbols 䊊 and • denote that a
particle picks up oxygen within the upper layers, 䊐 and
+ within layers of the same level, and 䉫 and 䉭 within the
lower layers, respectively. Also, symbols 䊊, 䊐 and 䉫
denote concentrations higher than or equal to that of the
particle’s destination layer, and •, + and 䉭 denote a corresponding lower concentration. The term “higher (lower)
concentration” denotes an oxygen concentration higher
(lower) than OLEV averaged across the final destination
depth layer of the labeled particles. Note that we use the
500 m or 1100 m layer as the nearest layer to the oxygen
minimum layer Z MIN for convenience.
The Atlantic Ocean:
Figure 6a shows where water parcels (labeled parti-
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
367
Fig. 6. Locations of oxygen enriched water sources for the layer Z MIN. a: 500 m layer of region A, b: that of region B, c: that of
region C, d: that of region D, e: that of region E, f: 1100 m layer of region G, g: that of region H (major route from the South
Pacific to the North Pacific is shown by a solid curve), h: 500 m layer of region I, i: 1100 m layer of region J, j: that of region
K, k: that of region L, l: that of region M, and m: that of region O. The symbols are defined in Table 2.
368
N. Imasato et al.
cles) on the 500 m level of region A pick up oxygen. Particles which pick up higher oxygen concentration (marked
䊊) come from the upper layers of the Arctic Sea and the
south-east of Greenland. Particles with higher oxygen
concentration (marked 䉫) come from the lower layers of
the Labrador Basin where velocity vectors on the 500 m
level (Fig. 2B) are directed from the Davis Strait to the
Labrador Sea. On the other hand, waters of lower oxygen
concentration move from the area of the North Atlantic
Subtropical Gyre.
Although the oxygen minimum layer of region B
appears between the 500 m to 1100 m levels, the distribution for the 500 m (Fig. 6b) layer is shown. Many particles with higher oxygen concentration (marked 䊊) are
distributed in the interior region of the North Atlantic
Fig. 6. (continued).
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
369
Fig. 6. (continued).
370
N. Imasato et al.
Subtropical Gyre (Fig. 2B), and the rest (marked 䉫) are
distributed throughout the lower layers of the Labrador
Basin.
For the 500 m layer of region C (Fig. 6c), surface
water from region B with higher oxygen concentration
(marked 䊊) sinks within the interior region of the subtropical gyre, and surface water is also supplied from the
ACC region of F and K. Water with higher oxygen concentration (marked 䉫) upwells from the lower layers of
the Brazil Current in region E and also from the North
Atlantic Subtropical Gyre in the western part of region
C.
For the 500 m layer of region D (Fig. 6d, upwelling
region), upper layer waters with higher concentration
(marked 䊊) sink within the interior region of the North
Atlantic Subtropical Gyre and within the interior region
of the South Atlantic Subtropical Gyre. The rest (marked
䊊) comes from the ACC of region F via the South Atlantic Subtropical Current and the North Brazil Current. On
the other hand, lower layer waters of higher concentration (marked 䉫) upwell from the lower layers of region
D under the westward Equatorial Currents (Fig. 2C).
For region E of the South Atlantic (Fig. 6e), the layer
ZMIN appears at the 500 m level. Upper layer waters with
higher concentration come from the interior region of the
South Atlantic Subtropical Circulation and from the ACC
region and move northward through the eastern area of
the South Atlantic. Lower concentration waters (marked
䉭) upwell from lower layers of the equatorial region and
the northern part of the South Atlantic.
Although no figure is shown, for region F, higher
concentration water sinks from the surface layer of regions F, K and N.
Fig. 6. (continued).
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
371
The Pacific Ocean:
For region G (Fig. 6f), the ZMIN layer appears at the
1100 m level. Most water of higher oxygen concentration (marked 䊊) sinks from surface layers of the interior
region of the North Pacific Subtropical Gyre. The other
part (marked 䉫) upwells from the lower layers of the interior region of the North Pacific Subarctic Gyre. On the
other hand, waters with lower concentration (marked •, +
and 䉭) come from many layers of the eastern North Pacific.
For region H, the layer ZMIN appears between the 800
m to 900 m levels, though we also show the distribution
for the 1100 m (Fig. 6g) level. Upper waters (marked 䊊)
sink from the interior region of the North Pacific Subtropical Gyre, and lower waters (marked 䉫) upwell from
the boundary region between the North Pacific Subtropical Gyre and the Equatorial Counter Current (ECC). Waters with higher concentration originate from the western
part of the region H and the South Pacific. Waters with
lower concentration (marked +) come from the eastern
part of region H. Note the narrow supply zone off northeast Australia (~10°S, ~152°E) where many particles enhance their oxygen content. As this narrow zone of enhancement is located on the route of the Pacific SEC, the
oxygen enriched water is transported into the North Pacific and the Indian Ocean across the equator, thereby
supporting the speculation of Reid (1962) that oxygen is
transported from the South Pacific to the North Pacific.
Reid (1962) further showed that, in the Eastern Equatorial Pacific (corresponding to region I of this paper),
the residence time of water is long because of the sluggish circulation, and the consumption of oxygen is high
due to the high productivity in the surface layer. On the
other hand, Wyrtki (1962) showed that oxygen is supplied to the oxygen minimum layer only by vertical and
horizontal diffusion and by water ascending from deeper
levels. The 500 m level of region I (Fig. 6h) is the destination for waters of higher oxygen concentration originating from the South Pacific. Upper layer waters (marked
䊊) from the interior region of the South Pacific Subtropical Gyre sink and move into this level, and later, these
waters are transported by the Pacific SEC to the ZMIN layer
of region I through the narrow supply zone off north-east
Australia and the ECC region at 500 m depth. Other contributions come from the upper (marked 䊊) and lower
(marked 䉫) layers around the equatorial region.
For region J, the ZMIN layer appears at the 1500 m
level. Figure 6i (1100 m layer) shows that water with
higher oxygen concentration (marked 䊊 and 䊐) at the
top of the oxygen minimum region comes from the upper
layers on the south side of the interior region of the South
Pacific Subtropical Gyre and from the south Indian Ocean
via the ACC. On the other hand, water with lower concentration (marked + and 䉭) originates from the north372
N. Imasato et al.
ern region of the South Pacific Subtropical Gyre.
For region K, the ZMIN layer appears at the 1800 m
level. Figure 6j shows that most of the higher concentration water (marked 䊊) comes from region N and the southeast of region M of the Indian Ocean. The rest comes from
the upper layers in the east of region K and the south of
region J.
The Indian Ocean:
For region L, the ZMIN layer appears at the 1100 m
level (Fig. 6k). Waters with lower concentration (marked
+ and 䉭) on the 1100 m level come from the Arabian
Sea, and waters with higher concentration (marked 䊐 and
䉫) come from the southern part of region L and the Bay
of Bengal.
For region M (Fig. 6l), the ZMIN layer appears at the
1100 m level. Waters with lower concentration come from
the lower and the same level of the northern portion of
region M. On the other hand, waters with higher concentration come from the south of region M and also from
the northern portion of the Pacific SEC (marked 䊊 and
䊐). Other sources of higher oxygen concentration water
are the Indian SEC and the south of Australia. In a similar way to regions J in the south Pacific and E in the South
Atlantic, waters with lower and higher concentrations
originate from the northern and southern areas of region
M, respectively.
Although a figure for region N is not shown, the
major part of higher concentration water (marked 䊊)
comes from region N and the southern part of region M.
The rest comes from the eastern part of region K. Water
with lower concentration (marked +) comes from the
Great Australian Basin.
For region O, the ZMIN layer appears on the 1100 m
level. Figure 6m shows that higher oxygen content water
(marked 䊊) sinks from regions F, K and N, and around
Antarctica. Other waters of higher oxygen concentration
(marked 䊐 and 䉫) upwell due to the ACC in the central
part of region O.
3.4 Processes taking place near the oxygen minimum
layer
In order to examine what happens near the level of
the oxygen minimum layer, we define a contribution rate
HPiQj:
H Pi Qj = O Pi Qj VPi Qj
∑ ∑ O Pi Rk VPi Rk
R
(2 )
k
where the quantities O PiQj and VPiQj denote oxygen concentration and volume of water carried from layer j of
region Q to layer i of region P, respectively. The concept
of H PiQj is illustrated in Fig. 7, where a rectangle enclosed
by a double square shows layer i of region P. This rate
HPiQj denotes the contribution of waters which come from
Fig. 7. Illustration of the concept of the contribution rate HPiQj,
and the four rates contributing to oxygen concentration
within a layer (Fig. 8).
layer j of region Q to the calculated oxygen concentration of layer i in region P. Also, the following relations
hold;
VPi = ∑ ∑ VPi ,
(3)
∑ ∑ H Pi Rk = 1.
( 4)
Rk
R
R
k
k
The vertical profiles of contribution rates, H PiRk, for
the four representative regions, H, J, B and A, are shown
in Fig. 8 where the vertical axis is the depth of level i.
These contribution rates consist of four components: i.e.,
we consider contributions from a layer within the region
under consideration (rate I, thick solid line), from layers
above and below (rates II and III, thick and thin broken
line respectively) and from layers at the same depth level
but in other oceanic regions (rate IV, solid line). The concept of these four contributions is illustrated in Fig. 7. In
Fig. 8, the symbol 䊊 shows the depth of the observed
oxygen minimum (ZMIN) averaged throughout the layer
of the region under consideration, and the symbol 䉭
shows the depth of maximum oxygen difference (∆O2).
Figure 8A shows the distribution for the region H,
where the rate I has a minimum between 500 m~1000 m
depth, and reaches 90% at surface layer and the depths
below 1500 m. On the other hand, rate II decreases rap-
Fig. 8. Vertical profile of the contribution rate HPiQj. (A): Region H, (B): Region J, (C): Region B and (D): Region A.
Thick solid line: Contribution from the layer under consideration (rate I), thick broken line: from “upper layers” (rate
II), broken line: from “lower” layers (rate III), and solid
line: from the same layer of other regions (rate IV). The
symbol 䊊 shows the depth of the observed oxygen minimum (Z MIN), and the symbol 䉭 shows the depth of maximum oxygen difference.
idly from the surface layer to the bottom and the value is
very small at depths below 1500 m. Rates III and IV have
a small maximum around 1000 m depth. The oxygen minimum layer Z MIN appears at the depth where the rate I is a
minimum and the rates III and IV maximize. The maximum difference ∆O2 appears at the depth where rate I
minimizes and rate II is large. Regions C, D, E, G, H, I, L
and M belong to this type. Figure 8B shows the distribution for region J. This second type is similar to that of
Fig. 8A, but rates III and IV are very small and the layer
ZMIN appears at a depth where the value of rate I is large.
Only region J belongs to this type.
For region B (Fig. 8C), the values of rates I, III and
IV are small over a wide range between 500 m to 2000 m
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
373
where rate II is large. Both the ZMIN layer and the maximum difference layer ∆O2 appear at a depth of 800 m.
Regions B, F, K and N belong to this type. Figure 8D
shows that the distribution for region A is similar to that
of Fig. 8C, but the ZMIN layer and the maximum difference layer ∆O2 appear at a depth where the rates I and II
are relatively small and on the other hand, rate III is relatively large. Regions A and O show this behaviour. However, for region A, rate II has a large maximum at the
deep level of 2000 m, but for region O, rate III has a large
value over a wide range between 500 m to 2500 m and
rate II is relatively small.
Figure 8 offers very important information on the
water movement around the level ZMIN. It shows that, for
many regions, the contribution rate I is a minimum at or
near the level ZMIN. If water parcels in the layer ZMIN remain static over a number of years, these parcels alone
will contribute to the oxygen concentration of the layer.
Therefore, if HPiQj = 0, VPiQj must be zero, because OPiQj
is not zero even at the oxygen minimum layer. This implies that, if the contribution rate I for the layer ZMIN is
very small, many water parcels which pick up oxygen in
layer ZMIN must rapidly move out of that layer. Note that
if ∆O2 at layer i in region P (denoted as ∆OPi hereafter) is
large for layers above ZMIN, this indicates that water parcels sinking from the upper layers should consume a large
amount of oxygen.
Figure 8 also shows that the contribution rate II (thick
broken line) is large near Z MIN and decreases toward the
bottom. However, only for the behavior illustrated in Fig.
8D does the contribution rate II maximize below ZMIN.
This fact shows that surface water (including that of the
euphotic layer) within regions A and O sinks to depths of
2000 m or more, and that upper layer water takes its place
after losing oxygen due to biochemical activity in and
under the euphotic layer. Figure 8 also shows that, for
many regions, contribution rate III (broken line) is relatively small everywhere, i.e., the lower layer waters
should be relatively stagnant.
This leads to the following conclusion relating to the
characteristics of waters at the oxygen minimum layer: A
large fraction of the water which picks up oxygen within
this layer leaves to be replaced by water which originates
within the upper layers and from layers at the same depth
level which have depleted oxygen concentration due to
biochemical processes.
3.5 The Lagrangian oxygen consumption rate
The quantity of oxygen corresponding to ∆O Pi must
be consumed as a water parcel travels to its destination
after picking up oxygen. Therefore, we next estimate a
Lagrangian oxygen consumption rate which, for water of
layer i of region P, is given by
CPi = ∆OPi/TPi,
(5)
where TPi is a relevant time scale (travel time) for this
process, averaged over the water parcels which enter layer
i of region P after picking up oxygen. Figure 9 shows the
vertical profiles of T Pi, and the symbol 䊉 shows the depth
of the oxygen minimum layer ZMIN. This figure shows
that water parcels which move into the oxygen minimum
layer require the longest time scales.
Figure 10 shows the vertical profiles of the
Lagrangian oxygen consumption rate CPi and again, the
symbol 䊉 shows the depth of the ZMIN layer. The profiles
for regions A, B, K and N show some unique features.
The consumption rate for region A is very small and becomes negative between 1800 m to 2800 m. However,
this negative value is attributed to negative values of ∆OPi
Fig. 9. Vertical profiles of the travel time of particles (unit in yrs). (A): The Atlantic, (B): The Pacific and (C): The Indian and
Southern Ocean. The symbol 䊉 shows the depth of the oxygen minimum layer (Z MIN).
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N. Imasato et al.
for this range and it is probably within the error of the
calculations. Small absolute values of ∆OPi and small
travel times T Pi indicate that oxygen is transported directly from the euphotic layer of region A to deep layers
with small consumption. The profiles of consumption rate
for regions K and N have a maximum around the depth
of the oxygen minimum layer (~1500 m) because the difference ∆OPi has a maximum at this level, although time
scales T Pi maximize. The profile of consumption rate for
region B has a small maximum around 800 m to 1500 m.
This maximum is attributed to the fact that the travel time
for this range has a minimum value. However, the consumption rate for region B should be considered to be
constant over depth in a similar way to that of region A.
The profiles of the consumption rate for the other
regions decrease with depth. However, these do not follow the exponential law that is expected in the one dimensional diffusion model. The consumption rates for the
dissolved oxygen minimum layer are distributed within a
range from 0.013 to 0.100 ml/l/yr (Fig. 10 and Table 3).
The average for regions located at high latitudes (A B, F,
G, K, N and O) is 0.022 ml/l/yr, and that for the other
regions located at low and middle latitudes (C, D, E, H,
I, J, L and M) is 0.041 ml/l/yr. Consumption rates within
the euphotic layer of the regions located at high latitudes
are small with an average value of 0.065 ml/l/yr, whereas
the averaged value for the regions located at low and midlatitudes is 0.26 ml/l/yr. The averaged value for the depth
layer between 150 m to 800 m is 0.021 ml/l/yr for regions at high latitudes, and 0.059 ml/l/yr for other regions.
In contrast, the consumption rates for depths below 800
m show no distinct difference between the two groups,
and the averaged value is 0.013 ml/l/yr (Table 3). Note
that the rate for regions A and B of the North Atlantic is
very small from the sea surface down to the deep layers.
For all regions, values of the consumption rate for the
euphotic layer vary widely, and an averaged value is 0.20
ml/l/yr. The averaged value for layers from 150 m to 800
m is 0.043 ml/l/yr and that for layers from 800 m to 3000
m is 0.012 ml/l/yr (Table 3). Primary productivity evaluated from the map of Zeitzschel (1973) is shown in Table
3. We could not find clear relation between the primary
productivity and the present Lagrangian local oxygen
consumption rates (Table 3).
Water parcels consume oxygen en route to their destinations after absorbing oxygen. Strictly speaking, the
present consumption rates show only the oxygen consumption averaged over the path. However, we assumed
that the oxygen was consumed within the layer of the basin
where particles finally came to rest (i.e., their “terminal
basin”). Unfortunately, global observations for comparison with the present Lagrangian oxygen consumption
rates are not available. Examination of Fig. 9 shows that
many particles pick up oxygen within the terminal basin.
Therefore, we tentatively compare the present oxygen
consumption rates with previous OUR (oxygen utilization rate) results.
Jenkins (1982) proposed a logarithmic vertical distribution of OUR for the eastern North Atlantic, which
yields a value of 0.377 ml/l/yr at Z = 100 m depth and
0.115 ml/l/yr at Z = 500 m. The former is 2.1 times larger
than the averaged value at the 100 m level of regions B,
C and D found in this study, and the latter is 2.4 times
larger than our results for the 150 m~800 m depth range.
By using CFC-11 apparent ages, Warner et al. (1996)
obtained a value of OUR of 0.336 ml/l/yr and 0.202 ml/l/
yr averaged along 47°N and 24°N sections of the Pacific
Ocean, respectively. The former is 1.5 times larger than
the consumption rate on the 100 m level of region G and
the latter is 0.78 times larger than that on the 100 m level
Fig. 10. Vertical profiles of oxygen consumption rate (unit in ml/l/yrs). (A): The Atlantic, (B): The Pacific and (C): The Indian
and Southern Ocean. The symbol 䊉 shows the depth of the oxygen minimum layer (Z MIN).
Study of Water Motion at the Dissolved Oxygen Minimum Layer and Local Oxygen Consumption Rate
375
Table 3. Oxygen consumption rate at the oxygen minimum layer (Z MIN), and layers at 100 m (euphotic layer), at 150 m to 800 m
and at 800 m to 3000 m.
*The value of the region I is excluded.
**The value of the region N is excluded.
***Average calculated from the map of Zeitzschel (1973).
of region I. These values are 1.7 times greater than the
present Lagrangian consumption rates, although this may
be due to the different concepts applied in the two methods of evaluation.
4. Conclusion
By using the Euler-Lagrangian method, vertical profiles of oxygen concentration produced by the movement
of water parcels have been calculated for the regions of
the global ocean defined in Fig. 3. A total of 105 labeled
particles were numerically tracked backward in time for
50 years in a three-dimensional velocity field calculated
by using a prognostic GCM. We assumed that a particle
picks up oxygen either in the euphotic layer or at the place
of maximum oxygen concentration defined along the path
of the particle.
A layer in which large differences between the observed and calculated oxygen concentrations exist lies
near or above the oxygen minimum concentration layer
ZMIN. To understand the relation between the three-dimensional velocity field and depth of layer Z MIN, we first ex-
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N. Imasato et al.
amined where water parcels pick up oxygen, and then,
introduced four oxygen contribution rates. For the North
Atlantic and the North Pacific, particles pick up oxygen
of higher concentration in the western and northern regions. The SECs transport oxygen of higher concentration to mid-latitudes of the northern hemisphere across
the equator. On the other hand, for region L of the North
Indian Ocean, a source of water with higher oxygen concentration exists within the Bay of Bengal (eastern area
of the region). For the southern hemisphere, a source of
water with low oxygen concentration exists within the
northern and eastern sides of the region. Waters containing higher oxygen concentration are brought into region
M from the South Pacific through the Indonesian seas.
For the dominant upwelling regions D and I, the ECC
and the SEC assume an important role in oxygen transport.
The present oxygen contribution rates consist of four
components—namely from a layer within the region under consideration (rate I), from layers above and below
(rates II and III) and from layers at the same depth level
as this layer but in other oceanic regions (rate IV). We
found that, for the Z MIN layer, the contribution rate I is
very small whereas rate II is large. This means that water
parcels which pick up oxygen within the ZMIN layer of
the region under consideration are rapidly removed from
that layer and that water within the upper layers takes its
place. Therefore, if upper layer waters flow into the ZMIN
layer after consuming oxygen corresponding to ∆OPi, the
observed oxygen minimum concentration layer should
also be reproduced in this model. Estimated oxygen consumption rates averaged over all regions are 0.20 ml/l/yr
for the euphotic layer, 0.043 ml/l/yr for depths between
150 m to 800 m and 0.012 ml/l/yr for depths between 800
m to 3000 m. These values are about a half of the previous OUR results obtained from Jenkins (1982).
We used backward tracking for a relatively short
period of 50 years. The present method has an assumption in picking up oxygen, and it will produce a maximum difference between observed and calculated oxygen concentrations, and therefore, a maximum consumption of oxygen. However, it is necessary to compare the
present results with those from numerical experiments in
which labeled particles are deployed only in the euphotic
layer and tracked forward in time for a longer period of
perhaps several thousand years.
Acknowledgements
The authors wish to express their thanks to Dr. J. P.
Matthews of Kyoto University and Dr. J. R. Toggweiler
of Princeton University for their critical reading of the
manuscript. Numerical calculation was performed on a
FACOM VP2600 and M1800 of the Data Processing
Center of Kyoto University.
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