Journal of Oceanography, Vol. 56, pp. 655 to 666, 2000
Roles of Physical Processes in the Carbon Cycle Using
a Simplified Physical Model
MASAHIKO F UJII1*, MOTOYOSHI IKEDA1,2 and YASUHIRO Y AMANAKA1,2
1
Graduate School of Environmental Earth Science, Hokkaido University,
N10W5, Kita-ku, Sapporo 060-0810, Japan
2
Frontier Research System for Global Change,
Seavans North 7F, 1-2-1 Shibaura, Minato-ku, Tokyo 105-0023, Japan
(Received 20 December 1999; in revised form 26 June 2000; accepted 26 June 2000)
A simplified physical model is proposed in this article to describe differences among
basins in substance distributions which were not well described by previous simplified models. In the proposed model, the global ocean is divided into the Pacific/Indian Ocean (PI), the Atlantic Ocean (AT), the Southern Ocean and the Greenland/
Iceland/Norwegian Sea. The model is consisted of five physical parameters, namely
the air-sea gas exchange, the thermohaline circulation, the horizontal and vertical
diffusions, and the deep convection in the high-latitude regions. Individual values of
these parameters are chosen by optimizing model distribution of natural 14C as a
physical tracer. The optimal value for a coefficient of vertical diffusion in the lowlatitude region is 7.5 × 10–5 [m2s –1]. Vertical transports by the Antarctic Bottom Water and the North Atlantic Deep Water are estimated at 1.0 Sv and 9.0 Sv. Globalmean air-sea gas exchange time is calculated at 9.0 years. Using these optimal values,
vertical profiles of dissolved inorganic carbon without biological production in PI
and AT are estimated. Oceanic responses to anthropogenic fluctuations in substance
concentrations in the atmosphere induced by the industrialization and nuclear bomb
are also discribed, i.e., the effects appear significantly in AT while a signal is extremely
weak in PI. A time-delay term is effective to make the PI water older near the bottom
boundary.
Keywords:
⋅ Carbon cycle,
⋅ physical process,
⋅ simple model,
⋅ 14C.
bal carbon cycle only by observations. Thus, numerical
modeling has been used for discussing the global carbon
cycle in the ocean as well as observations.
Several simplified physical models have been suggested for these few decades. Oeschger et al. (1975) tried
to explain the CO2 concentration in the atmosphere using
a box-diffusion model consisting of four boxes; the atmosphere, the terrestrial biosphere, the mixed layer and
the diffusive deep sea. However, the solubility of CO 2 in
the ocean is dependent upon temperature, and hence, both
physical and chemical processes are rather different between in the low and high latitudes. Although the polar
region occupies less than 20% in area over the global
ocean, it should be considered separately from the other
due to a large CO2 sink of the atmosphere. Therefore, simplified models have been modified to include several
mechanisms in the high-latitude region. In upwelling-diffusion model (Hoffert et al., 1980), the whole deep sea is
divided into the downwelling high-latitude region and the
other upwelling region. In multi-box model (Siegenthaler
1. Introduction
Since CO2 is one of the major greenhouse gases,
understanding the global carbon cycle becomes essential
to predict the global warming. Especially, the ocean as a
huge reservoir of carbon plays a significant role in the
global carbon cycle and climate change. The amount of
carbon in the atmosphere has been accurately estimated
by direct observations. As for the ocean, though pre-industrial CO2 concentrations are estimated by previous
studies such as Quay et al. (1992), there are still quite
large difference in the estimation among several studies.
A vertical carbon flux between the surface and deep layer
in the ocean has not been estimated accurately either, and
this inaccuracy primarily keeps us away from understanding the carbon cycle mechanism in the ocean exactly. In
addition, it is difficult to synthesize an image of the glo* Corresponding author. E-mail: [email protected]
Copyright © The Oceanographic Society of Japan.
655
and Wenk, 1984), two boxes of the warm and cold surface ocean are set as surface mixed layers. To consider
the isopycnal mixing in the high-latitude region as well
as the downwelling, the lateral exchange of the intermediate water between the high and low latitude regions is
introduced in outcrop-diffusion (Siegenthaler, 1983) and
high-latitude exchange/interior diffusion-advection
(HILDA) model (Joos et al., 1991; Siegenthaler and Joos,
1992; Shaffer and Sarmiento, 1995). On the other hand,
3-D ocean general circulation models (OGCMs) have recently been applied in order to describe explicitly or implicitly the global carbon cycle in the ocean (Bacastow
and Maier-Reimer, 1990, 1991; Sarmiento and Orr, 1991;
Najjar et al., 1992; Sarmiento et al., 1992; Anderson and
Sarmiento, 1995; England, 1995; Yamanaka and Tajika,
1996, 1997).
In the ocean, carbon exists in several forms;
particulate organic carbon (POC), calcium carbonate
(CaCO 3), dissolved organic carbon (DOC) and dissolved
inorganic carbon (ΣCO2 ) which contains dissolved CO2.
POC in the ocean is provided by the rivers, is produced
by phytoplanktons in process of photosynthesis in the
euphotic zone, and partly accumulates on the sea floor.
Some phytoplanktons and zooplanktons produce CaCO 3
in their shell parts. Both POC and CaCO 3 are exported
downward, and these downward flows of carbon affected
by planktons are called the biological and alkalinity
pumps, respectively. Once POC and CaCO3 are dissolved,
the distributions are dominated by water motion. The
processes of water motion include horizontal and vertical diffusions, wind-driven and thermohaline circulations,
and a deep convection in the high-latitude region in winter. In addition, there is CO2 exchange between the surface layer and the atmosphere due to sea water solubility
and biogenic photosynthesis and respiration. Totally, carbon distribution in the ocean is determined by all of these
processes.
A method of modeling is used to study the global
carbon cycle in the ocean. Our purpose is to genarate and
verify a model with essential physical processes in the
oceanic carbon cycle. As for this purpose, simplified
physical models are more appropriate than OGCMs. In
comparison with relatively complicated OGCMs, they
have advantage to make easy execution in many parameter studies, and to pick up several essential mechanisms
out of various phenomena in the ocean. Among simplified models above, HILDA has enough physical parameters and can describe most realistic image of substance
distribution in the global ocean. HILDA can also describe
differences of substance concentrations between the low
and high latitude region. However, as the Geochemical
Ocean Sections Study (GEOSECS) data show, obvious
differences in substance concentrations between the Pa-
656
M. Fujii et al.
cific/Indian (PI) and the Atlantic Ocean (AT) exist. In
addition, residence time of each substance is significantly
different between PI and AT. Considering the anthropogenic carbon transition with time, for example, it is necessary to discuss differences among substances. Neither
HILDA nor the other simplified physical models can describe these differences. These differences cannot be described only dividing model region of the low latitude in
these models into PI and AT.
To describe these differences keeping the simplicity
in HILDA, a simplified physical model is proposed which
is described in the following section. In Section 3, a tracer
and data used in this model are described. Results obtained by this study is mentioned in Section 4. Optimal
values of physical parameters and model distributions of
ΣCO2 and anthropogenic substances using these parameters are discussed. In Section 5, parameter values in this
study are compared with those in previous studies. A new
boundary condition is also suggested. In the final section, the results are summerized.
2. Model
2.1 Model description
HILDA is one of simplified physical models applied
to describe distributions of substances such as temperature, natural and bomb-produced 14 C, 13 C,
chlorofluorocarbons, phosphate, dissolved oxygen and
anthropogenic ΣCO2 (Joos et al., 1991; Siegenthaler and
Joos, 1992; Shaffer and Sarmiento, 1995). There are five
boxes in HILDA, one in the atmosphere and four in the
ocean. Four boxes in the ocean are the low-latitude surface layer (LS), the low-latitude deep layer (LD), the highlatitude surface layer (HS) and the high-latitude deep layer
(HD). Only LD has continuous vertical resolution, in
which vertical profiles of a tracer concentration can be
discussed. The other regions are non-dimensional boxes.
HILDA includes several physical parameters to describe
global ocean circulation; k (a constant coefficient of vertical turbulent diffusion in LD), q (a rate of lateral exchange between LD and HD), u (a constant exchange
velocity between HS and HD), w (a constant upwelling
velocity of the thermohaline circulation), and gLS and gHS
(air-sea gas exchange velocities in the low and high latitude region, respectively). In LD, for example, conservation equation for a tracer is,
∂φ LD ( z )
∂t
=k
∂ 2φ LD ( z )
∂φ ( z )
− w LD
− q(φ LD ( z ) − φ HD ) + SLD ( z )
2
∂z
∂z
(1)
low and high latitude region are divided into two, PI and
AT, SO and GIN, respectively. The horizontal and vertical boundaries are 5°C contour in annual-mean SST and
50 m depth, respectively, the same as in Shaffer and
Sarmiento (1995). The boxes of LD (in PI) and LD′ (in
AT) have the vertical resolution of 50 m (totally 76 layers). The others (LS in PI, LS′ in AT, HS and HD in SO,
HS′ and HD′ in GIN) have no resolution. PI is connected
with SO, and AT with both SO and GIN.
2.2 Conservation equations for a tracer
Conservation equations for a tracer φ in each region
are as follows. The equation in LD is,
Fig. 1. Schematic view of YOLDA model. LD and LD′ have
the vertical resolution. Broken and dashed lines denote
thermocline circulations originating in the surface layers
of GIN and SO, respectively.
where φ(t): a tracer concentration; S(t): a tracer sink or
source. The upward vertical coordinate z is defined as
positive. In all terms above, the area of LD (=3.02 × 10 14
[m2]) is eliminated.
To represent differences of tracer distributions between PI and AT, the low-latitude region in HILDA must
be classified into PI and AT. As origins of water are different between PI and AT, the high-latitude region in
HILDA also has to be classified into the Southern Ocean
(SO) and the Greenland/Iceland/Norwegian Sea (GIN).
Since tracer concentrations and values of physical parameters are specific to the basins, these basins should have
their particular values for tracer concentrations and physical parameters. In addition to resolution of the different
properties in PI and AT, the mean balance is also modified by the separation of the global ocean to PI and AT.
For example, w((∂φ LD(z))/∂z), the advection term in LD
in Eq. (1), is modified to wPI((∂ φ PI(z))/∂z) in PI and
w AT ((∂ φ AT (z))/∂z) in AT, where w PI and φ PI (z) are a
upwelling velocity and a tracer concentration in PI, and
wAT and φ AT(z) are those in AT, respectively. In such a
case, the advection effects in PI and AT are not identified
to those in LD even though the tracer concentration and
the upwelling velocity in LD are equal to the means of
them between PI and AT. It is noted that there exist
nonlinear effects related to multiplying different parameters and corresponding concentrations. So in this study,
a simplified physical model is constructed whose tracer
concentrations and values of physical parameters are
given independently in all basins to represent differences
between PI and AT.
Figure 1 shows the schematic view of our model
(yoked high-latitude exchange/interior diffusionadvection (YOLDA) model). In YOLDA, boxes of the
α (1 − δ )
∂φ LD ( z )
∂t
∂ 2φ LD ( z )
∂φ ( z )
− α (1 − δ )( wGIN + wSO ) LD
2
∂z
∂z
−α (1 − δ )q(φ LD ( z ) − φ HD ) + α (1 − δ )SLD ( z ).
= α (1 − δ )k
(2 )
Boundary conditions of LD are, at z = –50 m,
φ LD(z) – φLS = 0
(3)
and at the bottom (z = –3850 m),
k
∂φ LD ( z )
− ( wGIN + wSO )(φ LD ( z ) − φ HD ) + Sbottom = 0.
∂z
( 4)
Similarly, the equation in LD′ is,
α ′(1 − δ )
∂φ LD ′( z )
∂t
∂ 2φ LD ′( z )
∂φ ′( z )
− α ′(1 − δ )( wGIN ′ + wSO ′) LD
2
∂z
∂z
−α ′(1 − δ )q ′(φ LD ′( z ) − φ HD ′) − α ′(1 − δ )q(φ LD ′( z ) − φ HD )
= α ′(1 − δ )k
+α ′(1 − δ )SLD ( z ).
(5)
Boundary conditions of LD′ are, at z = –50 m,
φ LD′(z) – φLS ′ = 0
(6)
and at the bottom,
k
∂φ LD ′( z )
− wGIN ′(φ LD ′( z ) − φ HD ′)
∂z
− wSO ′(φ LD ′( z ) − φ HD ) + Sbottom ′ = 0.
Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model
(7)
657
Conservation equations in LS, LS′, HS, HS′, HD and
HD′ are,
(HS′)
α ′δDs
(LS)
∂φ HS ′
∂t
= α ′δ s ′ gHS ′(φair − φ HS ′) + (αwGIN + α ′ wGIN ′)(1 − δ )
∂φ
α (1 − δ ) Ds LS
∂t
⋅(φ LS ′ − φ HS ′) − α ′δu′(φ HS ′ − φ HD ′) + α ′δSHS ′
= α (1 − δ )g LS (φair − φ LS ) − α (1 − δ )k
(
∂φ LD ( z )
∂z z = −50
+α (1 − δ )( wGIN + wSO ) φ LD ( z ) z = −50 − φ LS
+α (1 − δ )SLS
(11)
(HD)
)
(8)
∂φ HD
∂t
= α (1 − δ )wGIN (φ HD ′ − φ HD )
αδD
+(1 − δ )(αwSO + α ′ wSO ′)(φ HS − φ HD )
(LS′)
+αδu(φ HS − φ HD ) + α (1 − δ )q ∫
∂φ ′
α ′(1 − δ ) Ds LS
∂t
= α ′(1 − δ )g LS ′(φair − φ LS ′) − α ′(1 − δ )k
+α (1 − δ )wGIN φ HS + (1 − δ )
(
(
+α ′(1 − δ )wSO ′ φ LD ′( z ) z = −50 − φ LS ′
+α ′(1 − δ )q ∫
)
−50
−3850
∂φ LD ′( z )
∂z
z = −50
⋅ α ′ wGIN ′φ LD ′( z ) z = −50 − (αwGIN + α ′ wGIN ′)φ LS ′
+α ′(1 − δ )SLS ′
−50
−3850
(φ LD ( z) − φ HD )dz
(φ LD ′( z) − φ HD )dz + αδSHD
(12)
(HD′)
)
α ′δD
∂φ HD ′
∂t
= (1 − δ )(αwGIN + α ′ wGIN ′)(φ HS ′ − φ HD ′)
( 9)
+α ′δu′(φ HS ′ − φ HD ′)
+α ′(1 − δ )q ′ ∫
−50
−3850
(φ LD ′( z) − φ HD ′)dz + α ′δSHD ′
(13)
(HS)
αδDs
where α: a rate of PI and SO area on global ocean (0.74);
∂φ HS
∂t
= αδ s gHS (φair − φ HS ) + α (1 − δ )( wGIN + wSO )(φ LS − φ HS )
+α ′(1 − δ )wSO ′(φ LS ′ − φ HS ) − αδu(φ HS − φ HD ) + αδSHS
Table 1. The optimal values of the parameters in each experiment (without and with time-delay effect).
(10)
Fig. 2. Vertical profiles of ∆14C in LD and LD′ with the optimal values of parameters. 䊉, 䊊 and * show GEOSECS data
in LD, LD′ and HD, respectively. Model results are shown
in solid and dashed lines (LD and LD′), and in values (HS,
HD, HS′ and HD′).
658
M. Fujii et al.
Without time-delay
effect
k [×10 – 5 m2 s – 1 ]
q [×10 – 1 1 s – 1 ]
q′ [×10 – 1 1 s – 1 ]
u [×10 – 7 ms – 1 ]
u′ [×10 – 7 ms – 1 ]
wS O [×10 – 8 ms – 1 ]
wS O ′ [×10 – 8 ms – 1 ]
wGIN [×10 – 8 ms – 1 ]
wGIN′ [×10 – 8 ms – 1 ]
g LS [×10 – 7 ms – 1 ]
g LS ′ [×10 – 7 ms – 1 ]
g HS [×10 – 7 ms – 1 ]
g HS ′ [×10 – 7 ms – 1 ]
7.5
1.2
30.0
1.0
19.0
0.25
0.72
3.8
2.2
2.4
2.4
0.6
2.0
With time-delay
effect
7.5
2.4
30.0
1.0
19.0
0.44
1.3
6.7
3.9
2.4
2.4
0.6
2.0
α′: a rate of AT and GIN area on global ocean (0.26); δ : a
ratio of SO on PI plus SO, or GIN on AT plus GIN (0.16);
δs: a rate of SO area free from sea ice on PI and SO (0.10);
δ′s : a rate of GIN area free from sea ice on AT and GIN
(0.10); Ds: a constant depth of the surface layer (50 m);
D: a constant depth of the deep layer (3800 m). In all
equations above, the global ocean area (=3.60 × 1014 [m2])
is eliminated.
Most of physical parameters introduced in HILDA
are also modified. As for parameters of q, u, gLS and gHS,
non-primed ones denote parameters in PI or SO, and
primed ones in AT or GIN. k is set to common in both PI
and AT. Since a deep-water source is also divided into
two (SO and GIN), the Antarctic Bottom Water (AABW)
and the North Atlantic Deep Water (NADW) should be
classified. In YOLDA, wSO and wSO′, and wGIN and wGIN′
indicate constant upwelling velocities of AABW and
NADW, respectively.
3. Tracer and Data
Physical parameter values are determined to minimize the model-data misfits in the tracer concentration.
In Shaffer and Sarmiento (1995), both temperature and
natural 14C are used as tracers. However, as pointed out
by Siegenthaler and Joos (1992), it is not appropriate to
describe distributions of both temperature and 14C simultaneously using horizontally non-dimensional models like
HILDA and YOLDA. Compared with 14C, temperature
varies significantly with latitude, especially in the lowlatitude regions of LS and LS′. In this study, therefore,
only natural 14C is used as a tracer to determine the optimal values of the physical parameters.
As 14C is the radioisotope, it needs the source/sink
terms in the deep layers. According to Shaffer and
Sarmiento (1995), the terms can be written in LD and
HD, for example, as follows;
SLD(z) = –λφLD(z)
(14)
SHD = – λDφHD
(15)
where λ, the radioactive decay rate for 14C, is 3.84 ×
10–12 [s –1].
In this study, 14 C and ΣCO 2 data obtained by
GEOSECS are used. As referred above, annual mean
SST = 5°C contours are chosen for the boundary between
the low and high latitude region. According to this definition, Station 1–5, 10–14, 18–66 and 91–121 are in LS′
and LD′, 201–278, 295–347, 403–428 and 434–451 in
LS and LD, 6–9 and 15–17 in HS′ and HD′, 67–90, 279–
294 and 429–433 in HS and HD. Since the Pacific Ocean
is 2.3 times as wide as the Indian Ocean, the data in LS
and LD are weighted by area. In LS, LS′, HS, HS′, HD
and HD′, data values are averaged. In LD and LD′, data
are vertically set to the depth at z = –250, –500, –750,
–1000, –1250, –1500, –1750, –2000, –2250, –2500,
–2750, –3000, –3250, –3500, –3750 m prepared for comparing with model results.
In this study, only natural 14C is adopted as a tracer.
However, GEOSECS data include bomb-produced 14C
too, so we exclude 14C data above 1000 m-depth and in
the North Atlantic Ocean which are strongly affected by
bomb-produced 14C as discussed by Broecker and Peng
(1982).
4. Results
4.1 Optimal values of the parameters
As mentioned above, the physical parameters are
determined to minimize model-data misfits of natural 14C
distribution in the ocean. In previous studies, as will be
referred in Discussion, the vertical diffusion coefficients,
the upwelling velocities and the air-gas exchange velocities have been estimated by observations and modelings.
The parameters of the lateral exchange rate are newly
introduced in HILDA and there are no correspondings in
previous studies except for a few studies using HILDA.
Therefore, the value of the lateral exchange rate is more
uncertain than the values of vertical diffusion coefficients,
upwelling velocities and air-gas exchange velocities. One
of the most remarkable advantages in YOLDA is able to
describe the clear difference in substance concentration
between LD and LD′, and to obtain the appropriate values of parameters which control substance distributions
in LD and LD′. Shaffer and Sarmiento (1995) estimated
parameter values using least mean square fits of model
results to corresponding data. While only data-model
misfits in substance concentration in LD were discussed
in HILDA, we must optimize the difference in substance
distribution between LD and LD′ as well as using least
mean square data-model fits in each basin in YOLDA.
At first, we focus on optimizing k, wSO, wSO′, wGIN,
wGIN′, q and q′ with setting ∆ 14C values in boxes except
LD and LD′ to their observational correspondings on the
assumption that the other parameters are not so effective
to substance distribution in LD and LD′. After obtaining
these best-fit values, and letting ∆14C values in HD and
HD′ be calculated numerically, u and u′ are optimized to
mininize model-data misfits in HD and HD′, respectively.
Finally, ∆14C values in the surface layers are also numerically calculated, and gHS, gHS′, gLS and gLS ′ are tuned to
minimize model-data misfits in HS, HS′, LS and LS′, respectively. The optimal value of each parameter is as in
Table 1 (without time-delay effect). With these values,
vertical profiles in LD and LD′ are shown in Fig. 2. Sensitivity to each parameter is shown in Fig. 3.
The most effective parameters to control 14C concentrations in LD and LD′, and difference in 14C concen-
Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model
659
Fig. 3. Vertical profiles of ∆14C in LD and LD′. 䊉, 䊊 and * are the same as in Fig. 2. (a)–(k) Case for changing value of each
parameter with the other parameters set to the optimal values: k in (a), upwelling velocities (wSO , wSO ′, wGIN and wGIN′) in (b),
q in (c), q′ in (d), u in (e), u′ in (f), g LS in (g), g LS′ in (h), g HS in (i) and g HS ′ in (j). Dashed, broken and solid lines show model
results for 0.5, 1 and 1.5 times the optimal value of each parameter, respectively. Model results for each case in HS, HD, HS′
and HD′ are also shown.
660
M. Fujii et al.
Fig. 3. (continued).
Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model
661
tration between LD and LD′, are k and upwelling velocities (wSO, wSO′, wGIN and wGIN′). Parameter k controls 14C
concentrations in any levels in LD and LD′, especially in
the intermediate layer of 1000–2000 m depth in LD (Fig.
3(a)). Parameters of wSO, wSO′, wGIN and wGIN ′ are also
effective to determine 14C concentrations in the deep layer
below 2000 m-depth in both LD and LD′ (Fig. 3(b)). The
effects of q and q′ are smaller than expected according to
Shaffer and Sarmiento (1995); while ∆14C difference between 0.5 and 1.5 times the optimal values of q and q′ at
2000 m depth is about 40‰ in Shaffer and Sarmiento
(1995), it is at most 20‰ in this study. Parameter q influences 14C distributions in both LD and LD′ (Fig. 3(c)),
while q′ has little influence on the distribution in LD (Fig.
3(d)). Parameter q′ controls 14C concentrations at the same
extent in the deep layer, while q particularly controls the
concentrations in the intermediate layer at around 2000
m depth. Above and below this depth, parameters k and
w, respectively, are more dominant. Roles of parameters
u and u′ are similar to those of q and q′, respectively, but
their effects are more restricted to their own regions; quantitative change of parameter u hardly influences the concentration in LD′ (Fig. 3(e)). Parameter u′ effects 14C
concentrations in both basins, but the effect is very small
(Fig. 3(f)). Parameters gLS and gLS′ also have strong effects in the corresponding basins. They control 14C concentrations at the same extents in any level (Figs. 3(g)
and 2(h)). Parameters gHS and gHS′ also have similar effects, but their effects on LD and LD′ are much smaller
(Figs. 3(i) and 3(j)).
4.2 Σ CO2 concentrations
With the optimal values of physical parameters, distributions of other tracers can be reproduced using
YOLDA. CO 2 is a tracer whose distribution in the ocean
is determined by both physical and biogeochemical processes. The parameters of gLS, gLS′, gHS and gHS′ are invalid,
for the air-sea gas exchange velocity of CO 2 is different
from that of 14C. When the biogeochemical processes are
eliminated, the sink/source of ΣCO2 is only at the sea
surface. Hence the sink/source terms are added to the
equations in LS, LS′, HS and HS′ as follows;
SLS
(
)

K2 LS 2[ ΣCO 2 LS ] − [ Ac ]

= ksγ LS ( pCO 2 )air −
γ LS K1LS [ Ac ] − [ ΣCO 2 LS ]

2




(16)
(
)
(
)
S ′ LS

K2 LS 2[ ΣCO′ 2 LS ] − [ Ac ]

= ksγ LS ( pCO 2 )air −
γ LS K1LS [ Ac ] − [ ΣCO′ 2 LS ]

SHS

K2 HS 2[ ΣCO 2 HS ] − [ Ac ]

= ksγ HS ( pCO 2 )air −
γ HS K1HS [ Ac ] − [ ΣCO 2 HS ]





(17)
2




(18)
2
S ′ HS
(
)

K2 HS 2[ ΣCO′ 2 HS ] − [ Ac ]

= ksγ HS ( pCO 2 )air −
γ HS K1HS [ Ac ] − [ ΣCO′ 2 HS ]

2


 (19)

where k s: a piston velocity of CO2 (1.6 × 10–5 [ms–1] (calculated according to Wanninkhof, 1992)); γ: a solubility
of CO 2 (γLS = 3.24 × 10 –2 [mol kg –1atm –1], γHS = 6.29 ×
10 –2 [mol kg–1atm –1] (Weiss, 1974)); K1 : the first dissolution constants of carbonic acid (K1LS = 9.41 × 10–7,
K1HS = 6.33 × 10 –7 (Mehrbach et al., 1973)); K2: the sec-
Fig. 4. Vertical profiles of ΣCO2 in LD and LD′ ( µ mol/kg). Thin solid and dashed lines show the case without air-sea CO2
exchange in LD and LD′, respectively. Thick solid and dashed lines show the case with air-sea CO 2 exchange in LD and LD′,
respectively. Model results of each case (without and with air-sea CO2 exchange, respectively) in HS, HD, HS′ and HD′ are
also shown.
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M. Fujii et al.
ond dissolution constants of carbonic acid (K2LS = 6.59 ×
10 –10, K2HS = 3.53 × 10–10 (Mehrbach et al., 1973));
[ΣCO2]: ΣCO2 concentration; [Ac]: carbonate alkalinity;
(pCO2 )air and [A c] in sea surface are set to 280 [ppmv]
and 2250 [µeq/kg], respectively. As for γ, K1 and K2, normalized by (pCO2)air of 280 ppm and salinity of 35 [psu],
values at 20°C in the low-latitude region and 0°C in the
high-latitude region are used.
Vertical ΣCO2 profiles in LD, LD′, HD and HD′ are
shown in Fig. 4. In the case of no air-sea interaction of
CO2, ΣCO2 concentrations are uniform all over the ocean;
air-sea CO2 exchange generates vertical ΣCO2 profiles in
LD and LD′ which are denser in the deep layer than in
the surface layer. The larger concentration in LD′ than in
LD in YOLDA is caused by huge inflow of NADW into
LD′ which has large solubility of CO2. AABW, which also
has large solubility, penetrates LD directly, but the income is smaller than that of NADW into LD′.
4.3 Distributions of anthropogenic substances
4.3.1 Artificial change of 14C distribution
14
C concentration in the atmosphere has been decreasing since the middle of 18th century due to the industrialization (the Suess effect). Then it had dramatically increased in 1950’s and the first half of 1960’s, and
gradually decreased since the latter half of 1960’s because
of 14C contamination into the atmosphere caused by nuclear bomb and the following absorption by other reservoirs, respectively. In this study, the oceanic responses to
the Suess effect and nuclear-bomb effect are investigated
with YOLDA. 14C fluctuation in the atmosphere given in
this study is shown in Fig. 5(a). Model results of the oceanic responses to the 14C invasion in PI and AT are shown
in Figs. 5(b) and 5(c), respectively. Both influences of
the industrialization and nuclear bomb into the ocean are
significant in the upper layer above 1000 m depth of LD
and completely penetrates into all layers of LD′, while
these do not appear in the deep layer below 1000 m depth
of LD. These results suggest that AT is sensitive to atmospheric fluctuations which have the time scale of 10–
100 years, but these fluctuations are not enough in time
to change the tracer distribution in the deep layer of PI.
4.3.2 Anthropogenic Σ CO2
Since the dawn of the industrialization, (pCO2)air has
been increasing accompanied with the fossil-fuel combustion, the cement production and the deforestation.
Change of the oceanic ΣCO 2 distribution follows the
(pCO2 )air increase.
In this study, two case studies are carried out. In case
1, (pCO2)air is set to 280 ppmv. In case 2, (pCO2 )air has
been increased linearly from 280 to 350 ppmv for 250
years, for simplicity, though that is a little different from
observational corresponding. Figure 6 shows vertical
ΣCO2 concentration anomalies of case 2 from case 1 in
Fig. 5. (a) Atmospheric ∆14C value set in YOLDA according to
the Suess effect and the bomb-produced 14C contamination.
∆14C in 1750 is set to 0‰, and is decreasing linearly to
–20‰ in 1950, increasing linearly to 700‰ in 1965, and
decreasing linearly to 100‰ in 1990. (b), (c) Vertical profiles of ∆14C anomaly from pre-industrial level (∆14C = 0‰)
in LD (b) and LD′ (c) in YOLDA. Dashed lines; in 1950,
broken lines; in 1965, solid lines; in 1990. Model results of
each case (in 1950, 1965 and 1990, respectively) in HS,
HS′, HD and HD′ are also shown.
Fig. 6. Vertical profiles of anthropogenic ΣCO2 in YOLDA.
Lines and values are the same as in Fig. 2.
LD and LD′. This indicates that more anthropogenic ΣCO2
is dissolved in AT than in PI, and that the oceanic response is similar to the results obtained in Subsection
4.3.1.
Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model
663
5. Discussion
5.1 Parameter values
The parameter values obtained in this study are compared with those in the previous studies. In Joos et al.
(1991) and Siegenthaler and Joos (1992), with HILDA
whose DS and D are set to 75 m and 3725 m, respectively,
a vertical diffusion coefficient is estimated to be 1.5 ×
10 –5 + 2.3 × 10–4exp{(75 – |z|)/253} [m2s–1], decreasing
with depth. The coefficient at the depth between z = –400
m and z = –450 m corresponds to 7.5 × 10–5 [m2s –1], estimated in this study, set constant to keep one of characters
of YOLDA as a simplified model. In Shaffer and
Sarmiento (1995), a vertical diffusion coefficient is also
set constant, and the best-fit value is 3.2 × 10–5 [m2s–1],
about half as large as obtained in this study. In Shaffer
and Sarmiento (1995), both temperature and natural 14C
are used as tracers. As there is bomb-produced 14C influence in the upper layer, only temperature is used for fitting above 1000 m depth. In this study, on the other hand,
only natural 14C is used as a tracer, and model-data fitting is performed only below 1000 m depth. These differences between Shaffer and Sarmiento (1995) and this
study might cause the difference in best-fit value of k.
Although observations have not covered enough in
space and time, the canonical value obtained by observations is 1.0 × 10–5 [m2s–1] in the upper layer (Ledwell et
al., 1993), considerably small because of strong stratification in this depth, and it increases with depth to be
3.0 × 10 –4 [m2s –1] in the deep and bottom layer (Morris et
al., 1997). The difference in the vertical diffusion coefficient between the observations and this study might be
justified by the character of simplified models; they do
not include explicitly the thermocline, the processes of
wind-driven circulation in the upper layer, mesoscale
eddies and following vertical motion. In addition, strength
of thermohaline circulation is dependent on effects of
vertical diffusion coefficient (Bryan, 1987), but there are
little dependence of k on wSO, wSO′, wGIN and wGIN ′ in this
model.
Since the upwelling velocity in the deep layer is too
small to estimate directly by observation, modeling has
been used to estimate the velocity. The canonical globalmean upwelling velocity of the thermohaline circulation
is 1.2 × 10–7 [ms–1] (Munk, 1966 and Broecker and Peng,
1982). The values are 1.4 × 10 –8 [ms –1] in Joos et al.
(1991) and Siegenthaler and Joos (1992), 2.0 × 10 –8
[ms–1] in Shaffer and Sarmiento (1995), much smaller than
the canonical value. However, few previous studies have
already discussed the differences in the upwelling velocities among the basins. In this study, an upwelling velocity is divided into four; wSO, wSO′, wGIN and wGIN′, and
difference in upwelling velocities between AABW and
NADW can be discussed. Using upwelling velocities in
664
M. Fujii et al.
this study, vertical transports by thermohaline circulations
can be estimated; 8 Sv upward in PI, 2 Sv upward in AT,
1 Sv downward in SO and 9 Sv downward in GIN. For
NADW, the velocities are larger, but those of AABW are
smaller than the velocity estimated in previous studies
using HILDA. Schmitz (1995) estimated vertical transports according to the observations. Although he adopted
potential density anomaly as a vertical coordinate instead
of depth, the boundary between the upper and deep layer
was approximately 1500 m depth in non-polar areas. This
boundary is much deeper than that in this study, because
the intermediate water is also included in the upper layer
of his two-layer thermohaline conveyor belt. When potential density anomaly is used as a vertical coordinate,
layers outcrop at high latitudes. Therefore, the results of
thermohaline circulation in the high latitude in Schmitz
(1995) contains part of processes of q, q′, u and u′ as well
as wSO, wSO′, wGIN and wGIN′ in this study. Therefore, it is
possible for upwelling velocities in Schmitz (1995) to be
larger than those in this model. Using the values obtained
in Schmitz (1995), wSO, wSO ′, wGIN and wGIN′ are calculated to be 5.0 × 10 –9 [ms–1], 1.4 × 10–8 [ms–1], 4.5 ×
10 –8 [ms –1] and 7.2 × 10–8 [ms–1], respectively, a few factor larger than the optimal values in this study.
The conception of deep water outcrop at the surface
in the high-latitude region also appeared significantly in
Siegenthaler (1983). Such an isopycnal exchange can be
reproduced using both q and u in HILDA. The optimal
values of q–1 are about 540 years in Joos et al. (1991) and
Siegenthaler and Joos (1992), and 420 years in Shaffer
and Sarmiento (1995). The values of q–1 and q′ –1 obtained
in this study are about 2640 years and 110 years, respectively, whose residence time of water is much longer in
LD and much smaller in LD′ than that in LD in HILDA.
In YOLDA, areas of cross sections between LD and HD,
LD′ and HD, and LD′ and HD′ are not parameterized.
Taking into consideration that the cross section between
LD and HD is extraordinally large in the real ocean, q
value estimated in this study might be underestimated.
The optimal values of u are 1.2 × 10 –6 [ms–1] in Joos et
al. (1991) and Siegenthaler and Joos (1992), and 1.9 ×
10 –6 [ms–1 ] in Shaffer and Sarmiento (1995). In this study,
the optimal value of u′ is as large as in Shaffer and
Sarmiento (1995), while the value of u is much smaller
than that in HILDA, and it may imply that the vertical
mixing in winter is not so vigorous in the Southern Ocean.
Gas exchange time between the surface layer and the
atmosphere is 6.8 years common in LS and HS in Joos et
al. (1991) and Siegenthaler and Joos (1992), 6.8 years in
LS and 4.3 years in HS in Shaffer and Sarmiento (1995).
In this study, it is 6.6 years common in LS and LS′. It is
extraordinarily large, 26.4 years in HS, while it is 7.9 years
in HS′. Global mean gas exchange time calculated in this
study is 9.0 years. In the polar region, sea ice coverage
affects air-sea gas exchange, but δS and δ′ S are fixed to
0.10 in this study. In the Southern Ocean, real sea ice
coverage might be larger than estimated in this study, and
gas change rate in HS can be underestimated.
5.2 Boundary condition
A boundary condition at the bottom of the deep layer
is as Eqs. (4) and (7). It implies that the net flux of a
tracer brought by the vertical diffusion, the upwelling and
the tracer sink/source is zero at the boundary.
Biogeochemical processes are not included in this study,
and ΣCO2 has no sink/source at the boundary. Therefore,
this boundary condition is valid for ΣCO2 . In the case of
14
C, however, the sink/source term is necessary because
14
C decays, and therefore, ∆14C value decreases with time.
As LD is horizontally large, ∆ 14C value largely changes
in process of the horizontal advection from the south to
the north of LD. The boundary condition above cannot
include this effect, because there is no horizontal resolution.
To introduce this effect on 14C decay into YOLDA,
a time-delay effect is necessary in the boundary condition. Averaged ∆ 14C values are around –160‰ in HD and
–200‰ in LD, which correspond to 1450 and 1850 years,
respectively, in terms of an averaged apparent time. Therefore, it seems to take about 400 years for water to migrate from HD to LD. Here, to consider this time-dependent effect in LD, φ HD in Eqs. (2) and (4) is multiplied by
(1/2)t/τ, i.e.,
α (1 − δ )
∂φ LD ( z )
∂t
= α (1 − δ )k
∂ 2φ LD ( z )
∂φ ( z )
− α (1 − δ )( wGIN + wSO ) LD
2
∂z
∂z
t /τ


1
−α (1 − δ )q φ LD ( z ) − φ HD ×    + α (1 − δ )SLD ( z )


2


(20)
k
t

∂φ LD ( z )
1 /τ 
− ( wGIN + wSO ) φ LD ( z ) − φ HD ×    + Sbottom
 2 
∂z

=0
(21)
where τ is the half-life period of 14C, and t is set to 400
years. Using this process, ∆14C value is getting smaller
by 40‰ automatically in process of moving HD to LD
via the bottom of LD. In this case, the optimal values of
physical parameters are modified in q, wSO, wSO′, wGIN,
wGIN ′. The values are as in Table 1 (with time-delay effect). With these values, vertical profiles of 14C in LD
Fig. 7. Vertical profiles of ∆14C in YOLDA with time-delay
effect. Marks, lines and values are the same as in Fig. 2.
and LD′ are shown in Fig. 7. Without this effect, smaller
upwelling velocities are required to reproduce realistic
14
C distribution in the deep layer of LD. The lateral exchange rate must not be larger, otherwise ∆ 14C value of
upwelling water in LD become too large in process of the
lateral exchange with water in HD, which has larger ∆14C
value during longer time of upwelling. With the time-delay effect, these values are realistic even if the upwelling
velocities are larger. Therefore, the upwelling time of
water in LD becomes shorter and the lateral exchange
rate can also have larger value.
6. Conclusion
A simplified physical model is proposed in this study
to represent significant differences in the substance distributions among the basins, which cannot be sufficiently
described in HILDA and the other previous models. In
this model, only five physical parameters are introduced
and optimized to minimize the model-data misfits of 14C
as a physical tracer. Using these optimal values of the
physical parameters, the differences of artificial substance
distributions such as man-made 14C and anthropogenic
ΣCO2 , and differences in the physical processes of the
oceanic carbon cycle between PI and AT, are well reproduced. The results of anothropogenic substance distributions indicate that the oceanic response to these substances
penetrated from the atmosphere through the sea surface
is much faster and stronger in AT than in PI.
Compared with HILDA, the number of the physical
parameters is also almost doubled except for a constant
coefficient of the vertical turbulent diffusion (k) in this
study, and the model still retains its simplicity which is
one of the advantages in simplified models. In another
parameter study, k was also set different between PI and
AT, but little difference was found in the optimal values.
Therefore, k is set to uniform at both PI and AT in this
study. The optimal values of k, wSO, wSO′, wGIN and wGIN ′
obtained in this study are comparable with those in the
previous studies, though the upwelling velocities are much
smaller than the global-mean canonical value. Since the
other parameters were not divided into two, between PI
and AT, and SO and GIN, respectively in the previous
Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model
665
studies, there are no reference values for these parameters. However, the optimal values in AT and GIN are
relatively close to the global-mean values in the previous
studies, and much larger than those in PI and SO.
The boundary condition at the bottom of PI is discussed in this study. As shown in Table 1, there are differences in the optimal values of some physical parameters between with and without the time-delay effect. With
the time-delay effect, the value of q is twice, and the
upwelling velocities are 1.75 times, as large as those without the effect, respectively. It is because larger upwelling
velocities are permitted with the time-delay effect, and
hence, q have to be larger due to smaller upwelling time
in LD. However, the vertical profiles and the differences
in 14C concentrations between PI and AT are well described with both boundary conditions.
A future purpose based on this study is to provide a
reliable simplified model which includes biogeochemical
processes in the carbon cycle. The physical processes in
the carbon cycle have already been described in this study.
To introduce the biogeochemical processes, other parameters and tracers which can describe the biological and
alkalinity pumps are needed. With these processes in this
simplified model, the carbon cycle in the global ocean
will be clarified in the future work.
Acknowledgements
The work presented in this paper was financially
supported by the Ministry of Education, Science, Sports
and Culture of Japan. The authors appreciated fruitful
discussion with Drs. S. Tsunogai and S. Watanabe. Some
of the figures were produced by GFD-DENNOU Library.
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