scispace - formally typeset

Journal ArticleDOI

Behavior of Double-Hemisphere Thermohaline Flows in a Single Basin

01 Mar 1999-Journal of Physical Oceanography (American Meteorological Society)-Vol. 29, Iss: 3, pp 382-399

AbstractA coarse resolution, three-dimensional numerical model is used to study how external parameters control the existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin. Initially, the meridional surface density gradient is directly set to be larger in a ‘‘dominant’’ hemisphere than in a ‘‘subordinate’’ hemisphere. The two-hemisphere system has a broader thermocline and weaker upwelling than the same model with the dominant hemisphere only. This behavior is in accord with classical scaling arguments, providing that the continuity equation is employed, rather than the linear vorticity equation. The dominant overturning cell, analogous to North Atlantic Deep Water formation, is primarily controlled by the surface density contrast in the dominant hemisphere, which in turn is largely set by temperature. Consequently, in experiments with mixed boundary conditions, the dominant cell strength is relatively insensitive to the magnitude QS of the salinity forcing. However, QS strongly influences subordinate hemisphere properties, including the volume transport of a shallow overturning cell and the meridional extent of a tongue of low-salinity intermediate water reminiscent of Antarctic Intermediate Water. The minimum QS is identified for which the steady, asymmetric flow is stable; below this value, a steady, equatorially symmetric, temperature-dominated overturning occurs. For high salt flux, the asymmetric circulation becomes oscillatory and eventually gives way to an unsteady, symmetric, salt-dominated overturning. For given boundary conditions, it is possible to have at least three different asymmetric states, with significantly different large-scale properties. An expression for the meridional salt transport allows one to roughly predict the surface salinity and density profile and stability of the asymmetric state as a function of QS and other external parameters.

Topics: North Atlantic Deep Water (56%), Thermohaline circulation (53%), Water mass (52%), Thermocline (52%), Antarctic Intermediate Water (51%)

Summary (2 min read)

1. Introduction

  • Though the earth’s global thermohaline circulation is dominated by temperature (the deepest water is generally the coldest), salinity variations play a crucial role in determining the location of deep-water formation.
  • In the asymmetric state, one hemisphere will possess the densest surface water in the basin.
  • In contrast to these studies, the authors want to relate the strength of the thermohaline circulation directly to external parameters; to clarify the relation they use simpler geometry and forcing.
  • For simplicity the authors use a relatively idealized system here.

2. Numerical model

  • All experiments are conducted with MOM-2, the Modular Ocean Model version of the GFDL Model (Pacanowski 1996; Cox 1984), a B-grid (Arakawa and Lamb 1977) finite-difference discretization of the primitive equations that computes solutions by stepping forward in time.
  • The values chosen correspond to a linearization of the equation of state at surface pressure and a temperature of about 138C (see Table 1).
  • The salinity is driven by setting a zonally uniform surface salinity flux to represent the effects of freshwater fluxes produced by evaporation, precipitation, and runoff.
  • This parameterization has a stronger dynamical justification than horizontal diffusion, and allows numerical models to better represent the relatively thin thermocline and small deep-water formation regions of the real ocean and to eliminate spurious diapycnal diffusion in regions of strong horizontal gradients such as western boundary currents (Veronis 1975; Böning et al. 1995; Danabasoglu et al. 1994).
  • The Gent–McWilliams runs are conducted with a flux-corrected transport scheme added to MOM-2 by Weaver and Eby (1997).

3. Restoring boundary conditions

  • The authors conduct two-hemisphere experiments, which are forced only by restoring to a temperature profile that is asymmetric about the equator.
  • The degree of asymmetry between the hemispheres is small, yet the circulation must be qualitatively different from a symmetric experiment because deep water is required to spread from the dominant hemisphere to fill the deepest region of the other ‘‘subordinate’’ hemisphere.
  • The maximum buoyancy difference between the eastern and western boundaries is approximately bE 2 bW 5 0.25Db for all 1H and 2H runs, confirming the theoretical result of Marotzke (1997) and the hypothesis that the zonal buoyancy difference scales like Db.
  • For smaller DbP, the peak northward heat transport is roughly proportional to the subordinate cell volume transport.

4. Mixed boundary conditions

  • When the slightly asymmetric run with QS 5 1 is used as an initial condition for a high vertical resolution run with the same QS, the system falls into the intermediate asymmetric state.
  • Therefore, most of the variation in DS, which spans nearly two orders of magnitude in the experiments, can be explained by (14).
  • The low salinity tongue appears to be governed by a balance between southward advection of deep, low salinity from the northern boundary and downward diffusion of high salinity from the surface.

5. Conclusions

  • One hemisphere, which the authors call the ‘‘dominant’’ hemisphere, has the strongest meridional circulation, minimizing the exposure of surface water to the surface fluxes of salinity (or, more realistically, of freshwater) at any particular latitude.
  • Even a modest DbP forces the relatively small subpycnocline range of buoyancy to be filled by the dominant cell.
  • The location of the regime boundaries must be viewed with some caution because, in reality, the ocean is coupled to an atmosphere in which meridional transports of heat and moisture can affect the stability of a state (Nakamura et al.
  • A two-dimensional model shows that such a configuration is more unstable than a coupled model, in which moisture feedbacks are also included (Capotondi and Saravanan 1996).
  • None of their attempts produced the multiple states seen here, nor did they display the vanishing of the asymmetric state at low QS described above, so the authors do not describe the model details in this paper.

Did you find this useful? Give us your feedback

...read more

Content maybe subject to copyright    Report

382 V
OLUME
29JOURNAL OF PHYSICAL OCEANOGRAPHY
q 1999 American Meteorological Society
Behavior of Double-Hemisphere Thermohaline Flows in a Single Basin
B
ARRY
A. K
LINGER
Oceanographic Center, Nova Southeastern University, Dania Beach, Florida
J
OCHEM
M
AROTZKE
Center for Global Change Science, Massachusetts Institute of Technology, Cambridge, Massachusetts
(Manuscript received 26 May 1997, in final form 12 March 1998)
ABSTRACT
A coarse resolution, three-dimensional numerical model is used to study how external parameters control the
existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin.
Initially, the meridional surface density gradient is directly set to be larger in a ‘dominant’ hemisphere than
in a ‘subordinate’ hemisphere. The two-hemisphere system has a broader thermocline and weaker upwelling
than the same model with the dominant hemisphere only. This behavior is in accord with classical scaling
arguments, providing that the continuity equation is employed, rather than the linear vorticity equation.
The dominant overturning cell, analogous to North Atlantic Deep Water formation, is primarily controlled by
the surface density contrast in the dominant hemisphere, which in turn is largely set by temperature. Consequently,
in experiments with mixed boundary conditions, the dominant cell strength is relatively insensitive to the
magnitude Q
S
of the salinity forcing. However, Q
S
strongly influences subordinate hemisphere properties, in-
cluding the volume transport of a shallow overturning cell and the meridional extent of a tongue of low-salinity
intermediate water reminiscent of Antarctic Intermediate Water.
The minimum Q
S
is identified for which the steady, asymmetric flow is stable; below this value, a steady,
equatorially symmetric, temperature-dominated overturning occurs. For high salt flux, the asymmetric circulation
becomes oscillatory and eventually gives way to an unsteady, symmetric, salt-dominated overturning. For given
boundary conditions, it is possible to have at least three different asymmetric states, with significantly different
large-scale properties. An expression for the meridional salt transport allows one to roughly predict the surface
salinity and density profile and stability of the asymmetric state as a function of Q
S
and other external parameters.
1. Introduction
Though the earth’s global thermohaline circulation is
dominated by temperature (the deepest water is gener-
ally the coldest), salinity variations play a crucial role
in determining the location of deep-water formation.
The surface temperature distribution is roughly sym-
metric about the equator, but surface salinity has notable
north–south asymmetries [e.g., cf. Figs. 8.8 and 8.10 in
Peixoto and Oort (1992)], with winter northern North
Atlantic water roughly 0.5 psu saltier than australwinter
Weddell Sea water (Levitus and Boyer 1994). As a re-
sult, deep-water formation is equatorially asymmetrical
within the World Ocean, with substantial transports of
North Atlantic Deep Water crossing the equator and
flowing into the Southern Hemisphere [Speer and Mc-
Cartney (1991); Warren (1981) for a review of earlier
Corresponding author address: Dr. Barry A. Klinger, Oceano-
graphic Center, Nova Southeastern University, 8000 North Ocean
Drive, Dania Beach, FL 33004.
E-mail: klinger@ocean.nova.edu
work]. This asymmetry is interesting for purely ocean-
ographic reasons as well as for its influence on climate.
For example, the heat transport in the South Atlantic is
equatorward rather than poleward (e.g., Macdonald
1993).
As Rooth (1982) and Bryan (1986) have shown, using
a box model and a general circulation model, respec-
tively, such an asymmetry in salinity and meridional
overturning can occur even when the boundary condi-
tions are equatorially symmetric. Surface boundary con-
ditions form a relatively tight constraint on surface tem-
perature but can be thought of as equivalent to speci-
fying a flux of salinity rather than the salinity itself.
Because of these ‘mixed boundary conditions,’ more
than one circulation state can exist given such a set of
boundary conditions (Stommel 1961). In a single ocean
basin spanning the equator, it is possible to have either
equatorially symmetric temperature-dominated (T-dom)
sinking near the poles, equatorially symmetric salinity-
dominated (S-dom) sinking near the equator, or equa-
torially asymmetric deep-water formation at one pole
only (Welander 1986).

M
ARCH
1999 383KLINGER AND MAROTZKE
How overturning strength depends on external pa-
rameters has received relatively thorough scrutiny in
single-basin systems driven by temperature-only bound-
ary conditions (Bryan 1986; Colin de Verdiere 1988;
Winton 1996; Marotzke 1997) or freshwater-only
boundary conditions (Huang and Chou 1994). The two-
hemisphere, mixed-boundary-condition case has been
explored with two-dimensional models by Marotzke et
al. (1988), Thual and McWilliams (1992), Quon and
Ghil (1992, 1995), Cessi and Young (1992), Schmidt
and Mysak (1996), Vellinga (1996), and Dijkstra and
Molemaker (1997). When salinity forcing is sufficiently
stronger than temperature forcing, only the S-dom state
exists, and when temperature forcing is sufficiently
stronger than salinity forcing, only the T-dom state ex-
ists. It is only when both temperature and salinity forc-
ing are in some sense at intermediate strengths that the
equatorially symmetric states and the asymmetric state
can all exist [see Thual and McWilliams (1992) Fig. 3].
These two-dimensional studies did not relate the flow
strength and regime boundaries to parameters that could
be readily applied to three-dimensional basins in which
basin width, planetary rotation, and planetary radius
play a role. There has been no three-dimensional study
of this system in which forcing parameters were sys-
tematically varied, though Weaver and Sarachik (1991)
used such a model to study the time evolution of tran-
sitions from state to state.
The thermohaline circulation is a global system in
which the flow in each basin is influenced by that in
the other basins (Warren 1983; Gordon 1986; Rintoul
1991; Marotzke and Willebrand 1991; Stocker and
Wright 1991; England 1993; Macdonald and Wunsch
1996). This system has an extremely complicated de-
pendence on a multiplicity of parameters, including ba-
sin geometry (Hughes and Weaver 1994), atmospheric
freshwater transports between basins (Marotzke and
Willebrand 1991; Stocker et al. 1992), and the coupling
to the atmosphere (e.g., Mikolajewicz and Maier-Reimer
1994; Rahmstorf and Willebrand 1995; Weber 1998).
Therefore, it is useful to understand the less compli-
cated, single-basin cell as a stepping stone to under-
standing the more complete system.
The basic question of this paper is: How do the ex-
ternal parameters in a two-hemisphere, mixed-bound-
ary-condition system determine the temperature, salin-
ity, and overturning in the equatorially asymmetric
state? We subdivide this into two smaller problems. In
the asymmetric state, one hemisphere will possess the
densest surface water in the basin. Peterson (1979) and
Cox (1989) have shown that this water must dominate
the bottom of the entire basin (when the equation of
state is linear), but the resulting state has not been care-
fully studied. Thus, given such an asymmetric surface
density distribution, what is the resulting overturning
strength and pycnocline structure? This will be exam-
ined in section 3, which discusses experiments in which
the surface density is restored to a reference profile.
Then the full question can be answered if, for a given
mixed boundary condition, we can predict the resulting
surface density. We consider this question via mixed-
boundary-condition experiments in section 4.
Hughes and Weaver (1994) showed in an idealized
global GCM under mixed boundary conditions that At-
lantic overturning strength is linearly related to the bas-
inwide meridional gradient in zonally and vertically av-
eraged steric height (i.e., a double vertical integral of
zonally averaged density). Rahmstorf (1996) found in
his global GCM coupled to a diffusive atmospheric en-
ergy balance model that Atlantic overturning is pro-
portional to the zonally averaged middepth density dif-
ference between northern and southern Atlantic bound-
aries. In contrast to these studies, we want to relate the
strength of the thermohaline circulation directly to ex-
ternal parameters; to clarify the relation we use simpler
geometry and forcing. Wang et al. (1999a,b) used an
idealized, global, hybrid coupled GCM and Scott et al.
(1999) uncoupled and coupled box models to study in-
terhemispheric thermohaline flow and its interaction
with the atmosphere, in particular the effects of equa-
torially asymmetric atmospheric water vapor transports.
Here, we leave out asymmetries in forcing (except in
restoring-boundary-condition experiments) and detailed
considerations of ocean–atmosphere interactions, to fo-
cus on the rotating fluid dynamics of the interhemi-
spheric thermohaline circulation. The impact of wind,
nonlinearities in the equation of state, and north–south
asymmetries in the forcing are all important factors that
deserve careful treatment, and we defer these to a later
paper. For simplicity we use a relatively idealized sys-
tem here.
2. Numerical model
All experiments are conducted with MOM-2, the
Modular Ocean Model version of the GFDL Model (Pa-
canowski 1996; Cox 1984), a B-grid (Arakawa and
Lamb 1977) finite-difference discretization of the prim-
itive equations that computes solutions by stepping for-
ward in time. The domain is a sector of a sphere with
zonal and meridional boundaries and a flat bottom. De-
fault parameters are shown in Table 1; experiments with
any of these parameters changed are noted in the text
in section 4. The model is run at coarse, uniform hor-
izontal resolution with vertical grid spacing increasing
from 50 m at the surface to 500 m at the bottom. All
advective terms are retained in the temperature, salinity
and momentum equations, and density
r
is related to
temperature T and salinity S by
r
5
r
0
1
b
S 2
a
T, (1)
where
a
and
b
are the thermal and haline expansion
coefficients, respectively. The values chosen correspond
to a linearization of the equation of state at surface
pressure and a temperature of about 138C (see Table 1).
Though Gargett and Holloway (1992) argue that dif-

384 V
OLUME
29JOURNAL OF PHYSICAL OCEANOGRAPHY
T
ABLE
1. Summary of numerical experiments.
Parameter Symbol Value
Basin width, length
Basin depth
Vert. diffusivity momentum,
tracers
Hor. diffusivity momentum,
tracers
Isopycnal diffusivity
Expansion coefficients
T restoring timescale
Long, lat grid spacing
Number of levels
Momentum time step
Tracer time step
L,
f
p
H
(n
V
,
k
V
)
(n
H
,
k
H
)
k
r
a
,
b
t
dl, d
f
N
z
dt
M
dt
T
608,648
4500 m
(1, 0.5) 3 10
24
m
2
s
21
(250, 1.0) 3 10
3
m
2
s
21
2000 m
2
s
21
0.2 kg m
23
C
21
,
0.8 kg m
23
psu
21
30 days
3.758, 4.08
15
3600 s
5d
fusivities of T and S should be different, the parame-
terization of Zhang et al. (1998) shows this to be a
relatively small effect; here we use the same diffusivity
for both fields (see Table 1).
All walls and the bottom are insulating in both T and
S. Temperature is forced by restoring the surface layer
to a zonally uniform reference profile. The reference
profile as a function of latitude
f
in either hemisphere
is given by
1
T 5 T 1DT[cos(
pf
/
f
) 2 1], (2)
ep
2
where 2
f
p
#
f
#
f
p
, T
e
is the restoring surface tem-
perature at the equator, and DT is the restoring surface
temperature difference between the equator and the po-
lar boundary (in restoring boundary condition experi-
ments, this is DT
N
in the northern hemisphere and DT
S
in the southern hemisphere). Thus as we move north-
ward from the southern boundary, the restoring tem-
perature smoothly increases from a low of T
e
2DT
S
to
a high of T
e
and then decreases back to a low of T
e
2
DT
N
.
In the restoring-boundary-condition runs (section 3),
salinity is constant and hence no salinity forcing is nec-
essary. In the mixed-boundary-condition runs (section
4), the reference temperature is symmetric about the
equator (DT
N
5DT
S
). The salinity is driven by setting
a zonally uniform surface salinity flux to represent the
effects of freshwater fluxes produced by evaporation,
precipitation, and runoff. The dependence on latitude
for forcing strength Q
S
is given by
q
S
5 Q
S
cos(
pf
/
f
p
)/cos(
f
). (3)
This form represents the generally negative evaporation
minus precipitation (E 2 P) at high latitudes and pos-
itive E 2 P at low latitudes found on the real earth.
The real earth also has a narrow region of negative E
2 P near the equator, which we ignore here under the
assumption that the resulting shallow equatorial salinity
minimum has a relatively small effect on the large-scale
thermohaline circulation. The cosine factor in the de-
nominator is used so that the zonal integral of q
S
would
be a simple cosine in latitude, with no net salt added to
or removed from the basin.
Experiments are started with initial conditions of ei-
ther a resting, isothermal, isohaline (35 psu) ocean, or
a previous experiment. Each run is integrated until a
nearly steady state is reached, unless noted otherwise.
The usual criteria for steady state being reached is that
the drift in meridional volume transport exponentially
decreases over the last several centuries of the integra-
tion and is no more than 0.0025 Sv per century (Sv [
10
6
m
3
s
21
) at the end. Spot checks on selected runs
show that, when these criteria are met, other measures
such as temperature and salinity are also nearly steady.
In order to satisfy the Courant–Friedrichs–Levy crite-
rion at the lowest computational cost, a shorter time step
is used for the momentum equations than the tracer
equations (Bryan 1984). Each experiment generally
takes from 1000 to 5000 tracer years to reach steady
state, which takes on the order of 1 day of cpu time on
a DEC AlphaStation 250 4/266 workstation.
Most of the experiments are conducted using hori-
zontal diffusion of properties to parameterize mixing
induced by geostrophic eddies. Some runs with restoring
boundary conditions are also repeated with the ‘Gent–
McWilliams’ parameterization, which supplements iso-
pycnal diffusion of T and S with additional advection
by a tracer velocity representing the untilting of iso-
pycnals by baroclinic instability (Gent and McWilliams
1990; Gent et al. 1995). This parameterization has a
stronger dynamical justification than horizontal diffu-
sion, and allows numerical models to better represent
the relatively thin thermocline and small deep-water for-
mation regions of the real ocean and to eliminate spu-
rious diapycnal diffusion in regions of strong horizontal
gradients such as western boundary currents (Veronis
1975; Bo¨ning et al. 1995; Danabasoglu et al. 1994). The
Gent–McWilliams runs are conducted with a flux-cor-
rected transport scheme added to MOM-2 by Weaver
and Eby (1997). Flux-corrected transport is a finite dif-
ference scheme that attempts to retain the accuracy of
centered-difference schemes while also suppressing
nonphysical overshoots of temperature and salinity (a
property shared by the less accurate upstream differ-
encing scheme).
3. Restoring boundary conditions
a. Experiments
We conduct two-hemisphere experiments, which are
forced only by restoring to a temperature profile that is
asymmetric about the equator. We wish to understand
how the maximum meridional overturning volume
transport and the pycnocline structure of a double-hemi-
sphere overturning cell differ from the case of a single-
hemisphere system. As section 4 will show, the surface
density given by (2), with different values of DT in the

M
ARCH
1999 385KLINGER AND MAROTZKE
F
IG
. 1. Meridional overturning streamfunction (contours) and zonal average temperature (shading) for restoring BC
experiments, (a) 1H and (b) 2H, DT
N
5 0. Overturning contours are 2 Sv apart; isotherms are at 0.05, 0.1, 0.2, 0.4, and
0.8 of DT
S
5 308C. In this and all subsequent plots of overturning streamfunction, dashed, solid, and dotted contours
represent negative (southern sinking), positive (northern sinking), and zero values, respectively.
northern and southern hemispheres, is a reasonable ap-
proximation to the shape of the surface density profiles
produced by mixed-boundary-condition experiments.
In all the experiments, the southern hemisphere is
made the ‘dominant’ hemisphere by giving it the dens-
est surface water. Thus the dominant deep water, anal-
ogous to North Atlantic Deep Water in the Atlantic
Ocean, is formed in the southern hemisphere in our
experiments. We chose the southern hemisphere because
it happened to be the dominant hemisphere in the mixed-
condition experiments (section 4); since our experi-
ments have completely equatorially symmetric geom-
etry (unlike the real ocean), the choice of dominant
hemisphere is arbitrary. The weaker and deeper flow of
Antarctic Bottom Water does not appear in these ex-
periments because the equation of state is linear and
there is no circumpolar channel corresponding to the
Southern Ocean.
The relationship between the behavior in one-hemi-
sphere (‘‘1H’’) and two-hemisphere (‘‘2H’’) basins is
demonstrated by runs with DT
S
set to 308,68, and 18C.
In each of these experiments, we set DT
N
5 0, thus
exploring the case of most extreme equatorial asym-
metry first. For each 2H experiment, a 1H experiment
is run with forcing identical to the dominant hemisphere
of the corresponding 2H run. Outside of section 3b, ‘1H
experiment’ refers to an experiment with equatorial
symmetry rather than an actual wall at the equator.
These two variations are nearly identical (11.86 Sv over-
turning with the wall and 11.84 Sv with symmetry).
In another series of experiments, DT
S
is fixed while
DT
N
is varied. We are especially interested in the situ-
ation in which DT
N
is almost as large as DT
S
. In this
case, the degree of asymmetry between the hemispheres
is small, yet the circulation must be qualitatively dif-
ferent from a symmetric experiment because deep water
is required to spread from the dominant hemisphere to
fill the deepest region of the other ‘subordinate’ hemi-
sphere. In this series of experiments, DT
S
5 308C, while
DT
P
[DT
N
2DT
S
is set to 158,68,38, 1.58, 0.68, and
08C.
b. Dependence on dominant hemisphere temperature
gradient
The zonally integrated thermohaline circulation is
characterized by small, relatively intense downwelling
regions associated with deep convection and large areas
of weak, diffusively driven upwelling (Fig. 1). In runs
with DT
N
5 0, the presence of the nonconvecting hemi-
sphere means that a strong thermocline covers about
two times the area that it does in a single-hemisphere
run.
The classical scaling for upwelling velocity W, ther-
mocline depth D, and horizontal velocity V in large-
scale, buoyancy-driven circulation (Bryan and Cox
1967; Bryan 1987; Colin de Verdiere 1988) is based on
the vertical advective–diffusive balance,
wb
z
5
k
b
zz
, (4)
and thermal wind,
f
y
z
52b
x
, (5)
where f is the Coriolis parameter,
y
and w are merid-
ional and vertical velocities, and b 52g
r
/
r
0
is the
buoyancy (g is the gravitational acceleration, 9.8 m
2
s
21
). These equations yield the scale relations
W 5
k
/D, (6a)
fV/D 5Db/M, (6b)
where Db is the imposed meridional surface buoyancy
range and M is the basin zonal length scale. One might
ask whether the zonal buoyancy difference in (5) must

386 V
OLUME
29JOURNAL OF PHYSICAL OCEANOGRAPHY
scale like Db, but Marotzke (1997) demonstrates that
this is actually a reasonable assumption, and we show
below that it holds fairly well in our numerical exper-
iments. Another weakness of the classical scaling em-
ployed here (and indeed of the vertical mixing param-
eterization in the model) is that vertical or diapycnal
mixing in the ocean is known not to be uniform but
concentrated near the margins (e.g., Munk 1966;
Wunsch 1970; Armi 1978; Ledwell and Bratkovich
1995; Toole et al. 1997). Again, Marotzke (1997) has
shown that some scaling and numerical results are rea-
sonably insensitive to assumptions about how localized
the mixing is.
One more scale relation must be included in order to
close the system and find W, D, and V. Often this is
done using the linear vorticity relation (see Bryan 1987;
Colin de Verdiere 1988),
b
0
y
5 fw
z
, (7)
where
b
0
is the meridional gradient of f. However, this
equation does not apply to the western boundary current,
an important contributor to the zonal average of
y
. When
k
or Db is varied, this inapplicability does not matter,
because the western boundary current strength has the
same sensitivity to
k
and Db as the interior flow. How-
ever, the relationship between the western boundary and
the interior currents changes when the geometry of the
flow changes. Thinking of the deep flow as a homo-
geneous layer driven by a point source and a distributed
sink (Stommel et al. 1958; Stommel and Arons 1960),
we see that, if the sink area is changed but upwelling
speed w remains the same, the interior flow is unaffected
but the western boundary current must change to satisfy
continuity. In order to compare 2H flows to 1H, it is
therefore more appropriate to use the continuity equa-
tion (see Marotzke 1997; Winton 1996).
Assuming that the volume transport into the region
of deep-water formation equals the upwelling over al-
most the entire basin, we have
MDV 5 MLW, (8)
where L is the meridional length of the basin. Equations
(6) and (8) yield the scale relations
1/3
k
LM f
D 5 , (9a)
12
Db
1/3
2
Db
k
W 5 , (9b)
12
fLM
1/3
2
Db
k
L
V 5 , (9c)
22
12
Mf
1/3
22 2
Db
k
LM
F5MDV 5 , (9d)
12
f
where F is the meridional overturning streamfunction.
If linear vorticity (7) were used instead of continuity
(8), then (9) would be the same except that L would be
replaced with the radius of the earth, R. In one hemi-
sphere, L ø R, and the two assumptions about the ver-
tical velocity scale would yield the same result. In two
hemispheres with one of them nonconvecting, however,
L ø 2R, and thus the scaling containing the continuity
equation predicts that the two-hemisphere case will have
a broader thermocline and weaker vertical velocity,
whereas scaling containing the linear vorticity equation
predicts that the thermocline and vertical velocity will
be the same in the two cases.
We test the above scaling relationships with 2H (DT
N
5 0) and 1H experiments. In the 1H experiments, D }
Db
21/3
and w }Db
1/3
, as expected. Here, D is taken to
be the integral length scale of the zonal average tem-
perature at the equator,
00
D 5 zT dz T dz . (10)
EE
12@12
zz
00
In each run, water with temperature in the bottom 1%
of the temperature range for the water column is con-
sidered ‘subthermocline’ and is excluded from the cal-
culation. Here W is found by taking the maximum zonal
average vertical velocity at each latitude and averaging
this from latitudes 28 to 308S, which is much of the
region dominated by upwelling but excludes recircu-
lation close to the convection region. The total volume
transport of the meridional overturning cell is also
roughly proportional to Db
1/3
, though this scaling law
is closer to Db
1/2
for small Db because the upwelling
area decreases somewhat for smaller Db.
The maximum buoyancy difference between the east-
ern and western boundaries is approximately b
E
2 b
W
5 0.25Db for all 1H and 2H runs, confirming the the-
oretical result of Marotzke (1997) and the hypothesis
that the zonal buoyancy difference scales like Db. The
zonal buoyancy difference has a weak dependence on
L (2H runs have about a 20% smaller proportionality
constant). All these minor factors can be ignored in (9).
The factors of L
1/3
in (9) imply that, since 2
1/3
5 1.3,
each 2H run should have a 30% broader thermocline
and 30% weaker upwelling than the corresponding 1H
run. We measure the thermocline depth at the equator
as before, and average the maximum zonal average w
from 308Sto628N. The numerical experiments display
the relationship between 2H and 1H D and W predicted
by the scaling.
The combination of a somewhat weaker W and a larg-
er area of upwelling cause the total overturning volume
transport of the 2H experiments to be somewhat less
than double that of the 1H experiments: the scaling pre-
dicts a factor of 2
2/3
5 1.6, whereas actual values are
slightly higher (Table 2). Roughly equal amounts of
upwelling occur in both hemispheres. For DT
S
of 308C
and 68C, the convecting hemisphere has somewhat
greater upwelling than the nonconvecting hemisphere.
The western boundary current is stronger in this hemi-

Figures (17)
Citations
More filters

Journal ArticleDOI
Abstract: Because of its relevance for the global climate the Atlantic meridional overturning circulation (AMOC) has been a major research focus for many years. Yet the question of which physical mechanisms ultimately drive the AMOC, in the sense of providing its energy supply, remains a matter of controversy. Here we review both observational data and model results concerning the two main candidates: vertical mixing processes in the ocean's interior and wind-induced Ekman upwelling in the Southern Ocean. In distinction to the energy source we also discuss the role of surface heat and freshwater fluxes, which influence the volume transport of the meridional overturning circulation and shape its spatial circulation pattern without actually supplying energy to the overturning itself in steady state. We conclude that both wind-driven upwelling and vertical mixing are likely contributing to driving the observed circulation. To quantify their respective contributions, future research needs to address some open questions, which we outline.

574 citations


Cites result from "Behavior of Double-Hemisphere Therm..."

  • ...[116] Concerning the relative formation rates of NADW and AABW, it appears that they are anticorrelated in model experiments with variations in the buoyancy fluxes [Klinger and Marotzke, 1999]....

    [...]


Journal ArticleDOI
Abstract: The Modeling Eddies in the Southern Ocean (MESO) project uses numerical sensitivity studies to examine the role played by Southern Ocean winds and eddies in determining the density structure of the global ocean and the magnitude and structure of the global overturning circulation. A hemispheric isopycnal-coordinate ocean model (which avoids numerical diapycnal diffusion) with realistic geometry is run with idealized forcing at a range of resolutions from coarse (2°) to eddy-permitting (1/6°). A comparison of coarse resolutions with fine resolutions indicates that explicit eddies affect both the structure of the overturning and the response of the overturning to wind stress changes. While the presence of resolved eddies does not greatly affect the prevailing qualitative picture of the ocean circulation, it alters the overturning cells involving the Southern Ocean transformation of dense deep waters and light waters of subtropical origin into intermediate waters. With resolved eddies, the surface-t...

420 citations


Cites background from "Behavior of Double-Hemisphere Therm..."

  • ...In the picture of Bryan (1987), Klinger and Marotzke (1999), and Klinger et al. (2003) it is low-latitude diffusion that closes and drives the circulation....

    [...]


Journal ArticleDOI
Abstract: [1] We review teleconnections within the atmosphere and ocean, their dynamics and their role in coupled climate variability. We concentrate on teleconnections in the latitudinal direction, notably tropical-extratropical and interhemispheric interactions, and discuss the timescales of several teleconnection processes. The tropical impact on extratropical climate is accomplished mainly through the atmosphere. In particular, tropical Pacific sea surface temperature anomalies impact extratropical climate variability through stationary atmospheric waves and their interactions with midlatitude storm tracks. Changes in the extratropics can also impact the tropical climate through upper ocean subtropical cells at decadal and longer timescales. On the global scale the tropics and subtropics interact through the atmospheric Hadley circulation and the oceanic subtropical cell. The thermohaline circulation can provide an effective oceanic teleconnection for interhemispheric climate interactions.

343 citations


Cites background from "Behavior of Double-Hemisphere Therm..."

  • ...On the other hand, a slight asymmetry between the density forcings in the two poles can result in a dramatically asymmetric deep THC circulation [Klinger and Marotzke, 1999]....

    [...]


Journal ArticleDOI
Abstract: Variability of the thermohaline circulation (THC) has been analyzed in a long control simulation by the Met Office's Third Hadley Centre Coupled Ocean–Atmosphere General Circulation Model (HadCM3). It is shown that internal THC variability in the coupled climate system is concentrated at interannual and centennial time scales, with the centennial mode being dominant. Centennial oscillations of the THC can impact surface climate via an interhemispheric SST contrast of 0.1°C in the Tropics and more than 0.5°C in mid- and high latitudes. A mechanism is proposed based on detailed process analysis involving large-scale air–sea interaction on multidecadal time scales. Anomalous northward ocean heat transport associated with a strong phase of the Atlantic THC generates a cross-equatorial SST gradient. This causes the ITCZ to move to a more northerly position with increased strength. The extra rainfall resulting from the anomalous ITCZ imposes a freshwater flux and produces a salinity anomaly in the trop...

249 citations


Cites background from "Behavior of Double-Hemisphere Therm..."

  • ...Theoretical considerations (Marotzke 1997) and GCM experiments for idealized geometry (Klinger and Marotzke 1999) have shown that the maximum east–west density difference scales as the north–south surface density difference....

    [...]


Journal ArticleDOI
Abstract: [1] Oceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic models, up to and including oceanic and coupled ocean-atmosphere general circulation models. In this approach one follows the road from simple, highly symmetric model solutions, through a “bifurcation tree,” toward the observed, complex behavior of the system under investigation. The observed variability can be shown to have its roots in simple transitions from a circulation with high symmetry in space and regularity in time to circulations with successively lower symmetry in space and less regularity in time. This road of successive bifurcations leads through multiple equilibria to oscillatory and eventually chaotic solutions. Key features of this approach are illustrated in detail for simplified models of two basic problems of the ocean circulation. First, a barotropic model is used to capture major features of the wind-driven ocean circulation and of the changes in its behavior as wind stress increases. Second, a zonally averaged model is used to show how the thermohaline ocean circulation changes as buoyancy fluxes at the surface increase. For the wind-driven circulation, multiple separation patterns of a “Gulf-Stream like” eastward jet are obtained. These multiple equilibria are followed by subannual and interannual oscillations of the jet and of the entire basin's circulation. The multiple equilibria of the thermohaline circulation include deepwater formation near the equator, near either pole or both, as well as intermediate possibilities that bear some degree of resemblance to the currently observed Atlantic overturning pattern. Some of these multiple equilibria are subject, in turn, to oscillatory instabilities with timescales of decades, centuries, and millennia. Interdecadal and centennial oscillations are the ones of greatest interest in the current debate on global warming and on the relative roles of natural and anthropogenic variability in it. They involve the physics of the truly three-dimensional coupling between the wind-driven and thermohaline circulation. To arrive at this three-dimensional picture, the bifurcation tree is sketched out for increasingly complex models for both the wind-driven and the thermohaline circulation.

223 citations


References
More filters

Journal ArticleDOI
Abstract: A subgrid-scale form for mesoscale eddy mixing on isopycnal surfaces is proposed for use in non-eddy-resolving ocean circulation models. The mixing is applied in isopycnal coordinates to isopycnal layer thickness, or inverse density gradient, as well as to passive scalars, temperature and salinity. The transformation of these mixing forms to physical coordinates is also presented.

2,869 citations


"Behavior of Double-Hemisphere Therm..." refers background or methods in this paper

  • ...Some runs with restoring boundary conditions are also repeated with the ‘‘Gent– McWilliams’’ parameterization, which supplements isopycnal diffusion of T and S with additional advection by a tracer velocity representing the untilting of isopycnals by baroclinic instability (Gent and McWilliams 1990; Gent et al. 1995)....

    [...]

  • ...…boundary conditions are also repeated with the ‘‘Gent– McWilliams’’ parameterization, which supplements isopycnal diffusion of T and S with additional advection by a tracer velocity representing the untilting of isopycnals by baroclinic instability (Gent and McWilliams 1990; Gent et al. 1995)....

    [...]



Book
01 Feb 1992
Abstract: A review of our present understanding of the global climate system, consisting of the atmosphere, hydrosphere, cryosphere, lithosphere, and biosphere, and their complex interactions and feedbacks is given from the point of view of a physicist. This understanding is based both on real observations and on the results from numerical simulations. The main emphasis in this review is on the atmosphere and oceans. First, balance equations describing the large-scale climate and its evolution in time are derived from the basic thermohydrodynamic laws of classical physics. The observed atmosphere-ocean system is then described by showing how the balances of radiation, mass, angular momentum, water, and energy are maintained during present climatic conditions. Next, a hierarchy of mathematical models that successfully simulate various aspects of the climate is discussed, and examples are given of how three-dimensional general circulation models are being used to increase our understanding of the global climate "machine." Finally, the possible impact of human activities on climate is discussed, with main emphasis on likely future heating due to the release of carbon dioxide in the atmosphere.

2,287 citations


Journal ArticleDOI
Abstract: Physics of Climate is a suitable text for at least part of a general circulation course. The quantity and quality of information in this book are such that anyone involved in the study of the atmosphere or climate will wish to have it handy. In particular, anyone working with a general circulation model will want to see how his model compares with the observed world. Eight chapters are the core of the text. They cover: data description; observed states of the atmosphere, ocean, and cryosphere; exchanges between the atmosphere and the surface; and the budgets of water, angular momentum, and energy.

1,979 citations


"Behavior of Double-Hemisphere Therm..." refers background in this paper

  • ...8.8 and 8.10 in Peixoto and Oort (1992)], with winter northern North Atlantic water roughly 0.5 psu saltier than austral winter Weddell Sea water (Levitus and Boyer 1994)....

    [...]



Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "Behavior of double-hemisphere thermohaline flows in a single basin" ?

A coarse resolution, three-dimensional numerical model is used to study how external parameters control the existence and strength of equatorially asymmetric thermohaline overturning in a large-scale, rotating ocean basin.