EVAT 554
OCEAN-ATMOSPHERE
DYNAMICS
LECTURE 20
THERMOHALINE CIRCULATION
(CONTINUED)
Meridional Overturning Circulation
MORE REALISTIC MODEL
(Marotzke et al, 1988)
Assume the steady state
horizontal momentum balance
 fv  
1
ˆ a cos 
fu  
1
ˆ a
 p /   
 p /   
2
 u
V
z
2
2
 v
V
z
2
Zonally averaging across a
given basin yields,
 fv  
0
p ( )  p ( )
E
 ˆ a cos 
W
2

 u
V
z
0
2
2
fu  
0
1
ˆ a
 p /   
0
 v
V
z
0
2
Meridional Overturning Circulation
These can be combined to yield:
f
2v
0

2
V
v0
zzzz
p ( )  p ( )
 f
E
W
 ˆ a cos 
 p
V
0 yzz
Ignore explicit rotation, approximating
the meridional momentum equation as,
2
1
ˆ a
p /   A
 v
0
z
0
2
(Ad hoc “parameterization”)
We then have,
Av
 fv  
0
0 zzzz

p
0 yzz
p ( )  p ( )
E
 ˆ a cos 
W
2

 u
V
z
0
2
2
fu  
0
1
ˆ a
 p /   
0
 v
V
z
0
2
Meridional Overturning Circulation
These can be combined to yield:
f
2v
0

2
V
v0
zzzz
p ( )  p ( )
 f
E
W
 ˆ a cos 
 p
V
0 yzz
Ignore explicit rotation, approximating
the meridional momentum equation as,
2
1
ˆ a
p /   A
 v
0
z
0
2
(Ad hoc “parameterization”)
We then have,
Av
Av
0 zzzz
0 zzz

p

p
0 yzz
0 yz
Meridional Overturning Circulation
Invoke hydrostatic relationship
(will need convective adjustment!)
p
Av
v
0z
0 zzz
0 zzz
 
0
g
 0
 g
y
g  0

A y
Invoke linear equation of state
   (1   T   S )
0

v
0 zzz
Av

g 
A
0 zzz





p
T
y
0 yz

S
y






Meridional Overturning Circulation
Define “meridional overturning”
Streamfunction
 y w
0
 z  v

 zzzz

g 
A




T
y

0






S
y
Note that there is no time dependence
in this equation!
The time dependence comes from the
temperature and salinity equations

v
0 zzz

g 
A




T
y

S
y






Meridional Overturning Circulation
Define “meridional overturning”
Streamfunction
 y w
0
 z  v

 zzzz

g 
A




T
y

0
S
y






Note that there is no time dependence
in this equation!
The time dependence comes from the
temperature and salinity equations
2
 T / dt  v dT / dy  w dT / dz  k
0
0
0
0
0
 S / dt  v dS / dy  w dS / dz  k
0
0
0
0
0
 T
0
2
 [ qconv ]
0
2
 [ qconv ]
z
2
 S
z
The last term in each case represents explicit convective adjustment
Meridional Overturning Circulation
Define “meridional overturning” Impose Boundary Conditions
and integrate forward in time
Streamfunction
 y w
0
 z  v

 zzzz

g 
A




T
y

Equilibrate with restoring
surface boundary conditions
0
S
y






Note that there is no time dependence
in this equation!
The time dependence comes from the
temperature and salinity equations
2
 T / dt  v dT / dy  w dT / dz  k
0
0
0
0
0
 S / dt  v dS / dy  w dS / dz  k
0
0
0
0
0
 T
0
2
 [ qconv ]
0
2
 [ qconv ]
z
2
 S
z
kv T/z=K[T(y)- Ts]
kv S/z=K[S(y)- Ss]
Meridional Overturning Circulation
Define “meridional overturning” Impose Boundary Conditions
and integrate forward in time
Streamfunction
 y w
0
 z  v
Equilibrate with restoring
surface boundary conditions
0
kv T/z=K[T(y)- Ts]
kv S/z=K[S(y)- Ss]
Pole
Equator
Steady state circulation is
symmetric under these
boundary conditions
Pole
Meridional Overturning Circulation
Define “meridional overturning” Impose Boundary Conditions
and integrate forward in time
Streamfunction
 y w
0
 z  v
Switch over to mixed boundary
conditions
0
kv T/z=K[T(y)- Ts]
kv S/z=Q(y)
Pole
Equator
Pole
Symmetric circulation is unstable
with respect to infinitesimal
perturbations
Meridional Overturning Circulation
Even MORE realistic model
(Wright and Stocker, 1991)
Assume the steady state
horizontal momentum balance
 fv  
1
ˆ a cos 
fu  
1
ˆ a
 p /   
 p /   
2
 u
V
z
2
2
 v
V
z
2
Zonally averaging across a given
basin yields,
 fv  
0
p ( )  p ( )
E
 ˆ a cos 
W
2
 v
2

 u
V
z
0
2
fu  
0
1
ˆ a
 p /   
0
V
z
0
2
Meridional Overturning Circulation
Even MORE realistic model
(Wright and Stocker, 1991)
•More realistic parameterization
p ( )  p ( )  dp / d 
E
W
0
•Resolve individual basins
•Include surface windstress forcing
•Non-linear equation of state
•Equilibrate with mixed b.c.s
Zonally averaging across a given
basin yields,
 fv  
0
p ( )  p ( )
E
 ˆ a cos 
W
2
 v
2

 u
V
z
0
2
fu  
0
1
ˆ a
 p /   
0
V
z
0
2
Meridional Overturning Circulation
Even MORE realistic model
(Wright and Stocker, 1991)
•More realistic parameterization
p ( )  p ( )  dp / d 
E
W
0
•Resolve individual basins
•Include surface windstress forcing
•Non-linear equation of state
•Equilibrate with mixed b.c.s

Meridional Overturning Circulation
Even MORE realistic model
(Wright and Stocker, 1991)

Temperature
Salinity
Meridional Overturning Circulation
The most realistic ocean
model is the ocean general
circulation models (OGCM)
Some OGCMs support the
instability of the THC to future
climate change

OGCM

Meridional Overturning Circulation
Collapse of Thermohaline
Circulation in Response to
High-Latitude Freshening
Associated with High-latitude
Ice Melt

OGCM
Meridional Overturning Circulation
Possible “Ice Age” consequences?
Collapse of Thermohaline
Circulation in Response to
High-Latitude Freshening
Associated with High-latitude
Ice Melt

OGCM
Meridional Overturning Circulation
Possible “Ice Age” consequences?
Meridional Overturning Circulation
Possible “Ice Age” consequences?
2xC02
4xC02
GFDL COUPLED MODEL
Meridional Overturning Circulation
NORTH ATLANTIC OSCILLATION
For the
hemisphere on
the whole, the
warming or
cooling due to
the NAO is
probably a
zero-sum
game, but
regional
influences are
large
Explains enhanced warming in
certain regions of Northern
Hemisphere in past couple decades
Meridional Overturning Circulation
NORTH ATLANTIC OSCILLATION
North Atlantic Ocean and Atmosphere are Coupled
Meridional Overturning Circulation
NORTH ATLANTIC OSCILLATION
Positive NAO
implies increase
in THC
Heat Flux and Surface Wind
Anomalies Associated with
Positive Phase of “NAO”
Delworth, T.L., and Dixon, K.W., Implications of the Recent Trend in the Arctic/North Atlantic Oscillation for
the North Atlantic Thermohaline Circulation, Journal of Climate: Vol. 13, No. 21, pp. 37213727, 2001.
Meridional Overturning Circulation
NORTH ATLANTIC OSCILLATION
Positive NAO
implies increase
in THC
THC response to Imposed
NAO anomaly
Delworth, T.L., and Dixon, K.W., Implications of the Recent Trend in the Arctic/North Atlantic Oscillation for
the North Atlantic Thermohaline Circulation, Journal of Climate: Vol. 13, No. 21, pp. 37213727, 2001.