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EVAT 554OCEAN-ATMOSPHERE
DYNAMICS
THERMOHALINE CIRCULATION (CONTINUED)
LECTURE 20
Meridional Overturning Circulation
MORE REALISTIC MODEL (Marotzke et al, 1988)
2
2v/ˆ1u
zp
af V
2
2/
cosˆ1v
z
upa
f V
Assume the steady state horizontal momentum balance
20
2
00
v/
ˆ1u
zp
af V
Zonally averaging across a given basin yields,
20
2
0
u
cosˆ
)()(v
za
ppf V
WE
Meridional Overturning Circulation
These can be combined to yield:
yzzWE p
a
ppff VV
zzzz 002
02
cosˆ
)()(vv
20
2
00
v/
ˆ1u
zp
af V
20
2
0
u
cosˆ
)()(v
za
ppf V
WE
Ignore explicit rotation, approximating the meridional momentum equation as,
(Ad hoc “parameterization”)
20
2
0
v/
ˆ1
zAp
a
yzzzzzzpA
00v
We then have,
Meridional Overturning Circulation
These can be combined to yield:
yzzWE p
a
ppff VV
zzzz 002
02
cosˆ
)()(vv
Ignore explicit rotation, approximating the meridional momentum equation as,
(Ad hoc “parameterization”)
20
2
0
v/
ˆ1
zAp
a
yzzzzzzpA
00v
We then have,
yzzzzpA
00v
Meridional Overturning Circulation
yzzzzpA
00v
Invoke hydrostatic relationship (will need convective adjustment!)
gpz 00
ygA
0
0zzzv
)1(0
ST
Invoke linear equation of state
yS
yT
Ag
zzz0v
yAg
0
0zzzv
Meridional Overturning Circulation
yS
yT
Ag
zzz0v
Define “meridional overturning” Streamfunction
0vz
0wy
yS
yT
Ag
zzzz
Note that there is no time dependence in this equation!
The time dependence comes from the temperature and salinity equations
Meridional Overturning Circulation
Define “meridional overturning” Streamfunction
0vz
0wy
yS
yT
Ag
zzzz
Note that there is no time dependence in this equation!
The time dependence comes from the temperature and salinity equations
]conv[//v/20
2
00000q
z
TkdzdTwdydTdtT
]conv[//v/20
2
00000q
z
SkdzdSwdydSdtS
The last term in each case represents explicit convective adjustment
Meridional Overturning Circulation
Define “meridional overturning” Streamfunction
0vz
0wy
yS
yT
Ag
zzzz
Note that there is no time dependence in this equation!
The time dependence comes from the temperature and salinity equations
Impose Boundary Conditions and integrate forward in time
Equilibrate with restoring surface boundary conditions
v T/z=K[T(y)- Ts]
v S/z=K[S(y)- Ss]
]conv[//v/20
2
00000q
z
TkdzdTwdydTdtT
]conv[//v/20
2
00000q
z
SkdzdSwdydSdtS
Meridional Overturning Circulation
Define “meridional overturning” Streamfunction
0vz
0wy
Impose Boundary Conditions and integrate forward in time
Equilibrate with restoring surface boundary conditions
v T/z=K[T(y)- Ts]
v S/z=K[S(y)- Ss]
Steady state circulation is symmetric under these
boundary conditions
Pole Equator Pole
Meridional Overturning Circulation
Define “meridional overturning” Streamfunction
0vz
0wy
Impose Boundary Conditions and integrate forward in time
Switch over to mixed boundary conditions
v T/z=K[T(y)- Ts]
Pole Equator Pole
v S/z=Q(y)
Symmetric circulation is unstable with respect to infinitesimal
perturbations
Meridional Overturning Circulation
2
2v/ˆ1u
zp
af V
2
2/
cosˆ1v
z
upa
f V
Assume the steady state horizontal momentum balance
20
2
00
v/
ˆ1u
zp
af V
20
2
0
u
cosˆ
)()(v
za
ppf V
WE
Zonally averaging across a given basin yields,
Even MORE realistic model (Wright and Stocker, 1991)
Meridional Overturning Circulation
Even MORE realistic model (Wright and Stocker, 1991)
•More realistic parameterization ddppp
WE/)()(
0
•Resolve individual basins
•Include surface windstress forcing
•Non-linear equation of state
•Equilibrate with mixed b.c.s
20
2
00
v/
ˆ1u
zp
af V
20
2
0
u
cosˆ
)()(v
za
ppf V
WE
Zonally averaging across a given basin yields,
Meridional Overturning Circulation
Even MORE realistic model (Wright and Stocker, 1991)
•More realistic parameterization ddppp
WE/)()(
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 CirculationThe most realistic ocean
model is the ocean general circulation models (OGCM)
OGCM
Some OGCMs support the instability of the THC to future climate change
Meridional Overturning Circulation
OGCM
Collapse of Thermohaline Circulation in Response to High-Latitude Freshening
Associated with High-latitude Ice Melt
Meridional Overturning Circulation
Collapse of Thermohaline Circulation in Response to High-Latitude Freshening
Associated with High-latitude Ice Melt
OGCM
Possible “Ice Age” consequences?
Meridional Overturning CirculationPossible “Ice Age” consequences?
Meridional Overturning CirculationPossible “Ice Age” consequences?
2xC02
GFDL COUPLED MODEL
4xC02
Explains enhanced warming in certain regions of Northern Hemisphere in past couple decades
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
NORTH ATLANTIC OSCILLATIONMeridional Overturning Circulation
Meridional Overturning CirculationNORTH ATLANTIC OSCILLATION
North Atlantic Ocean and Atmosphere are Coupled
Meridional Overturning CirculationNORTH 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. 3721 3727, 2001.
Meridional Overturning CirculationNORTH ATLANTIC OSCILLATION
Positive NAO implies increase
in THC
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. 3721 3727, 2001.
THC response to Imposed NAO anomaly