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Periodic Fluctuations in Deep Water Formation Due to Sea Ice Raj Saha

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Periodic Fluctuations in Deep Water Formation Due to Sea Ice Raj Saha
Periodic Fluctuations in Deep Water Formation
Due to Sea Ice
Raj Saha
Mathematics and Climate Research Network, NSF
Bowdoin College, Department of Mathematics
Department of Physics & Astronomy, UNC Chapel Hill
Past Climate
100,000 year cycles
Abrupt warming, gradual cooling
Possibly due to large scale fluctuations in global
oceanic circulation
�2
��∆ 18 O �‰�� Benthic
�3
�4
�5
�6
�1.0
�0.8
�0.6
�0.4
Millions of Years
�0.2
0.0
Zachos et al. 2001
Past Climate
100,000 year cycles
Abrupt warming, gradual cooling
Possibly due to large scale fluctuations in global
oceanic circulation
�2
��∆ 18 O �‰�� Benthic
�3
�4
�5
�6
�1.0
�0.8
�0.6
�0.4
Millions of Years
�0.2
0.0
Zachos et al. 2001
Past Climate
100,000 year cycles
Abrupt warming, gradual cooling
Possibly due to large scale fluctuations in global
oceanic circulation
�2
��∆ 18 O �‰�� Benthic
�3
�4
�5
�6
�1.0
�0.8
�0.6
�0.4
Millions of Years
�0.2
0.0
Zachos et al. 2001
Past Climate
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
NGRIP
Past Climate
1,500 year cycles
Dansgaard-Oeschger (D-O) Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
NGRIP
Past Climate
1,500 year cycles
Abrupt warming, gradual cooling
Dansgaard-Oeschger (D-O) Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
NGRIP
Past Climate
1,500 year cycles
Abrupt warming, gradual cooling
Fluctuations most pronounced in the North Atlantic
Dansgaard-Oeschger (D-O) Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
NGRIP
Past Climate
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Quasi-periodic ice-sheet disintegration
Heinrich Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Quasi-periodic ice-sheet disintegration
Large amounts of freshwater dumped into the
North Atlantic
Heinrich Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Quasi-periodic ice-sheet disintegration
Large amounts of freshwater dumped into the
North Atlantic
Heinrich Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Quasi-periodic ice-sheet disintegration
Large amounts of freshwater dumped into the
North Atlantic
Heinrich Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Quasi-periodic ice-sheet disintegration
Large amounts of freshwater dumped into the
North Atlantic
Probable cause for abrupt shifts in ocean
circulation?
Heinrich Events
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Origin of the 1,500 year cycles? (external or internal?)
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
Past Climate
Origin of the 1,500 year cycles? (external or internal?)
Pattern of fluctuations between 50 kyr and 30 kyr
before present - How / Why?
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
a
1,500
1.5
3,000
3.0
4,500
4.5
6,000
6.0
3
Model Years ( x 10 )
7,500
7.5
D
Latitude (deg)
0.15 a
0.15
A
0.12
0.12
0.09
0.09
0.06
0.06
0.03
0.03
00
–0.03
-0.03
00
3
fwf
Ganopolski and Rahmstorf (2001)
9,000
9.0
0.5
0º N
EQ
4
–8
-8
–12
-12
-0.5
–1
-60º N
60S
–14
-14
–2
180W
180
120W
120W
30
30
60W
60W
0W
0
60E
60E
120E
120E
a
E
25
25
NADW (Sv)
NADW
(Sv)
-30º N
30S
180W
180
dB
–10
-10
0
-30º N
30S
0º N
EQ
2
Latitude (deg)
30º N
30N
1
20
20
15
15
10
10
180E
180
!"( o(°C)
C)
∆T
Latitude (deg)
9,000
9.0
6
30º N
30N
-60º N
60S
D
60º N
60N
60º N
60N
–16
-16
–18
-18
–5
–5.5
-5.5
–6
–6.5
-6.5
–7
–7.5
-7.5
e
C
00
1,500
1.5
3,000
3.0
4,500
4.5
6,000
6.0
3
Model
Years
Time
(yr)( x 10 )
7,500
7.5
NADW (Sv)
NADW
(Sv)
a
2
1
!F
∆Ffwf (Sv)
(Sv)
Leads to disruption in heat transport to
northern latitudes
9,000
9.0
55
–0.1
-0.1
00
!Ffwf (Sv)
0.1
0.1
0.2
0.2
)
00
–0.2
-0.2
9,000
9.0
)
,500
7.5
Freshwater from ‘purged’ ice sheets
destabilize circulation
Latitude (deg)
,500
7.5
The Freshwater Hypothesis
Other Proposed Mechanisms
Solar Influence?
Combination of two known solar cycles of 87 and 210
years
(Braun et al., 2005)
However, comparison of proxy records for the climate
and solar influence do not reveal a correlation
(Muscheler and Beer, 2006)
Oceanic Tidal Cycle?
1,800 year periodic variations in oceanic tides caused
by resonances in the orbits of Earth and Moon
(Keeling and Whorf, 2000)
However, there is a period mismatch
Internal Oceanic Mechanisms?
Several models produce fluctuations in the circulation
due to anomalies in polar sea surface salinity
(Winton and Sarachik, 1993; Sakai and Peltier, 1995;
Haarsma et al. 2001; de Verdiére et al. 2006)
However, the period of fluctuations are heavily
dependent on polar sea surface conditions
Questions
Origin of the 1,500 year cycles, pattern
Driven by external (astronomical) or internal (oceanic) mechanisms?
How are the D-O events connected to Heinrich events?
A Simple Dynamical Model
Goal:
A Simple Dynamical Model
Goal:
To examine the interaction between
circulation (deep water formation)
and sea ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
75º
1000 m
60º
6
5
5
1
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
1
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
75º
1000 m
60º
6
Tropical
5
5
1
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
1
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
6
5
5
1
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
1
75º
1000 m
60º
Subtropical
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
75º
1000 m
60º
6
5
5
1
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
Subpolar
1
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Polar
Sea-ice
75º
1000 m
60º
6
5
5
1
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
1
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
75º
1000 m
60º
6
5
5
1
Top Mixed Layer
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
45º
1
Sea-ice
A Simple Dynamical Model
Spatial Layout
75º
Sea-ice
75º
Sea-ice
1000 m
60º
45º
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
6
Bottom (Interior) Layer
5
1
5
1
A Simple Dynamical Model
Spatial Layout
Gildor and Tziperman (2001)
75º
Sea-ice
75º
Sea-ice
1000 m
60º
45º
8
7
2
6
3500 m
3
8
7
2
4
3500 m
45º
3
1000 m
60º
4
6
de Verdiére et. al. (2005)
5
1
5
1
A Simple Dynamical Model
Forcing
Applied Atmospheric Temperatures
Applied Surface Salinities
75º
+1
1000 m
60º
4
45º
6
-0.7
2
3
4
5
1
5
6
7
8
8
7
2
-0.2
1
3500 m
3
-0.1
Sea-ice
A Simple Dynamical Model
Physical Processes
!!!"!#!!!$%!!Surface pole-bound flow (Thermal)
TH
!!!&!#!!!$%!!Surface equator-bound flow (Haline)
SA
75º
60º
45º
!!
Sea Ice
!+1
!+2
1
!+1
3
2
!+w2
5
!+3
!+1
4
!+w3
6
!+2
7
!+3
8
!+3
Sea-ice
A Simple Dynamical Model
Physical Processes
Pressure driven circulation
!!!"!#!!!$%!!Surface pole-bound flow (Thermal)
TH
!!!&!#!!!$%!!Surface equator-bound flow (Haline)
SA
75º
60º
45º
!!
Sea Ice
!+1
!+2
1
!+1
3
2
!+w2
5
!+3
!+1
4
!+w3
6
!+2
7
!+3
8
!+3
Sea-ice
A Simple Dynamical Model
Physical Processes
Pressure driven circulation
!!!"!#!!!$%!!Surface pole-bound flow (Thermal)
TH
!!!&!#!!!$%!!Surface equator-bound flow (Haline)
SA
75º
60º
45º
Sea ice grows on the polar box
!!
Sea Ice
!+1
!+2
1
!+1
3
2
!+w2
5
!+3
!+1
4
!+w3
6
!+2
7
!+3
8
!+3
Sea-ice
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
Heat exchange with atmosphere
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
(salinity
forcing)due to thermal forcing and is given
Qi is the rate of heatEvaporation/Precipitation
transfer to the surface
layers
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi Advective
= Q̇i +transport
ρ0 Cp ψof
ρ0salt
Cp Di, j T j + Co(Ti ) + Q̇ice
i, j T
j +and
heat
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi,Diffusive
+ Co(T
j T j + ρtransport
0 Cp Di, j T
jheat
i ) + Q̇ice
of
and
salt
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j Convection
+ Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
Enthalpy of formation/melting
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Brine
rejection forcing and is given
Qi is the rate of heat transfer to the surface layers due to
thermal
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
ρ Lf
ρice is the density of ice and L f the latenticeheat
of fusion of ice.
A Simple
ρice is the density
ofDynamical
ice and L Model
f the latent heat of fusion of ice.
ning Equations
Governing Equations
ning Equations
overning equations describing the rates in change of temperature and salinity are
overning
equations describing the rates in change of temperature and salinity are
by
by
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
(3.30)
mi Cp Ṫi = Q̇i + ρ0 Cp ψi, j T j + ρ0 Cp Di, j T j + Co(Ti ) + Q̇ice
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.30)
(3.31)
mi Ṡi = ξi + ρ0 ψi, j S j + ρ0 Di, j S j + Co(Si ) + S0 Ḃ
(3.31)
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
Qi is the rate of heat transfer to the surface layers due to thermal forcing and is given
� �γ
�
�
ice
Q̇i = λ(Γi − Ti )� fice �
− 1� + 1�Ai + (−Le εA1 )
(3.32)
dice
γ
ice
Q̇i = λ(Γi − Ti ) fice
− 1 + 1 Ai + (−Le εA1 )
(3.32)
dice
λ is the heat exchange coefficient between
atmosphere and ocean, fice is the fraction
λ is
the heat
exchange
atmosphere
and ocean,
fice is the
fraction
ar
surface
area
coveredcoefficient
by sea ice,between
γ the heat
permeability
(insulation)
parameter,
Solutions
Circulation States
Haline
Oscillatory
Thermal
3
3
2
2
1
1
1
0
0
0
�1
�1
�1
Tropical E�P �Μ1 � ��10112kg �s�
4
"#$%&'($%)*+,-).!
!/)0-)!1 )3 567
3
SA
2
�2
0
500
1000
Model Years
1500
�2
0
500
1000
Model Years
1500
�2
0
TH
500
1000
Model Years
1500
Solutions
Domain of States
Oscillations
TH
SA
Solutions
Domain of States
No Sea Ice
TH
SA
Phase-space Trajectories of Advective Fluxes
!!
!4
!+1
!+2
1
!+1
5
!+3
3
2
!+w2
!+1
Sea Ice
4
!+w3
6
!+2
7
!+3
8
!+3
Phase-space Trajectories of Advective Fluxes
Phase-space Trajectories of Advective Fluxes (several initial states)
'()*+,-.!/012,3+12!4.56!7!!8!
96!:#2!;4<=>
With Sea Ice
With Sea ice: !min
?).-(!/012,3+12!4.56!7!48!
96!:#2!;4<=>
Phase-space Trajectories of Advective Fluxes (several initial states)
'()*+,-.!/012,3+12!4.56!7!!8!
96!:#2!;4<=>
No Sea Ice
With Sea ice: !min
?).-(!/012,3+12!4.56!7!48!
96!:#2!;4<=>
Solutions
Oscillation Periods: Relative Strength of Thermal to Salinity Forcing
Periods between 200 and 4,000 years
4000
Scale with ε/η
Depends on the rate of build up
and eradication of instabilities
Period �years�
3000
2000
1000
�0.015
�0.014
�0.013
Ε�Η
�0.012
�0.011
Solutions
Oscillation Periods: Geometry
Larger polar volume increases effective heat capacity of the system
Periods get longer with volume (heat capacity)
Since geometry is invariant, it can produce a persistent period
30
35
@A2)B!#[email protected]
FG#!H2-(=
Number of Instances �Frequency�
Number of Instances �Frequency�
35
25
20
15
10
5
0
0
@A2)[email protected]
30
25
20
IG#!H2-(=
15
10
5
500
Period �years�
1000
1500
2000
2500
3000
0
0
500
Period �years�
1000
1500
2000
2500
3000
Solutions
Animation
Mechanism of Oscillations
Atmosphere
Sea Ice
Insulating effect
3
Y3,4
"8
4
D3,4
Brine rejection
Y4,8
Heat exchanges from formation / melting
7
Y7,8
D7,8
D4,8
8
Convection
Mechanism of Oscillations
γ
Ḃ
Q̇ice
Oscillations
I
0
0
0
0
II
0
0
1
0
Insulating effect
III
0
1
0
0
Brine rejection
IV
0
1
1
0
V
1
0
0
1
VI
1
0
1
1
VII
1
1
0
1
VIII
1
1
1
1
Heat exchanges from formation / melting
Insulating effect is key to
oscillations in this system
Table 3.2: The three direct effects of sea ice, insulation (γ), brine rejecti
enthalpies of formation (Q̇ice ) are systematically switched on and off to
influence. Oscillations appear only when insulation is on, and for values
ability coefficient, γ < 0.7.
Mechanism of Oscillations
JK=5.-3+)K!LK.H!7,[email protected]
M)!JK=5.-3+)K!7,[email protected]
Insulating effect is key to
oscillations in this system
Mechanism of Oscillations
Advective Flux
Mechanism of Oscillations
Advective Flux
Mechanism of Oscillations
Advective Flux
Mechanism of Oscillations
Advective Flux
Heat Loss to Atmosphere
Mechanism of Oscillations
Advective Flux
Vertical Instability
Mechanism of Oscillations
Advective Flux
Start of Convection
Mechanism of Oscillations
Large heat loss from the polar surface ocean during sea ice retreats cool
the water, making it more dense and creating conditions for convection
Glacial Freshwater Scenario
Ice sheet growth and decay
Applied Atmospheric Temperatures
Increased tropical (global) evaporation
Increased freshwater anomalies at
high North Atlantic latitudes due
to ice sheet runoffs
Applied Surface Salinities
+1
-0.1
-0.2
-0.7
1
2
3
4
5
6
7
8
Glacial Freshwater Scenario: Ice Sheet Growth / Disintegration
Ice sheet growth and decay
Increased tropical (global) evaporation
Salinity Forcing ��107 kg �s�
5
0
�5
�10
�15
0
5000
10 000
Model Years
vective Flux �Μ1 � ��1011 kg �s�
Increased freshwater anomalies at
high North Atlantic latitudes due
to ice sheet runoffs
2.0
1.5
1.0
0.5
0.0
Glacial Freshwater Scenario: Ice Sheet Growth / Disintegration
Ice sheet growth and decay
7
Salinity Forcing
kg �s�
Salinity ��10
Forcing
��107 kg �s�
5
Increased tropical (global) evaporation
�5
0
�10
�5
�15
�10
0
5000
10 000
Model Years
�15
11
Tropical Advective
Flux �Μ1 � ��10
�s� 11
Tropical Advective
Flux �Μkg
1 � ��10 kg �s�
Increased freshwater anomalies at
high North Atlantic latitudes due
to ice sheet runoffs
50
0
5000
10 000
Model Years
2.0
1.5
2.0
1.0
1.5
0.5
1.0
0.0
0.5
�0.5
0.0
0
5000
�0.5
10 000
Model Years
0
5000
10 000
Observation and Model
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
�46
�100
�80
�60
�40
Kilo Years Before Present
¡ Model !
�20
0
Observation and Model
�34
∆ 18 O �‰� NGRIP
�36
�38
�40
�42
�44
65º N
Summer Insolation
�46
�100
�80
�60
�40
Kilo Years Before Present
�20
0
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice max
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice min
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Ice sheet growth phase
Sea ice / AMOC oscillations
Summer melting
A Cartoon of the Ice Sheet Cycles and D-O events
Sea ice / AMOC oscillations
Heinrich Event
Animated Cartoon
Animated Cartoon
Conclusion
Conclusion
Conclusion
Sea Ice initiates oscillations of the circulation
Conclusion
Sea Ice initiates oscillations of the circulation
Period of oscillations tied to geometry of the
system, hence robust
Conclusion
Sea Ice initiates oscillations of the circulation
Period of oscillations tied to geometry of the
system, hence robust
Ice sheet growth/decay cycles produced
observed D-O patterns
Conclusion
Sea Ice initiates oscillations of the circulation
Period of oscillations tied to geometry of the
system, hence robust
Ice sheet growth/decay cycles produced
observed D-O patterns
Weak (and therefore unstable) overturning circulation
during glacial periods
Freshwater anomalies could have triggered state
changes
In addition to freshwater, insolation variations can also
trigger abrupt state changes in the overturning
circulation, especially during early glacial periods
Sea ice may also serve as a similar trigger for glacialinterglacial cycles (Gildor and Tziperman, 2001)
Future Work
Carbon Storage in the Ocean: Dr. Irina Marinov, UPenn
Glacial - Interglacial Cycles
Interglacial Circulation
CO2
Unstable stratification
Small Sea Ice Extent
NADW
AABW
N
S
Gildor ,Tziperman, Toggweiler (2002)
Carbon Storage in the Ocean: Dr. Irina Marinov, UPenn
Glacial - Interglacial Cycles
Glacial Circulation
CO2
Stable stratification
Large Sea Ice Extent
NADW
AABW
N
S
Gildor ,Tziperman, Toggweiler (2002)
Reduction to Stommel: Andrew Roberts, UNC-Chapel Hill
Adding deep boxes and Sea ice to Stommel’s 2 box model
Equatorial
Polar
Acknowledgements
Chris Jones
John Bane
Pam Martin
Mary Lou Zeeman
Dorian Abbot
Ray Pierrehumbert
Mary Silber
Richard McGehee
Val Tenyotkin
Hassan Hatam
Thank You
Questions?
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