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A.V. Wilchinsky, D.L. Feltham & P.A. Miller
CPOM, UCL
A multi-thickness sea ice model A multi-thickness sea ice model accounting for sliding frictionaccounting for sliding friction
Talk structure
I.I. BackgroundBackground
II. Develop an improved model of multi-layer II. Develop an improved model of multi-layer sea ice dynamics using latest theorysea ice dynamics using latest theory
III. Incorporate it into the CICE codeIII. Incorporate it into the CICE code
IV. Simulate the ArcticIV. Simulate the Arctic
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Different floe thickness
Ice thickness distribution function g(h)
Fraction of floes of thicknesses, h, is described by g(h)
During deformation only ≈15% sea ice ridges
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1. Pressure ridging: Frictional motion of piling ice
blocks
2. Inter-floe frictional sliding
Sea ice stress contributions:Sea ice stress contributions:
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Yield curve grows (hardens) or shrinks (weakens) if the ice thickness increases or decreases.
>
Yield curveYield curve
-20(1- )AP heMean thick ice thickness
Thick ice concentration
In two layer model (thick ice + thin ice) sea ice strength is approximated
Ice strength
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II. Develop an improved model of multi-layer II. Develop an improved model of multi-layer sea ice dynamics using latest theorysea ice dynamics using latest theory
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In modern multi-layer modelsIn modern multi-layer models (Flato & Hibler, 1995):
2P h dh Ridging mode (loss+gain)
In realityIn reality (discrete simulation results; Hopkins, 1998):
Ridge thickness =>1/ 2h
Ridging Strength Potential energy change
3/ 2P h dh Ridging rate (loss)
Ridging Strength Friction in ridge piling up
Sea Ice Strength
70 25 50 75 10 0 12 5 1 5 0 1 7 5
0
0 .2
0 .4
0 .6
0 .8
1
s
r
r, a s
In modern multi-layer modelsIn modern multi-layer models (Flato & Hibler, 1995):
In realityIn reality (simulation result, Ukita & Moritz, 2000):
Their ratio is parameterized. No sliding in pure convergence.
It depends on deformation pattern:P
ure
dive
rgen
ce
She
ar
Pur
e co
nver
genc
e
Div
erge
nce=
She
ar
Con
verg
ence
=S
hear
Ridging work contributionSliding work contribution
Ridging and Sliding Work
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Incorporating more “reality” into sea ice models
- Use the law for the ridging ice strength3/ 2h
- Use the ridging and sliding strain-rate modes found by Ukita and Moritz for uniform thickness
- Account for the thickness difference by making use of sliding and opening participation functions that say that more sliding and opening occur in thinner ice.
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Derived sea ice stress
- 1 - 0 .8 - 0 .6 - 0 .4 - 0 .2 0
0
0 .0 5
0 .1
0 .1 5
0 .2
0 .2 5
0 .3
0 .3 5
I
II
R idg ing on ly S lid in g o n ly
a =0 s
a =0 r
( ) 1 ( ) ( ) ( )o r o r s sP P P P σ ε σ ε σ εOpening strength Ridging strength Sliding strength
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Normalised yield curves for regions A and B (Wadhams, 1992)
Composite yield curve shape
For submarine-measured ice thickness distribution:k = importance of sliding to ridging
Smoothed ice thickness distribution for regions A and B (Wadhams, 1992)
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III. Incorporate it into the CICE III. Incorporate it into the CICE codecode
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Incorporation into the Elastic Viscous Plastic model
21( , )ij
ij ijij
e ft T
ε
EVP model is tied to Hibler’s rheology through and e
General plastic rheology form, including our new model:
*( , ) ( , )I II I II σ ε ε 1 ε ε ε
Modified EVP model for general rheology:
*( , ) ( , )I II I IITt
σ
σ ε ε 1 ε ε ε
Ellipse aspect ratio
Relaxation time
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Modification in the CICE code components
New Rheology
New Ridging Rate(determined by ridging mode)
New Ice Strengths for ridging, sliding and opening
Ice thicknessEvolution
Ice Dynamics
Ice Thermodynamics
NEWNEW AFFECTEDAFFECTED
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IV. Simulate the ArcticIV. Simulate the Arctic
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3/ 2
0
2
0
20(1 )
( )
( )
r
Rr
H Cr
P h h dh
P h h dh
P H e
Used ridging strengths
Present:
Rothrock:
Hibler:
Mean thickness
Ice concentration
2.718281828459045235
Area loss
Area gain - loss
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Tuning
Comparison of the mean ice thickness in the Arcticgiven by the PRESENT and CICE model with the ERS derived. ERA-40 wind forcing data.
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The observed ice draft (m) along eight submarine cruise tracks from 1987 to 1997.
Comparisons with submarineice drafts.
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1.5
2
2.5
3
3.5
73 75 77 79 81 83 85 87 89
Latitude
Ice
draf
t (m
)
Observation (Present, Present)
(Present, Hibler) (Hibler, Hibler)
Mean ice thickness along submarinecruises. 1. Comparison with data.
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1.5
2
2.5
3
3.5
73 75 77 79 81 83 85 87 89
Latitude
Ice
draf
t (m
)
Observation (Present, Hibler)
(Hibler, Hibler) Paul's
Mean ice thickness along submarinecruises. 2. Comparison with Paul’s model
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1.5
2
2.5
3
3.5
73 75 77 79 81 83 85 87 89
Latitude
Ice
draf
t (m
)
Observations
(Hibler, Hibler)
(Present, Hibler), k=0.2
(Present less shear, Hibler), k=0.2
Mean ice thickness along submarinecruises. 3. Shear stress effect.
Maximum shear stress
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Results
I. A new isotropic model has been developed and incorporated into CICE that includes
1. More realistic plastic strength of multi-layer sea ice.
2. More realistic ridging rate.
II. Ice thickness distribution is better than CICE-produced, worse than given by Paul’s model.
III. Improvement due to a better ridging rate expression.
Further work
• Issues with multi-layer ice strengths (e.g. Rothrock’s)
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Energy partitions given by Ukita and Moritz’s kinematic model and Hopkins’ dynamic one.
Sliding strength
Ps*=k Pr
*
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Areal fraction of mean ice thickness. Present rheology. ERS covered area.
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Areal fraction of mean ice thickness. Hibler’s rheology. ERS covered area.
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1.5
2
2.5
3
3.5
1 2 3 4 5 6 7 8 9
Latitude
Ice
draf
t (m
)
(Present, Present) (Present, Hibler)
(Hibler, Hibler) (Hibler, Rothrock)
Mean ice thickness along submarinecrusies. 1. Ridging strength effect.