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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.