Arctic Sea Ice Modeling with
MPM
MPM Workshop
18 March 2008
K. Peterson1
D. Sulsky1
H. Schreyer2
1Department
of Mathematics and Statistics
2Department of Mechanical Engineering
University of New Mexico
1
Outline
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Background
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Components of Sea Ice Model
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Motivation – Why Sea Ice?
Satellite Data
Goal
Momentum equation
Constitutive model
Ice thickness distribution
Thermodynamics
Numerical Implementation - MPM
Satellite Data Based Kinematics
Beaufort Sea Calculations
Conclusions
2
Sea Ice Model Uses
„
Climate Modeling
science.hq.nasa.gov
„
Forecasting
www.climateprogress.org
„
Ice Structure Interactions
www.sandwell.com
3
Satellite Data
RADARSAT Geophysical Processor System
(RGPS)
*Kwok, R., D. A. Rothrock, H. L. Stern and G. F. Cunningham, Determination of Ice Age using Lagrangian 4
Observations of Ice Motion, IEEE Trans. Geosci. Remote Sens., Vol. 33, No. 2, pp. 392-400, 1995.
Goal
Want a numerically efficient sea ice model that includes
observational features such as leads and ridges and
uses available satellite data for verification
„
„
Lead
Ridge
Existing Sea Ice Models
„ Isotropic constitutive model
„ Generally use Eulerian
numerical schemes
Our Model
„ Anisotropic constitutive
model
„ Lagrangian material points
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Components of Sea Ice Model
Atmospheric Fluxes
Air Drag
Ice Thickness
Ocean Flux
2-D Dynamics
Momentum Balance
Ocean Drag
1-D Thermo
Constitutive Model
Flux Balance
Ice Thickness
Distribution
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Momentum Equation
= ice density
= ice thickness
= ice velocity
= stress tensor
= air drag
= water drag
= Coriolis parameter
7
Elastic-Decohesive Constitutive Model
Strain Rate
Elasticity
Failure Function
Decohesion
Flow Rules
- normal traction
- tangential traction
Schreyer, H., L. Monday, D. Sulsky, M. Coon, R. Kwok (2006), Elastic-decohesive Constitutive
Model for Sea Ice, J. of Geophys. Res., 111, C11S26, doi:10.1029/2005JC003334.
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Ice Thickness Distribution
= thickness distribution
= ice region area
= ice area with thickness
less than at time
Evolution Equation
= growth rate
= mechanical redistribution
(ridging)
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Ridging Function
thickness distribution of ice participating in ridging:
thickness distribution of newly ridged ice:
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Thermodynamics
Balance of Fluxes
Top
snow
ice
water
Bottom
Snow/Ice Interface
Diffusion
=
=
=
=
=
=
=
thickness
temperature
energy of melting at top
energy of melting at bottom
heat capacity
conductivity
extinction coefficient
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MPM for Sea Ice
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Ice Thickness Distribution in MPM
Discrete ice thickness categories
Solve in three pieces
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Horizontal Transport
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Transport in Thickness Space
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Redistribution
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Kinematics
No Cutoff
400 m Cutoff
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Beaufort Sea Calculations
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Using RGPS data for 23 Feb –
10 Mar 2004 in Beaufort Sea
region
Calculation setup
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10 km square background grid
4 material points per cell
Rigid material points for land
boundary
Including wind, ocean, and
Coriolis forces
Boundary conditions are RGPS
velocities linearly interpolated in
time
RGPS data used to initialize
leads in calculation
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Beaufort Sea Calculations
Initialization Day 54 (Feb 23)
Crack Orientations, days:536−547, u0=0.2km
700
600
500
400
300
200
100
0
−100
−200
−2300 −2200 −2100 −2000 −1900 −1800 −1700 −1600
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Beaufort Sea Calculations
Leads Day 70 (March 11)
MPM
Kinematics
Crack Orientations, days:696−707, u0=1.5km
MPM Crack pattern, day70, u0=0.4km, cutoff=1.5km
700
700
600
600
500
500
400
400
300
300
200
200
100
100
0
0
−100
−100
−200
−200
−2300 −2200 −2100 −2000 −1900 −1800 −1700 −1600
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−2300 −2200 −2100 −2000 −1900 −1800 −1700 −1600
Beaufort Sea Calculations
Det (F) Day 70 (March 11)
MPM
Kinematics
MPM detF, day70
detF, days:696−707
1.5
700
1.5
700
1.4
600
1.4
600
1.3
500
1.3
500
1.2
400
1.2
400
1.1
300
1.1
300
1
200
1
200
0.9
0.9
100
100
0.8
0.8
0
0
0.7
0.7
−100
−100
0.6
0.6
−200
−200
−2300 −2200 −2100 −2000 −1900 −1800 −1700 −1600
0.5
0.5
−2300 −2200 −2100 −2000 −1900 −1800 −1700 −1600
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Conclusions
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Have shown sea ice model using MPM
with Elastic-Decohesive constitutive model
Advantages over other models
MPM handles advection naturally
„ Elastic-Decohesive Model allows explicit
calculation of lead evolution
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Currently implementing ice thickness
distribution
Future work
Implement thermodynamic model
„ Connect to ocean and atmospheric models
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Acknowledgments
„
Prof. Deborah Sulsky
„
„
UNM Dept. of Mathematics and Statistics
Prof. Howard Schreyer
„
UNM Dept. of Mechanical Engineering
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www.jupiterimages.com
This work has been supported
by the NSF under Grant No.
DMS-0222253
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