(2) What is sea ice? And why do we care?
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(2) What is sea ice? And why do we care?.
(3) What is sea ice? And why do we care?. Credit: Damien Ringeisen.
(4) What is sea ice? And why do we care?. Credit: National Snow and Ice Data Center.
(5) What is sea ice? And why do we care?. Large scale fracture event.
(6) What is sea ice? And why do we care?. Fractures influence: Heat exchanges Mass balance Dynamics. Important to model accurately. Credit: Nils Fuchs.
(7) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium. Credit: NASA.
(8) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium called ice floes. Credit: NASA.
(9) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium called ice floes. is a brittle recohesive material. Credit: Damien Ringeisen.
(10) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium called ice floes. is a brittle recohesive material Changing floe size. Credit: Damien Ringeisen.
(11) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium called ice floes. is a brittle recohesive material Changing floe size. grows and ridges/rafts Credit: Damien Ringeisen.
(12) Sea ice: Physical properties. Sea Ice . . . is 2D granular medium called ice floes. is a brittle recohesive material Changing floe size. grows and ridges/rafts Changing floes. Credit: Damien Ringeisen.
(13) Sea Ice models.
(14) Sea Ice models Bases in Elastic-Plastic (Coon et al., 1974) Viscous-Plastic Material (Hibler, 1979) Used in 30 of 33 models (Stroeve et al., 2014) 100 km → < 1 km Angles : Modeled 6= Observed (Hutter et al., 2018).
(15) Sea Ice models Bases in Elastic-Plastic (Coon et al., 1974) Viscous-Plastic Material (Hibler, 1979) Used in 30 of 33 models (Stroeve et al., 2014) 100 km → < 1 km Angles : Modeled 6= Observed (Hutter et al., 2018).
(16) Sea Ice models Bases in Elastic-Plastic (Coon et al., 1974) Viscous-Plastic Material (Hibler, 1979) Used in 30 of 33 models (Stroeve et al., 2014) 100 km → < 1 km Angles : Modeled 6= Observed (Hutter et al., 2018). ρh. ∂~u = −ρ h f ~k × ~u + ~τair + ~τocean − ρ h ∇φ(0) + ∇ · σ ∂t.
(17) Sea Ice models Bases in Elastic-Plastic (Coon et al., 1974) Viscous-Plastic Material (Hibler, 1979) Used in 30 of 33 models (Stroeve et al., 2014) 100 km → < 1 km Angles : Modeled 6= Observed (Hutter et al., 2018). ρh. ∂~u = −ρ h f ~k × ~u + ~τair + ~τocean − ρ h ∇φ(0) + ∇ · σ ∂t.
(18) Sea Ice models Bases in Elastic-Plastic (Coon et al., 1974) Viscous-Plastic Material (Hibler, 1979) Used in 30 of 33 models (Stroeve et al., 2014) 100 km → < 1 km Angles : Modeled 6= Observed (Hutter et al., 2018). ρh. ∂~u = −ρ h f ~k × ~u + ~τair + ~τocean − ρ h ∇φ(0) + ∇ · σ ∂t σij = 2η ε̇ij + (ζ − η) ε̇kk δij −. P δij 2.
(19) Sea ice model : Yield Curve σII a. P. e=. b. a b. Standard: P = 2.75 · 103 N m−1 and e = 2. σ1 σI. σ2.
(20) High resolution simulation. High resolution simulation.
(21) Idealized Experiment Prescribed Strain. Sea ice. 2θ. Open boundary. Open water. Shoreline. In MITgcm (Marshall et al., 1997; Losch et al., 2010) Uniform thickness h = 1 m Uniform concentration C = 100 %.
(22) Results: 45 min.
(23) Results: 45 min. Initial fracture : after 5 seconds.
(24) Results: Elliptical yield curve e = 0.7. σII. e=1 e=2 e=4 P. σ1 σI σ2.
(25) Results: Elliptical yield curve e = 0.7. σII. e=1 e=2 e=4 P. σ1 σI σ2.
(26) Results: Elliptical yield curve. θ|e=2 = 34◦.
(27) Results: Elliptical yield curve. θ|e=0.7 = 61◦.
(28) Results: Elliptical yield curve µ 70. 1. 0.9. 0.8. 0.7. 0.6. 0.5. Elliptical yield curve 60 50. θ. ◦. 40 30 20 10 0. 1. 2. 3. 4 e. 5. 6.
(29) Results: Coulombic yield curve σII µ P. σ1 σI. σ2.
(30) Results: Coulombic yield curve.
(31) Results: Coulombic yield curve µ 70. 1. 0.9. 0.8. 0.7. 0.6. 0.5. Elliptical Ellipticalyield yieldcurve curve Coulombic yield curve. 60 50. θ. ◦. 40 30 20 10 0. 1. 2. 3. 4 e. 5. 6.
(32) Mohr’s circle τ. σ.
(33) Mohr’s circle τ. φ. σ.
(34) Mohr’s circle τ σII γ σI. σ.
(35) Mohr’s circle τ σII γ φ σI. σ.
(36) Mohr’s circle τ σII γ φ. σ. σI. 1 1 1 θth,ell (e) = arccos 1− 2 2 2 e . . . ; θth,c (µ) =. 1 arccos(µ) 2.
(37) Fitting modelled angles µ 70. 1. 0.9. 0.8. 0.7. 0.6. 0.5. Elliptical Ellipticalyield yieldcurve curve θθth,ell th,ell Coulombic yield curve θth,c. 60 50. θ. ◦. 40 30 20 10 0. 1. 2. 3. 4 e. 5. 6.
(38) Summary. Elliptical yield curve : No Fracture angles below 30◦ More shear strength → increase angle. Coulombic yield curve Possibility of smaller angle No kink in the yield curve!. Linked fracture angle/yield curve.
(39) We need a new yield curve and flow rule to model sea ice at high resolution as a granular material with fracture angles that compare to observations.. More details in Ringeisen et al. 2019.
(40) And now what?! Surface forcing and Material properties test Sea ice models are different Surface forcing tests: The fracture angle is different than before Because of gradients of stress in the ice. New Yield curve Teardrop yield curve (Zhang and Rothrock, 2005) Implementation pending: Problems with the mathematical formulation.
(41) Surface forcing. Fracture with surface forcing.
(42) Resolution and scale.
(43) Confinement.
(44) Initial conditions.
(45) References I Coon, M. D., Maykut, A., G., Pritchard, R. S., Rothrock, D. A., and Thorndike, A. S. (1974). Modeling The Pack Ice as an Elastic-Plastic Material. AIDJEX BULLETIN, No. 24(Numerical Modeling Report):1–106. Hibler, W. D. (1979). A Dynamic Thermodynamic Sea Ice Model. Journal of Physical Oceanography, 9(4):815–846. Hutter, N., Zampieri, L., and Losch, M. (2018). Leads and ridges in Arctic sea ice from RGPS data and a new tracking algorithm. The Cryosphere Discussions, pages 1–27. Losch, M., Menemenlis, D., Campin, J.-M., Heimbach, P., and Hill, C. (2010). On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations. Ocean Modelling, 33(1–2):129–144..
(46) References II Marshall, J., Adcroft, A., Hill, C., Perelman, L., and Heisey, C. (1997). A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research: Oceans, 102(C3):5753–5766. Stroeve, J., Barrett, A., Serreze, M., and Schweiger, A. (2014). Using records from submarine, aircraft and satellites to evaluate climate model simulations of Arctic sea ice thickness. The Cryosphere, 8(5):1839–1854. Zhang, J. and Rothrock, D. A. (2005). Effect of sea ice rheology in numerical investigations of climate. Journal of Geophysical Research: Oceans, 110(C8):C08014..
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