Sea ice has an important effect on global climate by reducing the heat transfer between the atmosphere and ocean and by reflecting incoming solar radiation. Additionally, sea ice can be an important navigational concern. For both of these reasons accurate and efficient models for sea ice are required. Current models have a number of limitations. In particular, the constitutive models used generally treat ice as isotropic when in fact the main observational features of ice are anisotropic leads and ridges. Also, the equations are typically solved using Eulerian methods that generate numerical errors when solving the transport equations for sea ice parameters related to ice thickness. To address these limitations the approach advocated here is to use an elastic-decohesive constitutive model for the ice and solve with the material-point method (MPM). MPM is a numerical method that uses two descriptions of the continuum to combine the best features of Lagrangian and Eulerian methods. Unconnected Lagrangian material points carry mass, velocity, stress, and other internal variables throughout the calculation. The material points model advection naturally, allow the determination of a sharp ice boundary, and can handle large deformations. The momentum equation is solved on a background grid to keep the computational work linear in the number of material points. The elastic-decohesive constitutive model is an anisotropic model that allows for explicit representation of leads in the sea ice. This is combined with an energy conserving thermodynamic model and an ice thickness distribution for a complete sea ice model. Calculations of ice deformation for a region in the Beaufort Sea are used to illustrate the model.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Howard Linn Schreyer
Third Committee Member
Fourth Committee Member
National Science Foundation, grant DMS-0222253 UNM Dean's Dissertation Fellowship
Sea ice--Arctic Regions--Mathematical models, Ocean-atmosphere interaction--Arctic regions--Mathematical models, Material point method, Sea ice--Beaufort Sea--Mathematical models.
Peterson, Kara. "Modeling Arctic sea ice using the material-point method and an elastic-decohesive rheology." (2009). https://digitalrepository.unm.edu/math_etds/40