An optimization approach to modeling sea ice dynamics, part 2; Finite ice strength effects

The effects of a finite ice strength on a new model for sea ice dynamics, deriving the internal pressure field from a global optimization problem, rather than a local rheology, are examined. Building on the promising results from the one-dimensional Lagrangian model described previously, here we add one of the key properties of sea ice. In order to investigate the behavior of the model under ice yielding, the equations are cast in an Eulerian framework, now allowing for variable thickness. The model is first tested under conditions of infinite ice strength, to ensure that the numerics behave as desired. A finite ice strength is incorporated into the model as a second optimization step, minimizing the change in ice thickness necessary to satisfy the upper bound on the pressure, whereby ice strength is taken to be a linear function of thickness, following typical parameterizations in the literature. The theory is implemented numerically, and several test cases are discussed, which show good agreement with physically based expectations.