Ice flow models are based on a continuum mechanical approach and hence solve equations for the balance of mass, momentum and energy or enthalpy. The equations are closed with constitutive relations, in our case a flow law for ice that describes the viscous deformation behavior of polycrystalline ice. The resulting fields for ice velocities, temperature and thickness are hence the solutions of boundary value problems.

The numerical models discretize the mathematical equations either using finite differences or finite elements and with this the choice of the numerical mesh is done. Finite elements are ideal for natural geometries like margins of ice sheets, as they use unstructured grids, while structured grids and finite differences obtain a regional refinement via nesting.

The ice flow models that are applied are partly own development, like TIMFD3 and COMice, while others are international community models like PISMISSM and SICOPOLIS. To date, the ice flow models are often limited by computational costs and an adequate resolution is still a challenge.

Particular challenges are the migration of the grounding line, the transition between inland ice and floating ice shelves, the evolution of calving fronts and the evolution of subglacial water channels beneath the ice streams. This requires often also development of concepts for theoretical descriptions of processes, which are subsequently turned into numerical models.

Ice modeling benefits highly from the concepts of other disciplines, ranging from solid mechanics, fluid mechanics to applied mathematics and is incorporated in a interdisciplinary field due to the interaction with ocean and atmosphere.

Unstructured Finite Element mesh of the Greenland ice sheet. (Graphic: Thomas Kleiner, Alfred-Wegener-Institut)