Modeling ice-sheets dynamics: forward and inverse problems

Large ice-sheets such as Greenland or Antarctica play a significant role in climatology and, in particular, in sea level rise. Ice-sheets behave like very viscous nonlinear fluids and can be modeled with highly nonlinear Stokes equations. The nonlinearities of the model, the large extension and complexity of the geometries and the lack of data make the problem very challenging from a mathematical and computational point of view.
In order to simulate the evolution of the ice-sheets and have an accurate prediction of the sea level rise, it is mandatory to know the current thermo-mechanical state (initial condition) of the system. Plenty of data about the current state of the ice-sheet on the surface (ice velocity, temperature, snow accumulation etc.) are available (e.g. from satellites). However, little is known about the thermo-mechanical state of the ice in the interior of the ice-sheet or at the interface between the ice-sheet and the bedrock.
In this talk, I give an overview of mathematical modeling of ice sheets and present some of the current challenges. Then, I present in more detail the inverse problem of estimating the parameters and the initial state of the ice-sheet. The inversion is performed using a large-scale PDE constrained optimization approach.