Modelling of the polar ice sheets is important to reconstruct its past, understand its current state and predict its evolution in the context of the global warming and rising sea levels. There are numerous mechanisms involved in the dynamics of ice sheets and these are climate-dependent. In particular there are two very important opposing mechanisms: the increase in the temperature which is supposed to lead to increased precipitation and thickening of the ice, and increased melting of the ice, which tends to reduce the mass of the ice sheets. To study these two mechanisms, we followed two approaches: characterize the ice sheets from direct observations (i.e., surface topography and ice flow velocities) or indirect observations (i.e., flow b...