In all glacier and ice sheet models, ice is commonly described as a viscous non-Newtonian fluid such that its motion is governed by 3D non-linear Stokes equations. However, most of the models implement simplified (shallow) equations to reduce the computational costs and achieve a finer resolution. For a long time, simulations were based on the single Shallow Ice Approximation (SIA) as it was the only model that could be run at large time and spatial scales. The SIA analytically describes the vertical velocity profile of the ice, and then is computationally very cheap to solve. However, the SIA only suits ice flow dominated by shear without basal sliding. Later, the Shallow Shelf Approximation (SSA) model has been considered as soon as it became computationally tractable. In contrast with the SIA, the SSA assumes no vertical variation of the velocity, and describes its horizontal distribution only. Thus, the SSA suits ice flow dominated by basal sliding (as prevailing over ice shelves). To be mechanically exhaustive, the modellers have turned to hybrid modelling approaches which combine both models, i.e. the SIA and the SSA. For instance, the linear combination SIA+SSA is the most simple hybrid model, however, it does not include any mutual feedback. When dealing with uneven basal geometries, this feedback gets effective such that the SIA+SSA is no longer suited.
The goal of this project is to develop a new hybrid model, the Multilayer Shallow Shelf Approximation (MSSA), which combines the SIA and the SSA in a non-linear way by a multilayer approach. More precisely, the ice thickness is seen as a pile of thin layers which can spread out, contract and slide over each other. While the deformation of each individual layer is described by the SSA, the sliding between layers is described by the SIA. Thanks to this approach, the MSSA suits to a much larger panel of ice flow than the SIA, SSA or SIA+SSA , including those of alpine-type glaciers where the vertical shear (described by the SIA) and the longitudinal extension (described by the SSA) of the velocity couple at most. Mathematically, the MSSA consists of a tridiagonal system of 2D non-linear elliptic equations similar to those of the SSA. Consequently, any solver developed for the SSA can be relatively easily generalized to solve the MSSA column-wise  without having to build a complex 3D mesh. So far, the MSSA model has been tested on simple experiments of ISMIP-HOM  and MISMIP . This project aims to lead further model comparisons (mechanical and numerical) for prognostic 3D simulations of ice sheets and mountain glaciers to better evaluate the capabilities of the MSSA in real cases of modelling. Another aspect to investigate is how to include the conservation of energy in the MSSA model, and how to discretize it in compliance with the multilayer approach.
- G. Jouvet (in press); Multilayer Shallow Shelf Approximation: minimisation formulation, finite element solvers and applications. Journal of Computational Physics.
- G. Jouvet (2015); A multilayer ice flow model generalising the Shallow Shelf Approximation. Journal of Fluid Mechanics, Vol. 764.