Guillaume Jouvet

Numerical simulation of Rhonegletscher from 1874 to 2100

Due to climatic change, many Alpine glaciers have significantly retreated during the last century. In this study we perform the numerical simulation of the temporal and spatial change of Rhonegletscher, Swiss Alps, from 1874 to 2007, and from 2007 to 2100. Given the shape of the glacier, the velocity of ice u is obtained by solving a 3D nonlinear Stokes problem with a nonlinear sliding law along the bedrock-ice interface. The shape of the glacier is updated by computing the volume fraction of ice @f, which satisfies a transport equation. The accumulation due to snow fall and the ablation due to melting is accounted by adding a source term to the transport equation. A decoupling algorithm allows the two above problems to be solved using different numerical techniques. The nonlinear Stokes problem is solved on a fixed, unstructured finite element mesh consisting of tetrahedrons. The transport equation is solved using a fixed, structured grid of smaller cells. The numerical simulation, from 1874 to 2007, is validated against measurements. Afterwards, three different climatic scenarios are considered in order to predict the shape of Rhonegletscher until 2100. A dramatic retreat of Rhonegletscher during the 21st century is anticipated. Our results contribute to a better understanding of the impact of climatic change on mountain glaciers.

Modelling the retreat of Grosser Aletschgletscher, Switzerland, in a changing climate

For more than a century Alpine glaciers have been retreating dramatically, and they are expected to shrink even more quickly over the coming decades. This study addresses the future evolution of Grosser Aletschgletscher, Switzerland, the largest glacier in the European Alps. A three-dimensional combined surface mass-balance and glacier dynamics model was applied. The ice flow was described with the full Stokes equations. The glacier surface evolution was obtained by solving a transport equation for the volume of fluid. Daily surface melt and accumulation were calculated on the basis of climate data. The combined model was validated against several types of measurements made throughout the 20th century. For future climate change, scenarios based on regional climate models in the ENSEMBLES project were used. According to the median climatic evolution, Aletschgletscher was expected to lose 90% of its ice volume by the end of 2100. Even when the model was driven using current climate conditions (the past two decades) the glacier tongue experienced a considerable retreat of 6 km, indicating its strong disequilibrium with the present climate. By including a model for the evolution of supraglacial debris and its effect in reducing glacier melt, we show that this factor can significantly slow future glacier retreat.

A new algorithm to simulate the dynamics of a glacier: theory and applications

We propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account by adding an interfacial term in the transport equation. An unstructured mesh with standard stabilized finite elements is used to solve the non-linear Stokes problem. The VOF function is computed on a structured grid with a high resolution. The algorithm is stable for Courant numbers larger than unity and conserves mass to a high accuracy. To demonstrate the potential of the algorithm, we apply it to reconstructed Late-glacial states of a small valley glacier, Vadret Muragl, in the Swiss Alps.

Steady, Shallow Ice Sheets as Obstacle Problems: Well-Posedness and Finite Element Approximation

We formulate steady, shallow ice sheet flow as an obstacle problem, the unknown being the ice upper surface and the obstacle being the underlying bedrock topography. This generates a free-boundary defining the ice sheet extent. The obstacle problem is written as a variational inequality subject to the positive-ice-thickness constraint. The corresponding PDE is a highly nonlinear elliptic equation which generalizes the

An adaptive Newton multigrid method for a model of marine ice sheets

p

Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

-Laplacian equation. Our formulation also permits variable ice softness, basal sliding, and elevation-dependent surface mass balance. Existence and uniqueness are shown in restricted cases which we may reformulate as a convex minimization problem. In the general case we show existence by applying a fixed point argument. Using continuity results from that argument, we construct a numerical solution by solving a sequence of obstacle

Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology

p

Modelling last glacial cycle ice dynamics in the Alps

-Laplacian-like problems by finite element approximation. As a real application, we compute the steady-state shape of the Greenland ice sheet in a steady pre...

Multilayer shallow shelf approximation

In this paper, we consider a model for the time evolution of three-dimensional marine ice sheets. This model combines the Shallow Ice Approximation (SIA) for the ice deformation, the Shallow Shelf Approximation (SSA) for the basal sliding, and the mass conservation principle. At each time step, we solve a scalar p-Laplace minimization-type problem with obstacle (SIA), a vectorial p-Laplace minimization-type problem (SSA) and a transport equation (mass conservation). The two minimization problems are solved using a truncated nonsmooth Newton multigrid method while the transport equation is solved using a vertex-centred finite volume method. Our approach is combined to an heuristic mesh adaptive refinement procedure to face the large gradients of the solution that are expected between the ice sheet and the ice shelf. As applications, we present some simulations of the Marine Ice Sheet Model Intercomparison Project MISMIP (2D and 3D) and validate our results against an analytic solution (2D) and other participant model results (3D). Further numerical results show that the convergence of our Newton multigrid method is insensitive to local refinements making our overall adaptive strategy fully efficient.

Numerical Analysis and Simulation of the Dynamics of Mountain Glaciers

The existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin solutions show unbounded shear stress and nonzero mass flux at the margin. Steady-state solutions with realistic margins, vanishing ice flux and vanishing shear stress are found numerically for ice sheets with Weertman-type sliding.