A comparison of Eulerian and Lagrangian methods for dating in numerical ice-sheet models

Abstract

ABSTRACT. Accurate dating in ice sheets is required for a correct interpretation of palaeoclimatic records and for incorporation of material characteristics in the flow law which depend on ice age. In this paper, we make a comparison between a Lagrangian and Eulerian approach to the ice advection problem in numerical ice-sheet models. This comparison is first performed for a schematic two-dimensional ice sheet of Nye^Vialov type with a prescribed stationary velocity field. Several cases are examined which incorporate basal melting, basal sliding and an undulating bed. A further comparison is made with an analytical solution for the ice divide. Both methods are also applied in a thermomechanical model of the Antarctic ice sheet for steady-state present-day conditions. Our main conclusion is that, for similar discretization parameters, the Lagrangian method produces less error than an Eulerian approach using a second-order upwinding finitedifference scheme, though the difference is small (51%) for the largest part of the model domain. However, problems with the Lagrangian approach are introduced by the dispersion of tracers, necessitating the use of interpolation procedures that are a main source of additional error. It is also shown that a cubic-spline approximation of Lagrangian trajectories improves accuracy, but such a method is computationally hardly applicable in large-scale ice-sheet models.

The GRISLI ice sheet model (version 2.0): calibration and validation for multi-millennial changes of the Antarctic ice sheet

“…time and location of ice 5 deposition for the vertical model grid points (Lhomme et al, 2005;Quiquet et al, 2013). For this, we use a semi-Lagrangian scheme following Clark and Mix (2002) in order to avoid the numerical instabilities of Eulerian schemes and information dispersion of Lagrangian schemes (Rybak and Huybrechts, 2003). For each timestep, the back trajectories of each grid points are computed and tri-linearly interpolated onto the model grid.…”

Temporally stable surface mass balance asymmetry across an ice rise derived from radar internal reflection horizons through inverse modeling

“…Both the ice flow field and the age field are solved using an Eulerian approach (Rybak and Huybrechts, 2003). We redefine the depth scale as ζ = (b + H − z)/H where z is the elevation above the bed, b is the bed elevation and H is the ice thickness.…”

The GRISLI ice sheet model (version 2.0): calibration and validation for multi-millennial changes of the Antarctic ice sheet

“…Addition-ally, glacial troughs may form a deepening bedrock from the grounding line towards the ice sheet centre. Such bed properties lead to the marine ice sheet instability (MISI; Weertman, 1974;Schoof, 2007) responsible for an irreversible retreat of the grounding line in response to an initial perturbation such as local sea level change and/or increase in basal melting rate below ice shelves. The latter two processes are expected to play a crucial role for the stability of the Antarctic ice sheet in the future (e.g.…”

“…Important improvements have been implemented in the model since its original version (Ritz et al, 2001). Notably, GRISLI now includes a basal hydrology model and an explicit flux computation at the grounding line based on the analytical formulations of Schoof (2007) or Tsai et al (2015). We perform a full calibration of the model based on an ensemble of 300 simulations sampling mechanical parameter space using a Latin hypercube method.…”