Documentation

Physical basis

Hydrostatic equilibrium

The position of the grounding line is determined by a flotation criterion: ice is floating if its thickness, LaTeX equation, is equal or lower than the floating height LaTeX equation defined as:

LaTeX equation

where LaTeX equation is the ice density, LaTeX equation the ocean density and LaTeX equation the bedrock elevation (negative if below sea level). Grounding line is therefore located where LaTeX equation:

LaTeX equation

Each element of the mesh is either grounded or floating: flotation criterion is determined on each vertex of the triangle and if at least one vertex of the triangle is floating, the element is considered floating and no friction is applied. Otherwise, if the three vertices are grounded, the element is considered grounded. We refer to this type of grounding line migration as 'SoftMigration'.

Sub-element parameterization can also be used to track the position of the grounding line within an element and improve accuracy of the results. The floating condition is a 2D field and the grounding line position is determined by the line where LaTeX equation, so it is located anywhere within an element. Some elements are therefore partly grounded and partly floating. Two different schemes of sub-element parameterizations have been implemented.

In the first case, the basal friction coefficient LaTeX equation is reduced to match the amount of grounded ice in the element as proposed by [Pattyn2006] and [Gladstone2010] but for a 2D element:

LaTeX equation

where LaTeX equation is the applied basal friction coefficient for the element partially grounded, LaTeX equation is the area of grounded ice of this element and LaTeX equation is the total area of the element. We refer to this type of grounding line parameterization as 'SubelementMigration'.

In the second case, the basal friction computed for partly grounded elements is integrated only on the part of the element that is grounded. This can be done simply by changing the integration area from the initial element to the grounded part of the element, over which the basal friction is unchanged. We refer to this type of grounding line parameterization as 'SubelementMigration2'.

The sub-element parameterizations are described in details in [Seroussi2014a].

Contact mechanics

Grounding line migration can be advantageously based on contact mechanics when solving the stress balance equations with a full-Stokes models [Nowicki2008,Durand2009].

This capability is currently under development.

Model parameters

The parameters relevant to the grounding line migration can be displayed by running:

>> md.groundingline
  • md.groundingline.migration: type of grounding line migration: 'SoftMigration', 'AgressiveMigration', 'SubelementMigration', 'SubelementMigration2', or 'None'

Running a simulation

To compute grounding line migration, the transient solution must be used and all solutions except the grounding line migration must be deactivated (see Transient solution):

>> md=solve(md,'Transient');

The first argument to solve is the model, the second is the nature of the simulation one wants to run.

References

  • G. Durand, O. Gagliardini, T. Zwinger, E. Le Meur, and R. C. A. Hindmarsh. Full Stokes modeling of marine ice sheets: influence of the grid size. Ann. Glaciol., 50(52):109-114, 2009.
  • R. M. Gladstone, V. Lee, A. Vieli, and A. J. Payne. Grounding line migration in an adaptive mesh ice sheet model. J. Geophys. Res., 115:1-19, Oct 27 2010.
  • S. M. J. Nowicki and D. J. Wingham. Conditions for a steady ice sheet-ice shelf junction. Earth Planet. Sci. Lett., 265(1-2):246-255, JAN 15 2008.
  • F. Pattyn, A. Huyghe, S. De Brabander, and B. De Smedt. Role of transition zones in marine ice sheet dynamics. J. Geophys. Res. - Earth Surface, 111(F2):1-10, APR 26 2006.
  • H. Seroussi, M. Morlighem, E. Larour, E. Rignot, and A. Khazendar. Hydrostatic grounding line parameterization in ice sheet models. Cryosphere, 8(6):2075-2087, Nov. 2014.