Glacial Isostatic Adjustment (GIA)
Physical basisThe ISSM/GIA model assumes that the ice sheet rests on top of the solid Earth, which is considered to be a simple two-layered incompressible continuum with upper elastic lithosphere floating on the viscoelastic (Maxwell material) mantle half-space. Coordinate transformations allow simple axisymmetric solutions for the deformation of pre-stressed solid Earth (subject to a normal surface traction of ice/ocean) to retrieve semi-analytical solutions of vertical displacement at the lithosphere surface. Vertical surface displacementVertical displacement at the lithosphere surface (i.e., ice/ocean-bedrock interface), , is the most relevant field variable for GIA assessment. For brevity, hereinafter, this is referred to as the GIA solution. Semi-analytical GIA solution is given by [Ivins1999]: where:
Assuming , the term can be written as follows: for : and for (i.e. the last load segment): where:
For , the inverse decay times are given by: and the amplitude factors by: Parameters appearing in Eqs. (5) and (6) are defined as follows: where:
with the following dimensionless parameters: where: The following set of non-dimensionlized parameters are defined, as needed to express dimensionless terms listed in Table 2: where:
Numerical implementationIn the Cartesian frame of ISSM, we treat the size of ice load as the property of mesh element and compute the GIA solution at each node of the element [Adhikari2014]. Individual 2-D (-plane) mesh elements are defined as the equivalence of footprint (i.e., projection onto the -plane) of cylindrical disc loads, ensuring that the corresponding element and disc both share the same origin and plan-form area. The height of ice load is then assigned to each element such that the average normal tractional force on the corresponding area of bedrock is conserved. At each node within the domain, the final GIA solutions are computed by integrating the solutions due to individual disc loads, defined as the property of mesh elements. Model parametersThe parameters relevant to the GIA solution can be displayed by running: >> md.gia
The solution will also use the following model fields:
ISSM ConfigurationTo activate the GIA model, add the following in the configuration script and compile ISSM: --with-math77-dir="$ISSM_DIR/externalpackages/math77/install"
Running a simulationTo run a simulation, use the following command: >> md=solve(md,'Gia');
The first argument is the model, the second is the nature of the simulation one wants to run. References
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