ASIS:Ism intro

Overview of ice sheet models
(Tony P initial description for distribution to interested parties)

Ice sheet models contain four main components:

1.	thickness solver;

2.	velocity solver;

3.	temperature solver;

4.	and a variety of routines for supplying boundary conditions.

The current ice sheet model is written in fortran90. It uses a regular, structured grid in the horizontal. The grid is staggered so that the two components of horizontal velocity are found at (i-½,j-½), and thickness and temperature etc are found at (i,j). A stretched coordinate system is used in the vertical because of the irregular nature of the upper (s) and lower (h either bedrock or the base of floating ice) ice surfaces. Calculations are performed in $$\sigma ={\left( s-z \right)}/{(s-h)}\;$$ and grid spacing in $$\sigma $$ can be defined as a non-linear function of z. The coordinate transform is fairly straight forward for vertical and first-order horizontal and time derivatives but far trickier for second-order terms. Typical horizontal grid spacing is ~20 km and time steps ~1 year; typically 10 to 20 levels are used in the vertical. We would like to go to finer than 5 km resolution.

The low aspect ratio (height scale over distance scale) of ice sheets means that various simplifications can be made to the momentum, energy and mass balances such that vertical terms are treated in a different way to horizontal ones (see below).

The target application is the West Antarctic ice sheet’s evolution over the next 100 to 1000 years, which has well-reported implications for global sea-level change. I believe mesh refinement is needed for two reasons.

1.	Large areas of the ice sheet flow very slowly (1 to 10 m/yr) and have little or no role in the dynamics that we are interested in (see Figure 1). The areas that are important are called ice streams and experience flow ~1 km/yr. They are typically several 100 kms long and ~50 km wide. The whole Antarctic ice sheet is ~5000 km wide and typically 2 to 4 km thick.

2.	The evolution of the ice sheet is largely a function of grounding-line migration (Figure 2). The grounding line is the point at which ice starts to float and separates grounded ice that experiences basal traction (high in the case of slow flowing ice, to low in the case of ice streams) from freely floating ice. A range of studies show that the dynamics in this area can only be adequately resolved using at fine spatial resolutions (~1 km).

It would also be very helpful to make use of the parallelization built into many adaptive mesh refinement packages

We will need to input a 5-km resolution DEM of the present-day ice sheet geometry (upper surface and bedrock etc), as well as boundary condition data on the same grid (e.g., surface temperature, geothermal heat flux and snow accumulation rates). Entire domain will be roughly that shown in Figure 1.



Ultimately we hope to couple the ice sheet code to large Earth-system models (with atmosphere and ocean models). We have done this already with our current model and hope to continue use of our existing coupler with any new ice sheet model.



Ancillary calculations
Boundary conditions such as air temperature, geothermal heat flux and snow accumulation rate have a complicated spatial pattern and are read from a 5-km grid covering the whole domain.

The other additional set of calculations is associated with water flow at the ice sheet base (bedrock-ice-sediment interface) and its effect on the rheology of underlying subglacial sediments. Water saturated sediments have a lower yield strength and therefore deform more easily, changing the basal boundary condition used in the velocity solver. This work is still largely in the development stage however it seems likely to involve the horizontal transport of water resulting in a 2d hyperbolic equation.

AMR work to date
We are also starting to progress with nested grids.