Preliminary results are presented on a solution of the two-dimensional time-dependent continuity equation for mass conservation governing ice-sheet dynamics. The equation is solved using a column-averaged velocity to define the horizontal flux in a finite-element formulation. This yields a map-plane model where flow directions, velocities, and surface elevations are defined by bedrock topography, the accumulation/ablation pattern, and in the time-dependent case by the initial surface configuration. This alleviates the flow-band model limitation that the direction of flow be defined and fixed over the course of the modeling experiment. The ability of the finite-element method to accept elements of different dimensions allows detail to be finely modeled in regions of steep gradients, such as ice streams, while relatively uniform areas, such as areas of sheet flow, can be economically accommodated with much larger elements. Other advantages of the finite-element method include the ability to modify the sliding and/or flow-law relationships without materially affecting the method of solution.
Modeling experiments described include a steady-state reconstruction showing flow around a three-dimensional obstacle, as well as a time-dependent simulation demonstrating the response of an ice sheet to a localized decoupling of the bed. The latter experiment simulates the initiation and development of an ice stream in a region originally dominated by sheet flow. Finally, a simulation of the effects of a changing mass-balance pattern, such as might be anticipated from the expected carbon dioxide warming, is described. Potential applications for such a model are also discussed.
SYMBOLS USED
a(x,y) Accumulation/ablation rate.
A Flow-law parameter.
B Sliding-law parameter.
CijC Global capacitance matrix.
f Fraction of the bed melted.
Fij,F Global load vector.
g Acceleration of gravity.
hj,h Ice-surface elevation.
H Ice thickness.
k(x,y) Constitutive equation constant of proportionality.
kij
Global stiffness matrix.
m Sliding-law exponent.
n Flow-law exponent.
ρ Density of ice.
σ(x,y) Ice flux.
t Time.
U Column-average ice velocity.
U
F Column-average deformation (flow) velocity.
U
S Sliding velocity.
v Variational trial function.
x,y Map-plane coordinates.