Crash Course in Glacier Dynamics
Kees van der Veen, University of Kansas August 5, 2009 Portland Summer Modeling School
What's the objective of an ice sheet model?
- Understand evolution of ice sheet given some forcing (global warming, etc.)
Fundamental equations: conservation of xxx
Conservation of Mass: Continuity Equation
- What comes in (flux, basal freezing if, accumulation if) to some control volume must go out (flux, basal melting if, ablation if).
- Assumption: ice is incompressible, so density is constant. Mass conservation ~ volume conservation
- Assumption: ignore firn layer (100-150m in Antarctica, less in Greenland)
- Shrink timestep & spatial step to infinitessimal to write as differential equation
Conservation of Momentum: Newton's second law
- , with zero acceleration
- so the sum of all forces must be zero.
- stresses are easier to work with than forces: stress is force per unit area
- Nine stress components:
- i: plane perpendicular to axis (x)
- j: direction of stress
- Stress tensor is symmetric, so and there are really only six distinct stress components
- 3 equations with 6 unknowns
Force balance in z