# Notes/vanderVeen Aug5

From Interactive System for Ice sheet Simulation

## 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

- Mass
- Energy
- Momentum

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:
**Failed to parse (Missing texvc executable; please see math/README to configure.): \sigma_{ij} <\math> * i: plane perpendicular to axis (x) * j: direction of stress * Stress tensor is symmetric, so <math> \sigma_{ij} = \sigma_{ji}**

and there are really only six distinct stress components

- 3 equations with 6 unknowns

Force balance in z

**Failed to parse (Missing texvc executable; please see math/README to configure.): F_z = 0 <\math> <math> \sigma_{zz}(z + \Delta z) \Delta x \Delta y + \sigma_{xz}(z+\Delta z) \Delta x \Delta y + \sigma_{yz}(z + \Delta z) \Delta x \Delta y**