# Difference between revisions of "Notes/vanderVeen Aug5"

From Interactive System for Ice sheet Simulation

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* Assumption: ice is incompressible, so density is constant. Mass conservation ~ volume conservation | * Assumption: ice is incompressible, so density is constant. Mass conservation ~ volume conservation | ||

* Assumption: ignore firn layer (100-150m in Antarctica, less in Greenland) | * Assumption: ignore firn layer (100-150m in Antarctica, less in Greenland) | ||

− | + | ||

− | + | <math> M \Delta x + H(x)U(x) - H(x + \Delta x) U(x + \Delta x) = \frac{\Delta H}{\Delta t} \Delta x </math> | |

− | + | ||

− | + | <math> \frac{\Delta H}{\Delta t} = -\frac{H(x + \Delta x)U(x+\Delta x) - H(x)U(x)}{\Delta x} + M </math> | |

+ | |||

+ | Shrink timestep & spatial step to infinitessimal to write as differential equation | ||

+ | |||

+ | <math> \frac{\partial H}{\partial t} = -\frac{\partial}{\partial x} HU + M </math> | ||

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* so the sum of all forces must be zero. | * so the sum of all forces must be zero. | ||

* stresses are easier to work with than forces: stress is force per unit area | * stresses are easier to work with than forces: stress is force per unit area | ||

− | * Nine stress components: | + | * Nine stress components: <math> \sigma_{ij} </math> |

− | <math> \sigma_{ij} </math> | + | |

* i: plane perpendicular to axis (x) | * i: plane perpendicular to axis (x) | ||

* j: direction of stress | * j: direction of stress |

## Revision as of 09:59, 5 August 2009

## 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:
- 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