Week 5: Glacier and ice sheet modelling Flashcards
Why do we model glaciers and ice sheets?
Predict future change
Reconstruct past change
Understand their controls
Glacier response to climate change
Predicting future change with models
SL rise contribution
Local change e.g. glaciers as a hazard
Reconstructing past change with models
Fluctuations of pale ice masses
Insight into longer term behaviour
Understanding glacier controls with models
Processes that influence change and feedbacks between
Glacier responses to climate change with models
Glacier length/thickness/flow speeds
Model building blocks
Accumulation
Ablation
Ice flow law
Ice flow law =
how ice gets from one point to another in a landscape
What do models allow us to do?
- Calculate ice surface (how it evolves/length evolves i.e. thicker = longer, thinner = shorter) within spatial framework
- Quantify ice flow; ice deformation/basal sliding
- Apply climate forcing; net mass balance
Flow line model
1 dimensional
Discrete points along flow
Grid size (often regular)
Very simple
Good for valley glaciers/constrained ice streams
Representation of space (2D/3D)
Grid in x, y (+z if 3D) direction
2D = plan view
3D = plan view but also divided vertically
More complicated/computationally expensive = lower resolution
Good for ice sheets/caps
Choice of model dimension and flow physics depends on:
Location of interest
Scientific question - prediction/process study
Resources: computational/data
Process understanding
Flow physics =
flow approximation/processes:
SIA (shallow ice approximation)
SSA (shallow shelf approximation)
1st order
2nd order
Full equations
Valley glacier model choice
All SIA
1/2/3D
Ice shelf model choice
All SSA
2/3D
Ice streams and marine terminating glaciers model choice
SSA to full equations
2/3D
Ice sheets model choice
SIA to full equations
3D
Ice thickness:
Add: flow in / accumulation
Take: flow out / ablation
Thickness change =
mass balance - change in ice flux along flow
Conservation of mass (continuity equation)
dH/dt = b - (1/w x d(qw)dx)
Mass balance (q) =
m3/yr
Udef (sliding due to deformation) x H
Can incorporate Glen’s Flow law
Assumptions in mass balance calculation
No basal sliding i.e. Ubasal = 0
No longitudinal stresses = shallow ice approximation (SIA)
Glenn 1955 deforming ice…
Colder = harder to deform up to -20/30’C
A = how quickly ice deforms for given ice T (constant)
How can you calculate mass balance? (b)
- Increases linearly with surface elevation S (b = x, S = y)
- Use separate model e.g. energy balance model (EBM), positive degree day models (PDD)
- require field data for validation/calibration - Create ‘scenarios’ for future mass balance
- IPCC
- CO2 levels det T/acc/abl - Use past measurements e.g. proxies
- Solve the equation
- discretisation
- solved for each grid point = dH/dt
- solve again and again to investigate time evolution
(lines spaced equally w.r.t time so further apart = faster glacier advance)
Inputs of glacier model
Run time/time step/grid size
Geometry (on grid): bed topography, reference width/thickness, ice surface
Model parameters: values for (1) net mass balance (2) flow-law values
Values for (1) net mass balance
ELA
b slope
