Week 5: Glacier and ice sheet modelling

Question 1

Why do we model glaciers and ice sheets?

Answer 1

Predict future change

Reconstruct past change

Understand their controls

Glacier response to climate change

Question 2

Predicting future change with models

Answer 2

SL rise contribution

Local change e.g. glaciers as a hazard

Question 3

Reconstructing past change with models

Answer 3

Fluctuations of pale ice masses

Insight into longer term behaviour

Question 4

Understanding glacier controls with models

Answer 4

Processes that influence change and feedbacks between

Question 5

Glacier responses to climate change with models

Answer 5

Glacier length/thickness/flow speeds

Question 6

Model building blocks

Answer 6

Accumulation
Ablation
Ice flow law

Question 7

Ice flow law =

Answer 7

how ice gets from one point to another in a landscape

Question 8

What do models allow us to do?

Answer 8

1. Calculate ice surface (how it evolves/length evolves i.e. thicker = longer, thinner = shorter) within spatial framework
2. Quantify ice flow; ice deformation/basal sliding
3. Apply climate forcing; net mass balance

Question 9

Flow line model

Answer 9

1 dimensional
Discrete points along flow
Grid size (often regular)
Very simple

Good for valley glaciers/constrained ice streams

Question 10

Representation of space (2D/3D)

Answer 10

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

Question 11

Choice of model dimension and flow physics depends on:

Answer 11

Location of interest

Scientific question - prediction/process study

Resources: computational/data

Process understanding

Question 12

Flow physics =

Answer 12

flow approximation/processes:

SIA (shallow ice approximation)

SSA (shallow shelf approximation)

1st order

2nd order

Full equations

Question 13

Valley glacier model choice

Answer 13

All SIA

1/2/3D

Question 14

Ice shelf model choice

Answer 14

All SSA

2/3D

Question 15

Ice streams and marine terminating glaciers model choice

Answer 15

SSA to full equations

2/3D

Question 16

Ice sheets model choice

Answer 16

SIA to full equations

3D

Question 17

Ice thickness:

Answer 17

Add: flow in / accumulation
Take: flow out / ablation

Question 18

Thickness change =

Answer 18

mass balance - change in ice flux along flow

Conservation of mass (continuity equation)

dH/dt = b - (1/w x d(qw)dx)

Question 19

Mass balance (q) =

Answer 19

m3/yr

Udef (sliding due to deformation) x H

Can incorporate Glen’s Flow law

Question 20

Assumptions in mass balance calculation

Answer 20

No basal sliding i.e. Ubasal = 0

No longitudinal stresses = shallow ice approximation (SIA)

Question 21

Glenn 1955 deforming ice…

Answer 21

Colder = harder to deform up to -20/30’C

A = how quickly ice deforms for given ice T (constant)

Question 22

How can you calculate mass balance? (b)

Answer 22

1. Increases linearly with surface elevation S (b = x, S = y)
2. Use separate model e.g. energy balance model (EBM), positive degree day models (PDD)
   - require field data for validation/calibration
3. Create ‘scenarios’ for future mass balance
   - IPCC
   - CO2 levels det T/acc/abl
4. Use past measurements e.g. proxies
5. 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)

Question 23

Inputs of glacier model

Answer 23

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

Question 24

Values for (1) net mass balance

Answer 24

ELA

b slope

Question 25

Values for (2) flow-law

Answer 25

A (ice softness)
n (usually 3)

N.B. A varies with ice T, may relate to ice T and ice thickness
Ice = cold at top then warmer deeper

Question 26

Outputs generated by glacier model

Answer 26

Glacier length and volume with time

Ice thickness/surface elevation

Net mass balance

Flux, velocity

Question 27

How can you validate/verify a model?

Answer 27

Observed values of:

• surface velocities
• surface elevations
• trimlines
• length record
• moraines
• terminus
• sea level record

Question 28

Trimline =

Answer 28

line that ice surface has reached to in past

Question 29

Hysterisis =

Answer 29

value lags behind changes in the effect causing it

Question 30

What is elevation-mass balance feedback?

Answer 30

If ice surface isn’t high enough ice can’t grow (e.g. after deglaciation)

e.g. Greenland ice sheet of today couldn’t form under modern conditions, it must have formed under a cooler past climate

Question 31

Is Greenland or Antarctica more sensitive to climate according to the Java Ice Sheet Model (J-ISM)?

Answer 31

Greenland

Question 32

Case studies

Answer 32

READ IN NOTES

Question 33

Modelling conclusions

Answer 33

Can tell us about past/present/future glacier behaviour

Range of processes (flow/basal sliding/ice shelves/hydrology/ocean warming)

Model must have an appropriate spatial framework (spatial grid resolution/dimension)

Needs to be given a forcing e.g. climate/mass balance

Needs data for input/tuning and validation