Week 2

Question 1

Is there a law for ice flow?

Answer 1

‘A universal constitutive law for ice flow does not exist’ (Paterson, 1983).

Question 2

What is balance velocity?

Answer 2

Balance velocities relate ice flux to glacier mass balance, it is a useful concept to determine whether a glacier is dynamically unstable.

Question 3

What defines ice flux for an idealised glacier of constant size and shape?

Answer 3

Ice flux through a cross-section should equal the sum of accumulation and ablation occurring upglacier of the section.
Based on this, glaciers with steeper mass balance gradients will have greater balance velocities.

Question 4

What is the ice discharge profile like downglacier?

Answer 4

Ice discharge increases from the head of the glacier to the ELA, then decreases towards the snout.

Question 5

What happens if balance velocity is greater than accumulation rate?

Answer 5

The glacier is redistributing more ice than it is building up, meaning it is probably reacting to a prior warmer climate.

Question 6

What is Stress?

Answer 6

Force per unit area, in Pascals, 1 Pa = 1 N / Msq, so the same force acting across a smaller area exerts a greater stress.

Question 7

What direction does normal stress act?

Answer 7

Perpendicular to a surface. A.K.A Tension or Compression.

Question 8

What direction does shear stress act?

Answer 8

Parallel to a surface.

It is basal shear stress that drives glacier flow.

Question 9

What is Yield Stress?

Answer 9

The stress at which a material begins to deform plastically. Non-permanent deformation is termed ‘elastic’.

Question 10

What is Strain?

Answer 10

Strain is the relative deformation of a material experiencing stress (e.g. change in length in a given dimension) and is unitless.
Rate of strain is the rate of change of shape.

Question 11

What are the 3 stress-strain relationships?

Answer 11

• Perfectly plastic material: remains rigid until applied stress reaches the yield stress.
• Linearly Viscous Material: Strain is linearly proportional to applied stress.
• Non-linearly viscous material: Strain increases non-linearly with applied stress. For ice strain rate increases non-linearly with stress.

Question 12

Glen’s Flow Law

Answer 12

e = At^n
e (epsilon): strain rate (what we want to know)
A: constant related to ice temp & other things.
t (tau): shear stress
n: constant (approx 3).

Question 13

What is Basal Sliding?

Answer 13

Differential motion between ice and the substrate, a.k.a. sliding at the ice-substrate interface.

Question 14

How does basal sliding occur?

Answer 14

• Water lubricates flow at the interface.
• Water rpessure reduces normal stress resulting in lower effective pressure.
  Rate of sliding depends largely on basal water pressure.

Question 15

What is substrate deformation?

Answer 15

Till underlies many glaciers, this mixture of sediments experiences stress from the overlying ice and can deform. The rates depend on various factors such as the pore water pressure in the till and it’s mechanical strength.

Question 16

Evidence for substrate deformation

Answer 16

• Differential motion of segmented rods in till beneath a glacier in Iceland (Boulton et al. 1979).
• Deformed palaeo subglacial sediment.

Question 17

Valley Glacier Velocity Profiles

Answer 17

Velocity is greatest at the top and centre of the glacier, where there is the accumulation of deformation of underlying ice and basal motion, and least friction from valley sides. This can be seen in surface patters on ice.

Question 18

Valley Glacier Velocity Profiles 2

Answer 18

• Flow rate between 10-100m per year by a combination of basal motion and internal deformation.
  Many tidewater glaciers and ice streams flow 100-1000m per year, moving mostly by basal motion. Jakobshavn Isbrae, Greenland flows 12km/yr.

Question 19

Limits on Ice Flow

Answer 19

• Bed roughness: ice must be transferred around obstacles.
• Regelation sliding (small bumps) melts ice in front of bump, and flows behind the bump to refreeze in lower pressure.
• Enhanced creep (big bumps) where ice crystals don’t melt but deform around basal obstacles.
• Friction from debris entrained by ice is proportional to force pressing them onto the bed (weight of overlying ice, normal stress).

Question 20

How do we quantify ice flow? 2 ways.

Answer 20

• Movement of stakes drilled into the ice, used with GPS antennae to produce a high temporal resolution but only at a few locations.
• Matching of patterns in sequential aerial photographs or satellite images, e.g. feature tracking, cross-correlation of brightness patterns. This can cover large areas at reasonable temporal spacing (days to weeks).

Question 21

What is thermal regime?

Answer 21

This is the variation in temperature of glacier ice. They are not uniformly cold.
- Parts of Greenland can be - 20, parts of Antarctic can be -40.
importantly ice has different characteristics at different temperatures.

Question 22

Controls on Ice Temperature

Answer 22

• Heat exchange within atmosphere. (Moreso in temperate regions).
• Geothermal heat flux, varies depending on tectonic setting. Global mean value sufficient to melt 6mm of ice per year.
• Frictional heat generated by ice (and water) flow. Derived from differential ice motion within the glacier, basal sliding and water flowing in contact with ice. This is typically only significant close to the ice base where melt rates can be 100x larger than geothermal rates. (for fast flowing glaciers).

Question 23

Describe a polar thermal regime

Answer 23

Air temperature is well below zero all year round. The ice-bed interface is below freezing too.

Question 24

Describe a temperate thermal regime

Answer 24

Air below zero in winter but above in summer, where surface derived meltwater may get to the ice-bed interface.
The ice-bed interface is at or above pressure melting point.

Question 25

Describe a polythermal (mixed) thermal regime

Answer 25

Tyypically temperate in the interior but cold at the margins.

Question 26

Ice Temperature/Depth profiles

Answer 26

Typically temperature increases with depth due to influence of shear heating, basal friction and geothermal heat flux. Even in cold regions basal ice may be at the pressure melting point if the overlying ice is sufficiently thick to reduce the melting point.

Question 27

How does thermal regime affect cold based glacier ice flow?

Answer 27

In cold glaciers the ice-bed interface is strong and can support high shear stresses. Hence internal deformation dominates ice motion. Some regelation and enhanced creep can occur at slow rates. Generally low velocities.

Question 28

How does thermal regime affect warm based glacier ice flow?

Answer 28

Ice bed interface is weak and ice readily slides over the substrate. Deformation of subglacial sediment may also occur. Generally high velocities.

Question 29

Cold based glacier characteristics

Answer 29

Relatively thin, shallow sloped, slow flowing glaciers where winter air temperatures are very low. (Canada, Antarctic dry valleys).
There is minimal potential for landscape alteration.

Question 30

Warm based glacier characteristics

Answer 30

Relatively steep and fast flowing glaciers in more temperate climates (e.g. Eu Alps and NZ).
Huge potential for landscape alteration.

Question 31

Glacier Behaviour Summary

Answer 31

Mass balance drives the system. Ice flow attempts to redistribute the mass and maintain a steady-state surface profile. Flow influenced by thermal regime and can affect ice temperature.
Together these determine the form and size of a glacier and its tendency to advance or retreat.