Glacier MotionGlacier Motion

chapter 4chapter 4

Glacier flowGlacier flow

““Without the flow of ice, life as we know Without the flow of ice, life as we know it would be impossible.”it would be impossible.”

Observed since 1700sObserved since 1700s Quantified: physical / mathematical Quantified: physical / mathematical

relationsrelations

Glacier movementGlacier movement First studied in the AlpsFirst studied in the Alps

James Forbes, Mer de Glace above Chamonix, James Forbes, Mer de Glace above Chamonix, 18421842

Louis Agassiz & students – mapped the Louis Agassiz & students – mapped the movements of Rhone Glacier, 1874 – 1882movements of Rhone Glacier, 1874 – 1882

silver mine of middle ages near Chamonix is silver mine of middle ages near Chamonix is now buried by Argentierre Glaciernow buried by Argentierre Glacier

all were larger in 1500s to 1800s: Little Ice Ageall were larger in 1500s to 1800s: Little Ice Age 18501850

19001900

Rhone Glacier?

Glacier movementGlacier movement MotionMotion

glaciers flow, expand, contractglaciers flow, expand, contract all motion is forward / downslope, outwardall motion is forward / downslope, outward

(retreat is NOT “up-valley flow”)(retreat is NOT “up-valley flow”) motion usually not apparent: ~ 0.5 m to >300 m / yrmotion usually not apparent: ~ 0.5 m to >300 m / yr

fastest where ice is thickest (~ ELA), w / water at basefastest where ice is thickest (~ ELA), w / water at base slower at base of ice compared to top of glacierslower at base of ice compared to top of glacier

velocity varies seasonallyvelocity varies seasonally winter – upper moves faster (new snow)winter – upper moves faster (new snow) summer – lower part moves faster due to more ablation summer – lower part moves faster due to more ablation

& less resistance& less resistance

Balance velocity and Balance velocity and dischargedischarge

Discharge thru each Discharge thru each cross-section:cross-section:

Q (x) = Q (x) = ( w ( wxx bbxx ) )

Balance (avg) Balance (avg) velocity:velocity: v (x) = Q (x) v (x) = Q (x) / A (x)/ A (x) not constantnot constant

(wedge diagram)(wedge diagram) steeper mass steeper mass

balance gradient balance gradient more mass more mass transfer transfer higher Q and vhigher Q and v

Glacier movement: stress and Glacier movement: stress and strainstrain

MotionMotion brittle fracture vs plastic flowbrittle fracture vs plastic flow causes: gravity acting on ice mass on a causes: gravity acting on ice mass on a

slopeslope stress = forces pushing / pullingstress = forces pushing / pulling

normal stress normal stress σσ = = ii g d g d shear stress shear stress = = ii g d sin g d sin effective shear strength effective shear strength * = c’ + (p* = c’ + (pii – p – pww) ) σσ

tan tan φφ all proportional to all proportional to depthdepth (within glacier or at (within glacier or at

bed)bed) strain = deformation of a body due to stressesstrain = deformation of a body due to stresses

What is “flow”?What is “flow”? Manifestations of deformation (strain)Manifestations of deformation (strain) ModeMode

elasticelastic brittlebrittle ductileductile

CharacterCharacter homogeneoushomogeneous inhomogeneousinhomogeneous

ShearShear pure pure simplesimple

Glacier movementGlacier movement MotionMotion

zzones of a glacierones of a glacier zone of fracture: brittle icezone of fracture: brittle ice

crevasses: tension cracks, top ~ 30 – 60 m depthcrevasses: tension cracks, top ~ 30 – 60 m depth zone of flow – plastic behavior (internal zone of flow – plastic behavior (internal

deformation)deformation) ice crystals slide past one anotherice crystals slide past one another especially if water presentespecially if water present in accum zone: flow down toward the bedin accum zone: flow down toward the bed in abl’n zone: flow upward & outward in abl’n zone: flow upward & outward irregular movement, so cracks form in the ice above irregular movement, so cracks form in the ice above

Glacier movementGlacier movement MotionMotion

zzones of a glacierones of a glacier zone of fracture: brittle icezone of fracture: brittle ice

crevasses: tension cracks, to ~ 30 – 60 m in depthcrevasses: tension cracks, to ~ 30 – 60 m in depth zone of flow: plastic behavior (internal deformation)zone of flow: plastic behavior (internal deformation)

ice crystals slide past one anotherice crystals slide past one another especially if water presentespecially if water present in accum zone: flow down toward the bedin accum zone: flow down toward the bed in abl’n zone: flow upward & outward in abl’n zone: flow upward & outward irregular movement, so cracks in ice above itirregular movement, so cracks in ice above it

causes of flow: gravitycauses of flow: gravity

Brittle deformation – Brittle deformation – crevassescrevasses

Long Long observedobserved

Results from Results from rapidly-rapidly-applied applied stressstress

Form many Form many distinctive distinctive patternspatterns

Mechanics of crevassingMechanics of crevassing

Observed patterns relate observed strain Observed patterns relate observed strain directly to the mechanics of stress couplesdirectly to the mechanics of stress couples

Crevasse Crevasse examplesexamples

Depth <30 – 40 Depth <30 – 40 m m

Tensional and Tensional and marginalmarginal

Terminal splaysTerminal splays Complex Complex

systemssystems

Crevasse Crevasse examplesexamples

IcefallsIcefalls

IcefallsIcefalls

Glacier movementGlacier movement MotionMotion

zones of a glacier: brittle fracture vs plastic zones of a glacier: brittle fracture vs plastic flowflow

causes of causes of flowflow: gravity acting on ice mass on a : gravity acting on ice mass on a slopeslope

temperate glacier will begin to flow when ~ 20 temperate glacier will begin to flow when ~ 20 m deep m deep on a 15° slopeon a 15° slope

Movement typesMovement types most depend on the state & flow of heat among most depend on the state & flow of heat among

the glacier – ground – air – waterthe glacier – ground – air – water

What is “flow”, really?What is “flow”, really?

Slip (planar)Slip (planar) externalexternal internal – internal –

intragranularintragranular Creep Creep

(intergranular)(intergranular) Phase change Phase change

(recrystallizatio(recrystallization)n)

Kenneth G. Libbrecht, Caltech

Hermann EngelhardtCaltech

Hermann EngelhardtCaltech

Glacier movementGlacier movement Movement typesMovement types

internal deformationinternal deformation plastic flow: internal creepplastic flow: internal creep

melting & refreezing of ice crystals under stressmelting & refreezing of ice crystals under stress sliding past one anothersliding past one another

faulting and foldingfaulting and folding can vary up- / down-glacier with gross velocity can vary up- / down-glacier with gross velocity

(compressional vs extensional flow)(compressional vs extensional flow) basal slidingbasal sliding deformation of soft subglacial sedimentsdeformation of soft subglacial sediments

Glacier flowGlacier flow

Creep quantified: Glen’s Flow Law Creep quantified: Glen’s Flow Law (Nye)(Nye) strain rate is proportional to shear stressstrain rate is proportional to shear stress

έέ = A = A ττ nn

A = f (temp); A = f (temp); 7x107x10-18-18 to 7x10 to 7x10-15-15 (at 0°C) (at 0°C) n = f (crystallinity ?); n = f (crystallinity ?); 1.5–4.2, 1.5–4.2, use ~ 3use ~ 3 shear stress proportional to height (depth) in glaciershear stress proportional to height (depth) in glacier

(V = k T(V = k T33 – ?) – ?)

Glacier movementGlacier movement Movement typesMovement types

internal deformationinternal deformation plastic flow: internal creepplastic flow: internal creep faulting and foldingfaulting and folding

basal slidingbasal sliding basal ice is near the pressure-melting point, basal ice is near the pressure-melting point,

water at the base of many glaciers water at the base of many glaciers lubrication lubrication enhanced basal creep around bumps enhanced basal creep around bumps efficient flow efficient flow regelation creep: melting regelation creep: melting refreezing refreezing temperate glaciers slide more than polar glacierstemperate glaciers slide more than polar glaciers

deformation of soft sediments below bed of glacierdeformation of soft sediments below bed of glacier

Thermal ClassificationCold

Polythermal

Warm

J.S. Kite, WVU

Univer Aber.

Basal sliding (regelation)

Glacier movementGlacier movement Movement typesMovement types

internal deformationinternal deformation basal slidingbasal sliding deformation of soft sediments below bed of deformation of soft sediments below bed of

glacierglacier ““Normal” glacier speeds ~ 0.5 m – >300 Normal” glacier speeds ~ 0.5 m – >300

m / yrm / yr Surging glaciers: moving fasterSurging glaciers: moving faster

Planforms of observed flowPlanforms of observed flow

Stakes across Stakes across glacierglacier

Resurvey Resurvey across timeacross time

Observed flow: Plan and Observed flow: Plan and profileprofile

Plan ViewPlan View parabolicparabolic septum (ice septum (ice

streams)streams) ProfileProfile

exponentialexponential non-zero at non-zero at

the bedthe bed

Modes of profile flowModes of profile flow

Total velocity =Total velocity = Internal velocityInternal velocity

laminarlaminar sum of processessum of processes

+ Basal slip+ Basal slip not if frozen to bednot if frozen to bed

+ Bed + Bed deformationdeformation if not rockif not rock

Observed Observed bed bed

deformationdeformation Inferred from Inferred from

structures in structures in tilltill

Measured from Measured from markers markers emplaced in emplaced in basal sediment basal sediment and recoveredand recovered

Shear Plane?

Structures of Structures of glaciersglaciers

What structures What structures do you see here?do you see here?[Grinnell Glacier][Grinnell Glacier]

Lenses, layers, Lenses, layers, fractures…fractures…

How do they How do they form?form?

Schematic Schematic mountain mountain

glacierglacier

Plan viewPlan view Cross-sectionCross-section

Schematic Schematic mountain mountain

glacierglacier

Detailed Detailed sectionsection

TerminusTerminus

Example – Malaspina GlacierExample – Malaspina Glacier Note Note

accommodatiaccommodation of on of Malaspina and Malaspina and Agassiz Agassiz glaciers into glaciers into increasingincreasing spacespace

Longitudinal Longitudinal compressioncompression

Unsteady Flow IUnsteady Flow I

Flow is NOT constantFlow is NOT constant Varies with season Varies with season

(snow load increases (snow load increases the strain rate)the strain rate)

Varies with bed Varies with bed resistance = f(water)?resistance = f(water)?

Varies unpredictably!Varies unpredictably!

Unsteady Flow II - OgivesUnsteady Flow II - Ogives

Unsteady Flow III – Kinematic Unsteady Flow III – Kinematic WavesWaves

Thickening increases Thickening increases depth linearlydepth linearly

Depth increases Depth increases stress linearlystress linearly

Stress increases Stress increases strain (flow) strain (flow) exponentiallyexponentially

Therefore, a pulse Therefore, a pulse propagates through propagates through the glacierthe glacier

Unsteady Flow IV – SurgesUnsteady Flow IV – Surges

Many glaciers Many glaciers (~10%) surge(~10%) surge Stagnant for yearsStagnant for years Increase in Increase in

thicknessthickness Surge!Surge!

Decouple from the Decouple from the bed?bed?

Surface fracturingSurface fracturing Thrusting?Thrusting?

Glacier movementGlacier movement ““Normal” glacier speeds ~ 0.5 m – >300 Normal” glacier speeds ~ 0.5 m – >300

m / yrm / yr Surging glaciers: fast movingSurging glaciers: fast moving

up to 110 m / dayup to 110 m / day (Kutiah Glacier, Pakistan – 11 km in 3 months)(Kutiah Glacier, Pakistan – 11 km in 3 months)

lasts 2 – 3 yearslasts 2 – 3 years Hubbard Glacier, 1987 – AlaskaHubbard Glacier, 1987 – Alaska

went from ~30–100 m / yr went from ~30–100 m / yr 5 km / yr 5 km / yr causescauses

Glacier movementGlacier movement ““Normal” glacier speeds ~ 0.5 m – >300 m / yrNormal” glacier speeds ~ 0.5 m – >300 m / yr Surging glaciers: fast moving – 100s of m / daySurging glaciers: fast moving – 100s of m / day

causes – not certain / more than one causecauses – not certain / more than one cause polar glacier becomes uncoupled from bedpolar glacier becomes uncoupled from bed stagnant ice dams up water in back, and floats the glacier; stagnant ice dams up water in back, and floats the glacier;

when water drains out, the surge stopswhen water drains out, the surge stops heavy precip = more accumulationheavy precip = more accumulation heavy avalanches = more accumulationheavy avalanches = more accumulation silting up of glacial tunnels and floating glacier – silting up of glacial tunnels and floating glacier – lots lots

of lakes on surfaces before surge movementof lakes on surfaces before surge movement

Surging TerminusSurging Terminus

Summary of Flow Process ISummary of Flow Process I

Summary of Summary of Flow Process Flow Process

IIII

One more thing …One more thing … Prediction of ice-sheet profiles (Nye, 1952)Prediction of ice-sheet profiles (Nye, 1952) Assume ice is a perfect plasticAssume ice is a perfect plastic

yield strength ~ 100 kPa (± 50 kPa)yield strength ~ 100 kPa (± 50 kPa) horizontal bedhorizontal bed altitude of ice surface at s inland from marginaltitude of ice surface at s inland from margin

h = (2 hh = (2 h00 s) s) 0.50.5

hh00 = = / / ii g g 11 11 h = (22 s) h = (22 s) 0.50.5

all in meters (can add sin all in meters (can add sin term for sloping bed?) term for sloping bed?) predicts parabolic profilepredicts parabolic profile

Good (not perfect) agreement with observed Good (not perfect) agreement with observed profilesprofiles

Remember – flow is one-Remember – flow is one-way!way!