1. Glacier Motion chapter 4

2. Glacier flow “Without the flow of ice, life as we know it would be impossible.” “Without the flow of ice, life as we know it would be impossible.” Observed since 1700s Observed since 1700s Quantified: physical / mathematical relations Quantified: physical / mathematical relations

3. Glacier movement First studied in the Alps First studied in the Alps James Forbes, Mer de Glace above Chamonix, 1842 James Forbes, Mer de Glace above Chamonix, 1842 Louis Agassiz & students – mapped the movements of Rhone Glacier, 1874 – 1882 Louis Agassiz & students – mapped the movements of Rhone Glacier, 1874 – 1882 silver mine of middle ages near Chamonix is now buried by Argentierre Glacier silver mine of middle ages near Chamonix is now buried by Argentierre Glacier all were larger in 1500s to 1800s: Little Ice Age all were larger in 1500s to 1800s: Little Ice Age 18501900 18501900

4. Rhone Glacier?

5. Glacier movement Motion Motion glaciers flow, expand, contract glaciers flow, expand, contract all motion is forward / downslope, outward all 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 / yr motion usually not apparent: ~ 0.5 m to >300 m / yr fastest where ice is thickest (~ ELA), w / water at base fastest where ice is thickest (~ ELA), w / water at base slower at base of ice compared to top of glacier slower at base of ice compared to top of glacier velocity varies seasonally velocity varies seasonally winter – upper moves faster (new snow) winter – upper moves faster (new snow) summer – lower part moves faster due to more ablation & less resistance summer – lower part moves faster due to more ablation & less resistance

6. Balance velocity and discharge Discharge thru each cross-section: Q (x) =  ( w x b x ) Discharge thru each cross-section: Q (x) =  ( w x b x ) Balance (avg) velocity: v (x) = Q (x) / A (x) Balance (avg) velocity: v (x) = Q (x) / A (x) not constant not constant (wedge diagram) (wedge diagram) steeper mass balance gradient  more mass transfer  higher Q and v

7. Glacier movement: stress and strain Motion Motion brittle fracture vs plastic flow brittle fracture vs plastic flow causes: gravity acting on ice mass on a slope causes: gravity acting on ice mass on a slope stress = forces pushing / pulling stress = forces pushing / pulling normal stress σ =  i g d normal stress σ =  i g d shear stress  =  i g d sin  shear stress  =  i g d sin  effective shear strength  * = c’ + (p i – p w ) σ tan φ effective shear strength  * = c’ + (p i – p w ) σ tan φ all proportional to depth (within glacier or at bed) all proportional to depth (within glacier or at bed) strain = deformation of a body due to stresses strain = deformation of a body due to stresses

8. What is “flow”? Manifestations of deformation (strain) Manifestations of deformation (strain) Mode Mode elastic elastic brittle brittle ductile ductile Character Character homogeneous homogeneous inhomogeneous inhomogeneous Shear Shear pure pure simple simple

9. Glacier movement Motion Motion z ones of a glacier z ones of a glacier zone of fracture: brittle ice zone of fracture: brittle ice crevasses: tension cracks, top ~ 30 – 60 m depth crevasses: tension cracks, top ~ 30 – 60 m depth zone of flow – plastic behavior (internal deformation) zone of flow – plastic behavior (internal deformation) ice crystals slide past one another ice crystals slide past one another especially if water present especially if water present in accum zone: flow down toward the bed in 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

11. Glacier movement Motion Motion z ones of a glacier z ones of a glacier zone of fracture: brittle ice zone of fracture: brittle ice crevasses: tension cracks, to ~ 30 – 60 m in depth crevasses: 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 another ice crystals slide past one another especially if water present especially if water present in accum zone: flow down toward the bed in 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 it irregular movement, so cracks in ice above it causes of flow: gravity causes of flow: gravity

13. Brittle deformation – crevasses Long observed Long observed Results from rapidly-applied stress Results from rapidly-applied stress Form many distinctive patterns Form many distinctive patterns

14. Mechanics of crevassing Observed patterns relate observed strain directly to the mechanics of stress couples Observed patterns relate observed strain directly to the mechanics of stress couples

15. Crevasse examples Depth <30 – 40 m Depth <30 – 40 m Tensional and marginal Tensional and marginal Terminal splays Terminal splays Complex systems Complex systems

16. Crevasse examples

17. Icefalls

18. Icefalls

19. Glacier movement Motion Motion zones of a glacier: brittle fracture vs plastic flow zones of a glacier: brittle fracture vs plastic flow causes of flow: gravity acting on ice mass on a slope causes of flow: gravity acting on ice mass on a slope temperate glacier will begin to flow when ~ 20 m deep on a 15° slope temperate glacier will begin to flow when ~ 20 m deep on a 15° slope Movement types Movement types most depend on the state & flow of heat among the glacier – ground – air – water most depend on the state & flow of heat among the glacier – ground – air – water

20. What is “flow”, really? Slip (planar) Slip (planar) external external internal – intragranular internal – intragranular Creep (intergranular) Creep (intergranular) Phase change (recrystallization) Phase change (recrystallization)

21. Kenneth G. Libbrecht, Caltech

22. Hermann Engelhardt Caltech

23. Hermann Engelhardt Caltech

24. Glacier movement Movement types Movement types internal deformation internal deformation plastic flow: internal creep plastic flow: internal creep melting & refreezing of ice crystals under stress melting & refreezing of ice crystals under stress sliding past one another sliding past one another faulting and folding faulting and folding can vary up- / down-glacier with gross velocity (compressional vs extensional flow) can vary up- / down-glacier with gross velocity (compressional vs extensional flow) basal sliding basal sliding deformation of soft subglacial sediments deformation of soft subglacial sediments

25. Glacier flow Creep quantified: Glen’s Flow Law (Nye) Creep quantified: Glen’s Flow Law (Nye) strain rate is proportional to shear stress strain rate is proportional to shear stress έ = A τ n έ = A τ n A = f (temp); 7x10 -18 to 7x10 -15 (at 0°C) A = f (temp); 7x10 -18 to 7x10 -15 (at 0°C) n = f (crystallinity ?); 1.5–4.2, use ~ 3 n = f (crystallinity ?); 1.5–4.2, use ~ 3 shear stress proportional to height (depth) in glacier shear stress proportional to height (depth) in glacier (V = k T 3 – ?) (V = k T 3 – ?)

26. Glacier movement Movement types Movement types internal deformation internal deformation plastic flow: internal creep plastic flow: internal creep faulting and folding faulting and folding basal sliding basal sliding basal ice is near the pressure-melting point,  water at the base of many glaciers  lubrication basal ice is near the pressure-melting point,  water at the base of many glaciers  lubrication enhanced basal creep around bumps  efficient flow enhanced basal creep around bumps  efficient flow regelation creep: melting  refreezing regelation creep: melting  refreezing temperate glaciers slide more than polar glaciers temperate glaciers slide more than polar glaciers deformation of soft sediments below bed of glacier deformation of soft sediments below bed of glacier

27. Thermal Classification Cold Polythermal Warm J.S. Kite, WVU

29. Univer Aber. Basal sliding (regelation)

30. Glacier movement Movement types Movement types internal deformation internal deformation basal sliding basal sliding deformation of soft sediments below bed of glacier deformation of soft sediments below bed of glacier “Normal” glacier speeds ~ 0.5 m – >300 m / yr “Normal” glacier speeds ~ 0.5 m – >300 m / yr Surging glaciers: moving faster Surging glaciers: moving faster

31. Planforms of observed flow Stakes across glacier Stakes across glacier Resurvey across time Resurvey across time

32. Observed flow: Plan and profile Plan View Plan View parabolic parabolic septum (ice streams) septum (ice streams) Profile Profile exponential exponential non-zero at the bed non-zero at the bed

33. Modes of profile flow Total velocity = Total velocity = Internal velocity Internal velocity laminar laminar sum of processes sum of processes + Basal slip + Basal slip not if frozen to bed not if frozen to bed + Bed deformation + Bed deformation if not rock if not rock

34. Observed bed deformation Inferred from structures in till Inferred from structures in till Measured from markers emplaced in basal sediment and recovered Measured from markers emplaced in basal sediment and recovered Shear Plane?

35. Structures of glaciers What structures do you see here? [Grinnell Glacier] What structures do you see here? [Grinnell Glacier] Lenses, layers, fractures… Lenses, layers, fractures… How do they form? How do they form?

36. Schematic mountain glacier Plan view Plan view Cross-section Cross-section

37. Schematic mountain glacier Detailed section Detailed section Terminus Terminus

38. Example – Malaspina Glacier Note accommodation of Malaspina and Agassiz glaciers into increasing space Note accommodation of Malaspina and Agassiz glaciers into increasing space Longitudinal compression Longitudinal compression

39. Unsteady Flow I Flow is NOT constant Flow is NOT constant Varies with season (snow load increases the strain rate) Varies with season (snow load increases the strain rate) Varies with bed resistance = f(water)? Varies with bed resistance = f(water)? Varies unpredictably! Varies unpredictably!

40. Unsteady Flow II - Ogives

41. Unsteady Flow III – Kinematic Waves Thickening increases depth linearly Thickening increases depth linearly Depth increases stress linearly Depth increases stress linearly Stress increases strain (flow) exponentially Stress increases strain (flow) exponentially Therefore, a pulse propagates through the glacier Therefore, a pulse propagates through the glacier

42. Unsteady Flow IV – Surges Many glaciers (~10%) surge Many glaciers (~10%) surge Stagnant for years Stagnant for years Increase in thickness Increase in thickness Surge! Surge! Decouple from the bed? Decouple from the bed? Surface fracturing Surface fracturing Thrusting? Thrusting?

43. Glacier movement “Normal” glacier speeds ~ 0.5 m – >300 m / yr “Normal” glacier speeds ~ 0.5 m – >300 m / yr Surging glaciers: fast moving Surging glaciers: fast moving up to 110 m / day up to 110 m / day (Kutiah Glacier, Pakistan – 11 km in 3 months) (Kutiah Glacier, Pakistan – 11 km in 3 months) lasts 2 – 3 years lasts 2 – 3 years Hubbard Glacier, 1987 – Alaska Hubbard Glacier, 1987 – Alaska went from ~30–100 m / yr  5 km / yr went from ~30–100 m / yr  5 km / yr causes causes

44. Glacier movement “Normal” glacier speeds ~ 0.5 m – >300 m / yr “Normal” glacier speeds ~ 0.5 m – >300 m / yr Surging glaciers: fast moving – 100s of m / day Surging glaciers: fast moving – 100s of m / day causes – not certain / more than one cause causes – not certain / more than one cause polar glacier becomes uncoupled from bed polar glacier becomes uncoupled from bed stagnant ice dams up water in back, and floats the glacier; when water drains out, the surge stops stagnant ice dams up water in back, and floats the glacier; when water drains out, the surge stops heavy precip = more accumulation heavy precip = more accumulation heavy avalanches = more accumulation heavy avalanches = more accumulation silting up of glacial tunnels and floating glacier – lots of lakes on surfaces before surge movement silting up of glacial tunnels and floating glacier – lots of lakes on surfaces before surge movement

45. Surging Terminus

46. Summary of Flow Process I

47. Summary of Flow Process II

48. One more thing … Prediction of ice-sheet profiles (Nye, 1952) Prediction of ice-sheet profiles (Nye, 1952) Assume ice is a perfect plastic Assume ice is a perfect plastic yield strength ~ 100 kPa (± 50 kPa) yield strength ~ 100 kPa (± 50 kPa) horizontal bed horizontal bed altitude of ice surface at s inland from margin altitude of ice surface at s inland from margin h = (2 h 0 s) 0.5 h = (2 h 0 s) 0.5 h 0 =  /  i g  11  h = (22 s) 0.5 h 0 =  /  i g  11  h = (22 s) 0.5 all in meters (can add sin  term for sloping bed?) all in meters (can add sin  term for sloping bed?) predicts parabolic profile predicts parabolic profile Good (not perfect) agreement with observed profiles Good (not perfect) agreement with observed profiles

49. Remember – flow is one-way!