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IntroductionModel Description
Results
Fracture Propagation in a High-orderIce-flow Model
Sam Pimentel Gwenn Flowers
Department of Earth SciencesSimon Fraser University
Northwest Glaciology Meeting, October 2008
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Aims
develop a sophisticated hydrologically coupled model ofice dynamics in large outlet Arctic glaciers
include high-order stresses (longitudinal stretching andlateral shearing) which play an essential role in thedynamics especially near the margins and when basalsliding is considerable
incorporate glaciohydraulic processes that link surfaceconditions with basal processes
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Aims
develop a sophisticated hydrologically coupled model ofice dynamics in large outlet Arctic glaciers
include high-order stresses (longitudinal stretching andlateral shearing) which play an essential role in thedynamics especially near the margins and when basalsliding is considerable
incorporate glaciohydraulic processes that link surfaceconditions with basal processes
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Aims
develop a sophisticated hydrologically coupled model ofice dynamics in large outlet Arctic glaciers
include high-order stresses (longitudinal stretching andlateral shearing) which play an essential role in thedynamics especially near the margins and when basalsliding is considerable
incorporate glaciohydraulic processes that link surfaceconditions with basal processes
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Aims
develop a sophisticated hydrologically coupled model ofice dynamics in large outlet Arctic glaciers
include high-order stresses (longitudinal stretching andlateral shearing) which play an essential role in thedynamics especially near the margins and when basalsliding is considerable
incorporate glaciohydraulic processes that link surfaceconditions with basal processes
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
IPY Project: Belcher Glacier on Devon Island
Sharing similarities with manyGreenland outlet glaciers, this is alarge, fast-flowing, tidewater glacier.
The Belcher Glacier Systemon the Devon Island Ice Cap
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model Overview
Flow-bandOne horizontal dimension (in the direction of the ice flow), onevertical dimension, and a parameterization of the width acrossthe flowline.
Mass balance, evolving surface
∂h∂t
= − 1W
∂(uhW )
∂x+ M,
h is the ice thicknesst is timeW represents the flowline widthu denotes the vertically averaged horizontal velocityM is the mass balance
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model Overview
Flow-bandOne horizontal dimension (in the direction of the ice flow), onevertical dimension, and a parameterization of the width acrossthe flowline.
Mass balance, evolving surface
∂h∂t
= − 1W
∂(uhW )
∂x+ M,
h is the ice thicknesst is timeW represents the flowline widthu denotes the vertically averaged horizontal velocityM is the mass balance
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model Overview
Flow-bandOne horizontal dimension (in the direction of the ice flow), onevertical dimension, and a parameterization of the width acrossthe flowline.
Mass balance, evolving surface
∂h∂t
= − 1W
∂(uhW )
∂x+ M,
h is the ice thicknesst is timeW represents the flowline widthu denotes the vertically averaged horizontal velocityM is the mass balance
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
High-order stress components
The model incoporates a multilayer longitudinal stressscheme following (Blatter, 1995) and (Pattyn, 2002)
The vertical normal stress is assumed to be hydrostatic
∂σzz
∂z= ρig
with the pressure (the sum of the normal stresses)departing from the hydrostatic pressure by the longitudinaldeviatoric stress P = σ
′xx + σ
′yy − ρig(s − z)
Unlike the full stress solution the pressure doesn’t includethe integrated horizontal gradient in vertical shear stress
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
High-order stress components
The model incoporates a multilayer longitudinal stressscheme following (Blatter, 1995) and (Pattyn, 2002)
The vertical normal stress is assumed to be hydrostatic
∂σzz
∂z= ρig
with the pressure (the sum of the normal stresses)departing from the hydrostatic pressure by the longitudinaldeviatoric stress P = σ
′xx + σ
′yy − ρig(s − z)
Unlike the full stress solution the pressure doesn’t includethe integrated horizontal gradient in vertical shear stress
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
High-order stress components
The model incoporates a multilayer longitudinal stressscheme following (Blatter, 1995) and (Pattyn, 2002)
The vertical normal stress is assumed to be hydrostatic
∂σzz
∂z= ρig
with the pressure (the sum of the normal stresses)departing from the hydrostatic pressure by the longitudinaldeviatoric stress P = σ
′xx + σ
′yy − ρig(s − z)
Unlike the full stress solution the pressure doesn’t includethe integrated horizontal gradient in vertical shear stress
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Thermomechanically coupled
- Solve an advective-diffusive heat equation- Temperature dependent flow-law parameter, as well as
coupling from internal friction from deformational heating
Sliding and Calving rules
- Options for sliding: no-slip, power-laws, Coulomb frictionlaw
- Options for calving: water-depth relation, floatationcriterion, crevasse formation
Coupled hydrology (in progress)
- Vertical fracture propagation- Englacial and subglacial components- Track energy exchange between water and ice
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Thermomechanically coupled
- Solve an advective-diffusive heat equation- Temperature dependent flow-law parameter, as well as
coupling from internal friction from deformational heating
Sliding and Calving rules
- Options for sliding: no-slip, power-laws, Coulomb frictionlaw
- Options for calving: water-depth relation, floatationcriterion, crevasse formation
Coupled hydrology (in progress)
- Vertical fracture propagation- Englacial and subglacial components- Track energy exchange between water and ice
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Thermomechanically coupled
- Solve an advective-diffusive heat equation- Temperature dependent flow-law parameter, as well as
coupling from internal friction from deformational heating
Sliding and Calving rules
- Options for sliding: no-slip, power-laws, Coulomb frictionlaw
- Options for calving: water-depth relation, floatationcriterion, crevasse formation
Coupled hydrology (in progress)
- Vertical fracture propagation- Englacial and subglacial components- Track energy exchange between water and ice
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model performance has been compared with
- benchmark solutions using model intercomparison exercises
- analytical solutions under simplifying assumptions
ISMIP-HOM Experiment E: Haut Glacier d’Arolla
test thevelocity/stresssolution of thenon-linearforce-balanceequations
use fixed geometry
no-slip basal b.c.
isothermalPimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model performance has been compared with
- benchmark solutions using model intercomparison exercises
- analytical solutions under simplifying assumptions
ISMIP-HOM Experiment E: Haut Glacier d’Arolla
test thevelocity/stresssolution of thenon-linearforce-balanceequations
use fixed geometry
no-slip basal b.c.
isothermalPimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Model Comparison
The blue lines show results from the high-order intercomparisonmodels (Pattyn et al., 2008).
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Toy Experiments
Experiment I: Calving
An experiment is tried to test the advance and retreat of amarine glacier.
Experiment II: Fracture Propagation
An experiment is tried to mimic the drainage of a supraglaciallake through fracture propagation to the bed.
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Toy Experiments
Experiment I: Calving
An experiment is tried to test the advance and retreat of amarine glacier.
Experiment II: Fracture Propagation
An experiment is tried to mimic the drainage of a supraglaciallake through fracture propagation to the bed.
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Toy Experiments
Experiment I: Calving
An experiment is tried to test the advance and retreat of amarine glacier.
Experiment II: Fracture Propagation
An experiment is tried to mimic the drainage of a supraglaciallake through fracture propagation to the bed.
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Experiment I: Calving
Calving criterion is basedon crevasse formation(Benn et al., 2007)
Assumes calving istriggered by the downwardpropagation of transversesurface crevasses
These crevasses open inresponse to down-glaciervariations in flow speed(longitudinal strain rates)
Taken from Benn et al., 2007
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Tidewater Outlet Glacier
Calving rate: uc = uT − ∂L∂t
L glacier lengthuT vertically averaged velocity at terminus
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Experiment II: Fracture Propagation
ObservationsSurface meltwater has been observed through water-drivenfracture propagation to reach the bed (Das et al., 2008)
ImportanceThis hydromechanical process creates a mechanism for therapid response of ice flow to climate change
Theoretical BasisLinear elastic fracture mechanics (van der Veen, 2007).
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Fracture Propagation
Taken from van der Veen, 2007
ice fracture toughness = 100 kPatensile stress = 43 kPaice thickness = 1123mwater injection = 1m/hrtime to reach bed = 43 days
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Future Work
Model moulin formation generated by concentrated flowpaths and frictional heating, simulate surface uplift causedby the sudden drainage of meltwater ponds, assess glacierspeed-up as a result of increased lubrication, and monitorthe closure of fractures because of refreezing.
Simulations of Belcher using field data for model inputs(e.g. glacier geometry from GPS and radar surveys; massbalance from long-term measurements; supraglacialdischarge from field observations) and for modelverification (e.g. GPS-derived ice-surface velocities).
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Future Work
Model moulin formation generated by concentrated flowpaths and frictional heating, simulate surface uplift causedby the sudden drainage of meltwater ponds, assess glacierspeed-up as a result of increased lubrication, and monitorthe closure of fractures because of refreezing.
Simulations of Belcher using field data for model inputs(e.g. glacier geometry from GPS and radar surveys; massbalance from long-term measurements; supraglacialdischarge from field observations) and for modelverification (e.g. GPS-derived ice-surface velocities).
Pimentel Fracture in Ice Flow Model
IntroductionModel Description
Results
Questions?
Pimentel Fracture in Ice Flow Model