Fracture Propagation in a High-order Ice-flow Model · Pimentel Fracture in Ice Flow Model. Introduction Model Description Results Future Work Model moulin formation generated by

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


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



Results

Aims






Results

Aims






Results

Aims






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



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



Results

Model Overview



∂h∂t

= − 1W

∂(uhW )

∂x+ M,




Results

Model Overview



∂h∂t

= − 1W

∂(uhW )

∂x+ M,




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



Results




∂σzz

∂z= ρig


′xx + σ





Results




∂σzz

∂z= ρig


′xx + σ





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



Results











Results











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


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


Results

Model Comparison

The blue lines show results from the high-order intercomparisonmodels (Pattyn et al., 2008).



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.



Results

Toy Experiments







Results

Toy Experiments







Results


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



Results

Tidewater Outlet Glacier

Calving rate: uc = uT − ∂L∂t

L glacier lengthuT vertically averaged velocity at terminus



Results


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).



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



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).



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).



Results

Questions?


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Fracture Propagation in a High-order Ice-flow Model · Pimentel Fracture in Ice Flow Model. Introduction Model Description Results Future Work Model moulin formation generated by