AGM 2007 Zürich1 Martina Schäfer LGGE, Grenoble (France) Emmanuel Le Meur, Catherine Ritz, Olivier...

Martina Schäfer AGM 2007 Zürich

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Martina SchäferMartina SchäferLGGE, Grenoble (France)LGGE, Grenoble (France)

Emmanuel Le Meur, Catherine Ritz, Olivier Gagliardini, Frank Emmanuel Le Meur, Catherine Ritz, Olivier Gagliardini, Frank PattynPattyn

Mountain glacier flow modelling:

a comparison of different models from Shallow Ice

Approximation to the Full-Stokes solution


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Overview

Models Objectives First runs

Conclusions Outlook

! preliminary

!


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Models (1)

inverse model

Model

geometric variations of the glacier surface

mass

b

ala

nce

other parameters

bedrock

sliding lawinitial surface

deformation lawT, , ...


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Models (2) Basics

q2q1

climat,

MB

ice flow

a H/t ? velocities


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Models (3) Velocities

given by

quasistatique equilibrium

deformation law

sliding law

boundary conditions

profiledeformation

sliding

glacier flow

depth


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Models (4) 4 models are compared differing in

simplifications of the equations

implementation

M SIA Le Meur and Vincent, 2003 SIA, 0th order

F SIA Pattyn, 2003 SIA, 0th order

F HO Pattyn, 2003 HO

Elmer www.csc.fi/elmer Full Stokes


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SIA basics Shallow Ice Approximation (SIA)

used for Antartica (Ice sheets)

used for some alpine glaciers

Ice sheet

[H]

[L]

=10-2 – 10 -3

[H]

[L]

alpin glacier

=100 – 10 -1

[H]aspect ratio =

[L]

Simplification of the equations

if small : for any characteristics

horizontal gradients are

neglected compared to vertical

ones


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SIA models used Two models are compared

Different implementations of the SIA (zeroth-order)

Le Meur and Vincent, 2003 (M)

Pattyn, 2003 (F,SIA)

Main difference

Le Meur: analytical velocities and fluxes, matrix equation for

new surface

Pattyn: numerical velocities and directly new surface


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Other models used Higher Order Model

Pattyn, 2003 (F,HO)

Less simplifications than in the SIA (0th-order)

Hydrostatical approximation

Horizontal gradients of the vertical velocity are small

compared to the vertical gradient of the horizontal

velocity

Full Stokes Model

Elmer (finite element model)

“No” simplifications


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Objectives? Which model can be used for which type of

glacier ?Cotopaxi

Saint Sorlin

Argentière


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Objectives? Which model can be used for which type of

glacier ?Cotopaxi

Saint Sorlin

Argentière

precision needed

role of deformation

role of sliding

role of mass balance

CPU time?


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Flattened hemi-sphere (1) axisymmetric glacier, flattened hemi-sphere on a

ramp of uniform slope

radius 500m

flattened: max. ice-thicness 150m

slope varies from 0 to 0.3

with and without mass balance (spheric, center

downhill)

initial and final surface velocity field, velocity profile

in one point, global geometry and snout position

slop

e

zoom


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Flattened hemi-sphere (2) global

geometry

(without MB

50years)

F longer than M

HO thicker than SIA

slop

e

to b

e do

ne


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Flattened hemi-sphere (3)

?snout positions:F -1200

M -1150

HO -1000

SIA too long, deforms too fast

(effect of neglected longitudinal stresses composants)

profile


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Flattened hemi-sphere (4) initial surface

velocities u

(indep. of MB)

zoo

m

u


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Flattened hemi-sphere (5) initial velocity

profile

(indep. of MB)

? same shape, but up to a

factor 10 too big in SIA

models,

same results for u, v and

w,

confirmes difference in

geometry

zoo

m

u

v

u

v


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Flattened hemi-sphere (6) dependence on the bedrock slope

differences in geometry and velocities independent of

bedrock slope

importance of surface slope

velocities after 50years

better agreement

velocities closer to equilibrium with geometry

with mass balance

better agreement in geometry

no amelioration for velocities

effect of mass balance dominates deformation


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Conic bedrock (volcan) (1) conic bedrock, “Cotopaxi-like”

glacier from 4800m to 5800m,

nearly const. ice-thicness of 40m

crater of 800m of diameter

without ice and zero mass balance

slope varies from 0.3 to 0.8

(real case 0.55)

mass balance “Antisana-like”:

linear from the snout to the EL and linear from the EL to the

summit, zero in the crater

initial and final surface velocity field, velocity profile in

one point, global geometry and snout position


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Conic bedrock (volcan) (3) geometry

no MB, 50years

SIA too long,

deforms too fast;

depending on the

bedrock slope


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Conic bedrock (volcan) (1) surface velocities

no MB, 50years

radial velocity

SIA too long,

deforms too fast;

depending on the

bedrock slope

?

same results as befor

but

dependence on bedrock

slope


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deformation is too fast with SIA models

velocities overestimated

surface too large

but: dominated by mass balance

dependence on the geometry of the glacier and its

bedrock

volcano glacier flat -> depending on the slope of the bedrock

spherical glacier -> its own aspect ratio is too important, no

dependence on the bedrock

Conclusions


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Outlook Finish the theoretical experiences

role of the mass balance

including sliding

including CPU time comparison

valley glacier shaped glacier

Real case experiences

Cotopaxi (volcano in Ecuador, measurements in January 2007)

Saint Sorlin (France, a lot of work is already done with a SIA model)

Open questions

which type of model should be used on on which type of glacier ?

comparison of CPU time and precision

AGM 2007 Zürich

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! Thank you for your !! attention !

AGM 2007 Zürich1 Martina Schäfer LGGE, Grenoble (France) Emmanuel Le Meur, Catherine Ritz, Olivier...

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