agm 2007 zürich1 martina schäfer lgge, grenoble (france) emmanuel le meur, catherine ritz, olivier...
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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
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! Thank you for your !! attention !