Martina Schäfer AGM 2007 Zürich 1 Martina Schäfer Martina Schäfer LGGE, Grenoble (France) LGGE, Grenoble (France) Emmanuel Le Meur, Catherine Ritz, Olivier Gagliardini, Frank Pattyn Emmanuel Le Meur, Catherine Ritz, Olivier Gagliardini, Frank Pattyn Mountain glacier flow modelling: a comparison of different models from Shallow Ice Approximation to the Full-Stokes solution
Mountain glacier flow modelling:. a comparison of different models from Shallow Ice Approximation to the Full-Stokes solution. Martina Schäfer LGGE, Grenoble (France) Emmanuel Le Meur, Catherine Ritz, Olivier Gagliardini, Frank Pattyn. Overview. Models Objectives - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Martina Schäfer AGM 2007 Zürich
1
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
Martina Schäfer AGM 2007 Zürich
2
Overview
Models Objectives First runs
Conclusions Outlook
! preliminary
!
Martina Schäfer AGM 2007 Zürich
3
Martina Schäfer AGM 2007 Zürich
4
Models (1)
inverse model
Model
geometric variations of the glacier surface
mass
b
ala
nce
other parameters
bedrock
sliding lawinitial surface
deformation lawT, , ...
Martina Schäfer AGM 2007 Zürich
5
Models (2) Basics
q2q1
climat,
MB
ice flow
a H/t ? velocities
Martina Schäfer AGM 2007 Zürich
6
Models (3) Velocities
given by
quasistatique equilibrium
deformation law
sliding law
boundary conditions
profiledeformation
sliding
glacier flow
depth
Martina Schäfer AGM 2007 Zürich
7
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
Martina Schäfer AGM 2007 Zürich
8
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
Martina Schäfer AGM 2007 Zürich
9
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
Martina Schäfer AGM 2007 Zürich
10
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
Martina Schäfer AGM 2007 Zürich
11
Martina Schäfer AGM 2007 Zürich
12
Objectives? Which model can be used for which type of
glacier ?Cotopaxi
Saint Sorlin
Argentière
Martina Schäfer AGM 2007 Zürich
13
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?
Martina Schäfer AGM 2007 Zürich
14
Martina Schäfer AGM 2007 Zürich
15
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
Martina Schäfer AGM 2007 Zürich
16
Flattened hemi-sphere (2) global
geometry
(without MB
50years)
F longer than M
HO thicker than SIA
slop
e
to b
e do
ne
Martina Schäfer AGM 2007 Zürich
17
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
Martina Schäfer AGM 2007 Zürich
18
Flattened hemi-sphere (4) initial surface
velocities u
(indep. of MB)
zoo
m
u
Martina Schäfer AGM 2007 Zürich
19
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
Martina Schäfer AGM 2007 Zürich
20
Flattened hemi-sphere (6) dependence on the bedrock slope
differences in geometry and velocities independent of