Mountain glacier flow modelling:

1. Martina Schäfer 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

2. Martina Schäfer Overview  Models   Objectives   First runs   Conclusions   Outlook  ! preliminary !

3. Martina Schäfer Models

4. Martina Schäfer Models (1) inverse model geometric variations of the glacier surface Model mass balance other parameters initial surface sliding law bedrock T,, ... deformation law

5. Martina Schäfer a velocities q2 q1 climat, MB ice flow Models (2) • Basics H/t? vd + vb

6. Martina Schäfer glacier flow profile deformation sliding depth Models (3) • Velocities • given by • quasistatique equilibrium • deformation law • sliding law • boundary conditions vd + vb

7. Martina Schäfer Models (4) • 4 models are compared differing in • simplifications of the equations • implementation vd + vb

8. Martina Schäfer Ice sheet [H] aspect ratio = [L] alpin glacier [L] [L] [H] [H] =10-2 – 10 -3 =100 – 10 -1 if  small : • Simplification of the equations SIA basics • Shallow Ice Approximation (SIA) • used for Antartica (Ice sheets) • used for some alpine glaciers for any characteristics horizontal gradients are neglected compared to vertical ones

9. Martina Schäfer 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

10. Martina Schäfer 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

11. Martina Schäfer Objectives

12. Martina Schäfer Argentière Cotopaxi Saint Sorlin Objectives ? Which model can be used for which type of glacier ?

13. Martina Schäfer Argentière Cotopaxi Saint Sorlin Objectives ? Which model can be used for which type of glacier ? • precision needed • role of deformation • role of sliding • role of mass balance • CPU time?

14. Martina Schäfer First runs

15. Martina Schäfer slope zoom 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

16. Flattened hemi-sphere (2) Martina Schäfer slope • globalgeometry(without MB50years) F longer than MHO thicker than SIA to be done

17. Flattened hemi-sphere (3) Martina Schäfer ? profile snout positions:F -1200 M -1150 HO -1000SIA too long, deforms too fast(effect of neglected longitudinal stresses composants)

18. Flattened hemi-sphere (4) Martina Schäfer zoom • initial surfacevelocities u(indep. of MB) u

19. Flattened hemi-sphere (5) Martina Schäfer zoom • initial velocityprofile(indep. of MB) v u u ? v same shape, but up to a factor 10 too big in SIA models,same results for u, v and w,confirmes difference in geometry

20. Flattened hemi-sphere (6) Martina Schäfer • 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

21. Martina Schäfer Conic bedrock (volcan) (1) • conic bedrock, “Cotopaxi-like” • glacier from 4800m to 5800m,nearly const. ice-thicness of 40m • crater of 800m of diameterwithout 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

22. Conic bedrock (volcan) (3) Martina Schäfer • geometryno MB, 50years SIA too long, deforms too fast; depending on thebedrock slope

23. Conic bedrock (volcan) (1) Martina Schäfer ? • surface velocitiesno MB, 50yearsradial velocity SIA too long, deforms too fast; depending on the bedrock slope same results as beforbutdependence on bedrock slope

24. Martina Schäfer Conclusions

25. Martina Schäfer Conclusions • 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

26. Martina Schäfer outlook

27. Martina Schäfer 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

28. ! Thank you for your !! attention !