Elmer/Ice Chinese-Finnish seminar, October 30 th 2012
NEW GENERATION ICE SHEET MODELS Shallow ice approximation is so 80 s! Thomas Zwinger 1) and... 1) CSC IT Center for Science Ltd. Espoo, Finland
... CSC: Juha Ruokolainen, Peter Råback, Mikko Lyly (now ABB) and Mika Malinen Arctic Centre, Rovaniemi: Martina Schäfer, John Moore (BNU/GCESS) BAS: Carlos Martin, Richard Hindmarsh BNU/GCESS: Liyun Zhao, John Moore ILTS, Univ. of Hokkaido, Sapporo: Hakime Seddik, Ralf Greve LGGE, UJF, Grenoble: Olivier Gagliardini, Fabien Gillet- Chaulet, Gaël Durand, Lionel Favier, Basile de Fleurian, Manu le Meur Univ. Swansea: Sue Cook, Ian Rutt Univ. Uppsala: Josefin Ahlkrona, Jonas Thies
The Big Picture Until recently no ice sheet model (ISM) capable of correctly dealing with the marine ice sheet (MIS) problem (IPPC AR4) Tightly linked to MIS: calving Currently no deeper understanding of basal sliding processes Influence of anisotropy in ice flow Glaciers in warming climates show cases
The Big Picture Greenland Sea level rise equivalent: ~7 m Antarctica Sea level rise equivalent: ~56 m
The Big Picture 5.11.2012 6
Ice Flow Dynamics Incompressible fluid (if firn is neglected) Small Froude number limit Stokes stress gradient = gravity Non-linear flow law Kinematic BC at free surface change in volume + ice flux = SMB
Why Full Stokes? Stokes in 3D : 4DOFs (u,v,w,p) Expensive! Greenland ice sheet (GIS): 1.7x10 6 km 2 500 m resolution -> 6x10 6 horizontal cells Approximations to the Stokes equation
Why Full Stokes? Shallow Ice Approximation (SIA) and Shallow Shelf Approximation (SSA) SIA: Only vertical stresses Continuity Equation elliptic Simplyfied momentum balance (PDE)
Why Full Stokes? Ice sheets and even glaciers are much longer than thick; generally SIA holds Limits of SIA and SSA: Everywhere where ε 0 does not hold
Elmer/Ice Elmer (open source FEM code) with additional routines (sliding, flowlaw,...) by CSC Usual settings: linear elements and standard Galerkin with Stabilized Finite Elements (semi)-lagrangian methods for convection E.g. Age/depth: Flow law viscosity changes by order of magnitudes bad conditioned system: Enhanced linear algebra http://elmerice.elmerfem.org
Marine Ice Sheets Ice sheet that terminates at sea Ice that passes the grounding line (GL) contributes to sea level rise (SLR) Pattyn & Naruse (2003) J. Glacio., 49, 166
Marine Ice Sheets Sudden change of stress field at GL boundary layer Layer of a few ice thicknesses where all stress components are important Either special flux condition Or full Stokes with ~200m grid Schoof, C. 2007. Marine ice sheet dynamics. Part 1: The case of rapid sliding. J. Fluid Mech., 573, 27-55 Schoof, C. 2011. Marine ice sheet dynamics. Part 2: A Stokes Flow contact problem. J. Fluid Mech., 679, 122 255.
(Mesh) Size matters Different steady states depending on resolution Consistent for Marine Ice Sheets G. Durand, O. Gagliardini, T. Zwinger, E. Le Meur, and R. Hindmarsh (2009) Full Stokes modeling of marine ice sheets: influence of the grid size, Annals Glaciol., 52, 109-114
Marine Ice Sheets Favier, L., Gagliardini, O., Durand, G., and Zwinger, T.: A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf, The Cryosphere, 6, 101-112, doi:10.5194/tc-6-101-2012, 2012
Sliding Different types of sliding surfaces Till (deforming sediment) Hard rock Strong involvement of bed hydrology Bedrock processes not really understood and hard to determine from observations Inverse Problem: Determine sliding conditions from surface velocities Variational method: use forward model
Sliding Schäfer, M., Zwinger, T., Christoffersen, P., Gillet-Chaulet, F., Laakso, K., Pettersson, R., Pohjola, V. A., Strozzi, T., and Moore, J. C.: Sensitivity of basal conditions in an inverse model: Vestfonna ice cap, Nordaustlandet/Svalbard, The Cryosphere, 6, 771-783, doi:10.5194/tc-6-771-2012, 2012
Calving 5.11.2012 18
Calving Columbia glacier, Alaska, USA Nye formulation Including water level inside crevasses Benn et al. Shift of terminus by 200 m well within the range of observations Highly sensitive to crevasse water depth S. Cook, T. Zwinger, I.C. Rutt, S.O Neel and T. Murray (2011) Testing the effect of water in crevasses on a physically based calving model, Annals Glac. 53,
Discrete particle model Elastic + viscous Brittle behaviour threshold stress Calving Project with AC/UoL (J. Moore) and UNIS (D. Benn) at Univ. Jyväskylä Simulation and visualization by Jan Åström (CSC)
Ice Sheets Mesh refinements with respect to the Hessian matrix of the observed surface velocities Seddik, H., R. Greve, T. Zwinger, F. Gillet-Chaulet and O. Gagliardini. (2011) Simulations of the Greenland ice sheet 100 years into the future with the full Stokes model Elmer/Ice. J. Glaciol., 58(209), 427-440
Anisotropy Mono-crystal strongly anisotropic Arrangement in grains = fabric Fabric influenced by shear history (ice flow) Feedback to ice flow via rheology Picture courtesy O. Gagliardini, UJF, Grenoble
Two models implemented GOLF CAFFE Anisotropy Flow pattern around domes strongly influenced by fabric Influence on age/depth horizonts: Isotropic With CAFFE Seddik H., R. Greve, T. Zwinger, and L. Placidi (2011) A full-stokes ice flow model for the vicinity of Dome Fuji, Antarctica, with induced anisotropy and fabric evolution, The Cryosphere, 5, 495-508
Glaciers on the Third Pole: Gurenheiko glacier Modelled surface mass balance Different climate scenarios Glaciers ΔT=0.02 K/a ΔT=0.05 K/a Work done within visit at BNU/GCESS with Liyun Zhao and John Moore
Glaciers Resolution of features, Midtre Lovénbreen: Prognostic simulation from 1977-2030
Glaciers T. Zwinger and Moore, J. C. (2009) Diagnostic and prognostic simulations with a full Stokes model accounting for superimposed ice of Midtre Lovénbreen, Svalbard, The Cryosphere, 3, 217-229, doi:10.5194/tc-3-217-2009
Conclusions and Outlook Full-Stokes overcomes limitation of approximations (SIA, SSA) Marine ice sheets, fast flow areas, steep glaciers Stokes model runs on continental scale Enhanced physics partly only on synthetic cases (MISMIP tests) Challenge: introduce the advanced physics on the large scale simulations Numerical Glaciology has to utilize High Performance Computing to meet these challenges
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