Dynamics of Ice Sheets and Glaciers (eBook)

Preface 7
Acknowledgements 9
Contents 11
Ice in the Climate System 15
The Terrestrial Cryosphere 15
Land Ice on the Present-Day Earth 15
An Excursion into the Past 17
Ice Sheets, Glaciers and Global Warming 18
Vectors, Tensors and Their Representation 21
Definition of a Vector, Basic Properties 21
Representation of Vectors as Number Triples 23
Tensors of Order 2 24
Higher Order Tensors 27
Vector and Tensor Analysis 28
Elements of Continuum Mechanics 31
Bodies and Configurations 31
Kinematics 32
Deformation Gradient, Stretch Tensors 32
Velocity, Acceleration, Velocity Gradient 35
Balance Equations 39
Reynolds' Transport Theorem 39
General Balance Equation 40
General Jump Condition 42
Mass Balance 43
Momentum Balance 44
Balance of Angular Momentum 47
Energy Balance 48
Constitutive Equations 51
Homogeneous Viscous Thermoelastic Bodies 51
Linear Elastic Solid 52
Newtonian Fluid 57
Constitutive Equations for Polycrystalline Ice 63
Microstructure of Ice 63
Creep of Polycrystalline Ice 64
Flow Relation 66
Glen's Flow Law 66
Regularised Glen's Flow Law 70
Smith-Morland Flow Law 71
Flow Enhancement Factor 72
Heat Flux and Internal Energy 73
Elasticity 74
Large-Scale Dynamics of Ice Sheets 75
Full Stokes Flow Problem 75
Field Equations 75
Boundary Conditions 79
Ice Thickness Equation 84
Hydrostatic Approximation 86
First Order Approximation 89
Shallow Ice Approximation 91
Driving Stress 97
Analytical Solutions 98
Simplified Problem 98
Vialov Profile 1
Bueler Profile 101
Numerical Methods 104
Terrain-Following Coordinate Transformation 105
Plane Strain Shallow Ice Equations 108
Discretised Ice Sheet Equations 111
Example: The EGIG Line of the Greenland Ice Sheet 117
Large-Scale Dynamics of Ice Shelves 124
Full Stokes Flow Problem 124
Field Equations, Boundary Conditions at the Free Surface 124
Boundary Conditions at the Ice Base 125
Boundary Conditions at the Grounding Line and Calving Front 127
Hydrostatic Approximation 129
Shallow Shelf Approximation 130
Ice Shelf Ramp 139
Numerical Methods 144
Mechanical Ice Shelf Problem 144
Weak Formulation 145
Discretisation of the Ice Shelf Domain 146
Galerkin Finite Element Method 148
Iteration 153
Example: The Ross Ice Shelf 154
Dynamics of Glacier Flow 157
Glaciers Versus Ice Sheets 157
Parallel Sided Slab 158
Scaling Arguments and Hierarchy of Approximations 163
First Order Plane Strain Approximation 167
Basal Sliding 169
General Remarks 169
Mean Sliding over Rough Hard Beds 170
Soft Beds on Sediment Layers 174
Numerical Methods for the Stress and Velocity Fields 176
Method of Lines 176
Global Discretisation Schemes 179
Vertical Velocity Component 184
Trajectories 186
Transverse First Order Flow Profiles 187
Applications and Limitations of Glacier Models 190
Information on Glaciers 190
Inverse Problems 191
The Shallowness of Glaciers 192
Discontinuities 195
Glacial Isostasy 197
Background 197
Structure of the Earth 199
Simple Isostasy Models 200
LLRA Model 200
ELRA Model 202
LLDA Model 204
ELDA Model 207
Analytical Solution for the Local Lithosphere 207
Numerical Methods 209
Local Lithosphere 209
Elastic Lithosphere 209
Relaxing Asthenosphere 210
Diffusive Asthenosphere 210
Model Intercomparison 211
Advanced Topics 214
Induced Anisotropy 214
Background 214
Anisotropic Generalisation of Glen's Flow Law 215
Proof of Anisotropy for the CAFFE Flow Law 220
Some Examples 222
Evolution of Anisotropy 228
Application to the EDML Core, Antarctica 231
Compressible Firn 235
Background 235
Densification of Firn 235
Constitutive Relation for Firn 237
Field Equations 239
Parallel Sided Slab 241
Temperate and Polythermal Glaciers 248
Background 248
Temperate Ice 248
Temperate Ice Surface 251
Temperate Ice Base 251
Transition Conditions at the CTS 253
Parallel Sided Polythermal Slab 257
Polythermal Glaciers 264
Enthalpy Formulation 266
Conclusions, Summary and Outlook 271
Errata to: Dynamics of Ice Sheets and Glaciers 273
References Cited or Recommended 276
List of Symbols 286
List of Acronyms 292
Index 294