The Physics of Glaciers

The Physics of Glaciers, Fourth Edition, discusses the physical principles that underlie the behavior and characteristics of glaciers. The term glacier refers to all bodies of ice created by the accumulation of snowfall, e. g. , mountain glaciers, ice caps, continental ice sheets, and ice shelves. Glaciology-the study of all forms of ice-is an interdisciplinary field encompassing physics, geology, atmospheric science, mathematics, and others. This book covers various aspects of glacier studies, including the transformation of snow to ice, grain-scale structures and ice deformation, mass exchange processes, glacial hydrology, glacier flow, and the impact of climate change. The present edition features two new chapters: "Ice Sheets and the Earth System and "Ice, Sea Level, and Contemporary Climate Change. The chapter on ice core studies has been updated from the previous version with new material. The materials on the flow of mountain glaciers, ice sheets, ice streams, and ice shelves have been combined into a single chapter entitled "The Flow of Ice Masses.

• Completely updated and revised, with 30% new material including climate change
• Accessible to students, and an essential guide for researchers
• Authored by preeminent glaciologists

1;Front Cover;1 2;Title Page;2 3;Copyright Page;3 4;Table of Contents;4 5;Preface to Fourth Edition;12 6;Preface to First Edition;13 7;Chapter 1. Introduction;14 7.1;1.1 Introduction;14 7.2;1.2 History and Perspective;15 7.3;1.3 Organization of the Book;19 7.4;Further Reading;22 8;Chapter 2. Transformation of Snow to Ice;24 8.1;2.1 Introduction;24 8.2;2.2 Snow, Firn, and Ice;24 8.2.1;2.2.1 Density of Ice;25 8.3;2.3 Zones in a Glacier;26 8.3.1;2.3.1 Distribution of Zones;28 8.4;2.4 Variation of Density with Depth in Firn;29 8.5;2.5 Snow to Ice Transformation in a Dry-snow Zone;32 8.5.1;2.5.1 Processes;32 8.5.2;2.5.2 Models of Density Profiles in Dry Firn;35 8.5.3;2.5.3 Reduction of Gas Mobility;38 8.6;2.6 Hoar Layers;39 8.7;2.7 Transformation When Meltwater Is Present;40 8.8;Further Reading;41 9;Chapter 3. Grain-Scale Structures and Deformation of Ice;42 9.1;3.1 Introduction;42 9.2;3.2 Properties of a Single Ice Crystal;43 9.2.1;3.2.1 Structure;43 9.2.2;3.2.2 Deformation of a Single Crystal;45 9.3;3.3 Polycrystalline Ice: Grain-scale Forms and Processes;46 9.3.1;3.3.1 Orientation Fabrics: Brief Description;46 9.3.2;3.3.2 Impurities and Bubbles;46 9.3.3;3.3.3 Texture and Recrystallization;48 9.3.4;3.3.4 Formation of C-axis Orientation Fabrics;56 9.3.5;3.3.5 Mechanisms of Polycrystalline Deformation;61 9.4;3.4 Bulk Creep Properties of Polycrystalline Ice;64 9.4.1;3.4.1 Strain Rate and Incompressibility;64 9.4.2;3.4.2 Deviatoric Stress;65 9.4.3;3.4.3 Bench-top Experiments: The Three Phases of Creep;65 9.4.4;3.4.4 Isotropic Creep Behavior;67 9.4.5;3.4.5 Controls on Creep Parameter A;77 9.4.6;3.4.6 Recommended Isotropic Creep Relation and Values for A;85 9.4.7;3.4.7 Anisotropic Creep of Ice;91 9.5;3.5 Elastic Deformation of Polycrystalline Ice;101 9.6;Appendix 3.1;101 9.7;Appendix 3.2: Data for Figure 3.16;102 10;Chapter 4. Mass Balance Processes: 1. Overview and Regimes;104 10.1;4.1 Introduction;104 10.1.1;4.1.1 Notes on Terminology;107 10.2;4.2 Surface Mass Balance;109
10.2.1;4.2.1 Surface Accumulation Processes;109 10.2.2;4.2.2 Surface Ablation Processes;112 10.2.3;4.2.3 Annual (Net) Balance and the Seasonal Cycle;113 10.2.4;4.2.4 Annual Glacier Balance and Average Specific Balances;115 10.2.5;4.2.5 Variation of Surface Balance with Altitude;115 10.2.6;4.2.6 Generalized Relation of Surface Balance to Temperature and Precipitation;117 10.2.7;4.2.7 Relation of Glacier-wide Balance to the Area-Altitude Distribution;121 10.3;4.3 Mass Balance Variations of Mountain Glaciers;122 10.3.1;4.3.1 Interannual Fluctuations of Balance;122 10.3.2;4.3.2 Cumulative Balance and Delayed Adjustments;124 10.3.3;4.3.3 Regional Variations of Mass Balance;126 10.4;4.4 Englacial Mass Balance;128 10.4.1;4.4.1 Internal Accumulation;128 10.4.2;4.4.2 Internal Ablation;128 10.5;4.5 Basal Mass Balance;129 10.5.1;4.5.1 Basal Accumulation;129 10.5.2;4.5.2 Basal Ablation;131 10.6;4.6 Mass Loss by Calving;134 10.6.1;4.6.1 The Calving Spectrum;135 10.6.2;4.6.2 Calving from Tidewater Glaciers;136 10.6.3;4.6.3 Calving from Ice Shelves;137 10.6.4;4.6.4 Calving Relations for Ice Sheet Models;140 10.7;4.7 Methods for Determining Glacier Mass Balance;140 10.8;4.8 Mass Balance Regimes of the Ice Sheets;144 10.8.1;4.8.1 Greenland Ice Sheet;144 10.8.2;4.8.2 Antarctic Ice Sheet;147 10.9;Further Reading;149 11;Chapter 5. Mass Balance Processes: 2. Surface Ablation and Energy Budget;150 11.1;5.1 Introduction;150 11.1.1;5.1.1 Radiation;151 11.1.2;5.1.2 Energy Budget of Earths Atmosphere and Surface;151 11.2;5.2 Statement of the Surface Energy Budget;153 11.2.1;5.2.1 Driving and Responding Factors in the Energy Budget;154 11.2.2;5.2.2 Melt and Warming Driven by Net Energy Flux;154 11.3;5.3 Components of the Net Energy Flux;155 11.3.1;5.3.1 Downward Shortwave Radiation;156 11.3.2;5.3.2 Reflected Shortwave Radiation;158 11.3.3;5.3.3 Longwave Radiation;161 11.3.4;5.3.4 Field Example, Net Radiation Budget;161 11.3.5;5.3.5 Subsurface Conduction and Radiation;163 11.3.6;5.3.6 Turbulen
t Fluxes;165 11.4;5.4 Relation of Ablation to Climate;173 11.4.1;5.4.1 Calculating Melt from Energy Budget Measurements;173 11.4.2;5.4.2 Simple Approaches to Modelling Melt;175 11.4.3;5.4.3 Increase of Ablation with Warming;178 11.4.4;5.4.4 Importance of the Frequency of Different Weather Conditions;181 11.4.5;5.4.5 Energy Budget Regimes;182 11.5;Further Reading;186 12;Chapter 6. Glacial Hydrology;188 12.1;6.1 Introduction;188 12.1.1;6.1.1 Permeability of Glacier Ice;189 12.1.2;6.1.2 Effective Pressure;190 12.2;6.2 Features of the Hydrologic System;190 12.2.1;6.2.1 Surface (Supraglacial) Hydrology;191 12.2.2;6.2.2 Englacial Hydrology;192 12.2.3;6.2.3 Subglacial Hydrology;194 12.2.4;6.2.4 Runoff from Glaciers;198 12.3;6.3 The Water System within Temperate Glaciers;207 12.3.1;6.3.1 Direction of Flow;207 12.3.2;6.3.2 Drainage in Conduits;210 12.3.3;6.3.3 Drainage in Linked Cavities;218 12.3.4;6.3.4 Subglacial Drainage on a Soft Bed;222 12.3.5;6.3.5 Summary of Water Systems at the Glacier Bed;225 12.3.6;6.3.6 System Behavior;227 12.4;6.4 Glacial Hydrological Phenomena;229 12.4.1;6.4.1 Jökulhlaups;229 12.4.2;6.4.2 Antarctic Subglacial Lakes;233 12.5;Further Reading;235 13;Chapter 7. Basal Slip;236 13.1;7.1 Introduction;236 13.1.1;7.1.1 Measurements of Basal Velocity;237 13.1.2;7.1.2 Local vs. Global Control of Basal Velocity ;239 13.2;7.2 Hard Beds;242 13.2.1;7.2.1 Weertmans Theory of Sliding;242 13.2.2;7.2.2 Observations at the Glacier Sole;246 13.2.3;7.2.3 Improvements to Weertmans Analysis;247 13.2.4;7.2.4 Discussion of Assumptions;249 13.2.5;7.2.5 Comparison of Predictions with Observations;250 13.2.6;7.2.6 How Water Changes Sliding Velocity on Hard Beds;251 13.2.7;7.2.7 Sliding of Debris-laden Ice;263 13.2.8;7.2.8 Sliding at Sub-Freezing Temperatures;266 13.2.9;7.2.9 Hard-bed Sliding: Summary and Outlook;267 13.3;7.3 Deformable Beds;268 13.3.1;7.3.1 Key Observations;269 13.3.2;7.3.2 Till Properties and Processes;270 13.3.3;7.3.3 Constitutive Behaviors;277 13.3.4;7.3
.4 Slip Rate ub on a Deformable Bed;282 13.3.5;7.3.5 Large-scale Behavior of Soft Beds;286 13.3.6;7.3.6 Continuity of Till;290 13.3.7;7.3.7 Additional Geological Information;292 13.4;7.4 Practical Relations for Basal Slip and Drag;293 13.5;Further Reading;296 14;Chapter 8. The Flow of Ice Masses;298 14.1;8.1 Introduction;298 14.1.1;8.1.1 Ice Flux;299 14.1.2;8.1.2 Balance Velocities;301 14.1.3;8.1.3 Actual Velocities;302 14.1.4;8.1.4 How Surface Velocities Are Measured;306 14.2;8.2 Driving and Resisting Stresses;308 14.2.1;8.2.1 Driving Stress and Basal Shear Stress;308 14.2.2;8.2.2 Additional Resisting Forces and the Force Balance;312 14.2.3;8.2.3 Factors Controlling Resistance and Flow;314 14.2.4;8.2.4 Effective Driving Force of a Vertical Cliff;320 14.3;8.3 Vertical Profiles of Flow;322 14.3.1;8.3.1 Parallel Flow;322 14.3.2;8.3.2 Observed Complications in Shear Profiles;324 14.4;8.4 Fundamental Properties of Extending and Compressing Flows;328 14.4.1;8.4.1 General Concepts;328 14.4.2;8.4.2 Uniform Extension or Compression;330 14.5;8.5 General Governing Relations;332 14.5.1;8.5.1 Local Stress-equilibrium Relations;333 14.5.2;8.5.2 General Solutions for Stress and Velocity;334 14.5.3;8.5.3 Vertically Integrated Force Balance;335 14.5.4;8.5.4 General Mass Conservation Relation (Equation of Continuity);343 14.5.5;8.5.5 Vertically Integrated Continuity Equations;344 14.6;8.6 Effects of Valley Walls and Shear Margins;351 14.6.1;8.6.1 Transverse Velocity Profile Where Basal Resistance Is Small;352 14.6.2;8.6.2 Combined Effects of Side and Basal Resistances;353 14.7;8.7 Variations Along a Flow Line;359 14.7.1;8.7.1 Factors Controlling Longitudinal Strain Rate;359 14.7.2;8.7.2 Local-scale Variation: Longitudinal Stress-gradient Coupling;360 14.7.3;8.7.3 Large-Scale Variation;364 14.8;8.8 Flow at Tidewater Margins;366 14.8.1;8.8.1 Theory;366 14.8.2;8.8.2 Observations: Columbia Glacier;368 14.9;8.9 Ice Sheets: Flow Components;369 14.9.1;8.9.1 Flow at a Divide;370 14.9.2;8.9.
2 Ice Streams;373 14.9.3;8.9.3 Ice Shelves;386 14.9.4;8.9.4 Transition Zone Between Grounded and Floating Ice;397 14.9.5;8.9.5 Flow Over Subglacial Lakes;398 14.10;8.10 Surface Profiles of Ice Sheets;398 14.10.1;8.10.1 Profile Equations;398 14.10.2;8.10.2 Other Factors Influencing Profiles;403 14.10.3;8.10.3 Relation Between Ice Area and Volume;408 14.10.4;8.10.4 Travel Times;409 14.10.5;8.10.5 Local-scale Relation of Surface and Bed Topography;410 14.11;Further Reading;411 15;Chapter 9. Temperatures in Ice Masses;412 15.1;9.1 Introduction;412 15.2;9.2 Thermal Parameters of Ice and Snow;413 15.3;9.3 Temperature of Surface Layers;414 15.4;9.4 Temperate Glaciers;418 15.4.1;9.4.1 Ice Temperature;418 15.4.2;9.4.2 Origin and Effect of Water;420 15.4.3;9.4.3 Distribution of Temperate Glaciers;421 15.5;9.5 Steady-state Temperature Distributions;422 15.5.1;9.5.1 Steady-state Vertical Temperature Profile;422 15.6;9.6 Measured Temperature Profiles;426 15.7;9.7 General Equation of Heat Transfer;429 15.7.1;9.7.1 Derivation of Equation;429 15.7.2;9.7.2 Boundary and Basal Conditions;432 15.8;9.8 Temperatures Along a Flow Line;433 15.8.1;9.8.1 Observations;434 15.9;9.9 Time-varying Temperatures;436 15.10;9.10 Temperatures in Ice Shelves;439 16;Chapter 10. Large-Scale Structures;442 16.1;10.1 Introduction;442 16.2;10.2 Sedimentary Layers;443 16.3;10.3 Foliation;443 16.3.1;10.3.1 Elongate Bubble Forms;447 16.3.2;10.3.2 Finite Strain;447 16.4;10.4 Folds;449 16.4.1;10.4.1 Folding in Central Regions of Ice Sheets;451 16.5;10.5 Boudinage;451 16.6;10.6 Faults;453 16.7;10.7 Implications for Ice Core Stratigraphy;454 16.8;10.8 Ogives and Longitudinal Corrugations;456 16.9;10.9 Crevasses;458 16.9.1;10.9.1 Patterns and Conditions for Occurrence;458 16.9.2;10.9.2 Crevasse Depth and Propagation;462 16.9.3;10.9.3 Related Tensional Features;464 16.10;10.10 Structural Assemblages;465 16.11;Further Reading;465 17;Chapter 11. Reaction of Glaciers to Environmental Changes;466 17.1;11.1 Introduction;
466 17.2;11.2 Reaction to Changes of Mass Balance: Scales;467 17.2.1;11.2.1 Net Change of Glacier Length;468 17.2.2;11.2.2 Simple Models for Response;469 17.2.3;11.2.3 Simple Models for Different Zones;474 17.3;11.3 Reaction to Changes of Mass Balance: Dynamics;477 17.3.1;11.3.1 Theoretical Framework;477 17.3.2;11.3.2 Ice Thickness Changes;482 17.3.3;11.3.3 Relative Importance of Diffusion and Kinematic Waves;489 17.3.4;11.3.4 Numerical Models of Glacier Variation;490 17.4;11.4 Reactions to Additional Forcings;496 17.4.1;11.4.1 Response of Glaciers to Ice and Bed Changes;496 17.4.2;11.4.2 Factors Influencing the Reaction of an Ice Sheet to the End of an Ice Age;498 17.4.3;11.4.3 Ice Flow Increased by Water Input;503 17.5;11.5 Changes at a Marine Margin;507 17.5.1;11.5.1 Conceptual Framework;508 17.5.2;11.5.2 The Tidewater Glacier Cycle;513 17.5.3;11.5.3 Interactions of Ice Shelves and Inland Ice;516 17.5.4;11.5.4 Forcing by Sea-level Rise;521 17.6;Further Reading;523 18;Chapter 12. Glacier Surges;524 18.1;12.1 Introduction;524 18.2;12.2 Characteristics of Surging Glaciers;526 18.2.1;12.2.1 Spatial Distribution and Relation to Geological Setting;526 18.2.2;12.2.2 Distribution in Time;527 18.2.3;12.2.3 Temperature Characteristics;528 18.2.4;12.2.4 Characteristics of Form and Velocity;529 18.3;12.3 Detailed Observations of Surges;530 18.3.1;12.3.1 Surges of Temperate Glaciers;530 18.3.2;12.3.2 The Role of Water: Variegated Glacier;533 18.3.3;12.3.3 Surges Where the Bed Is Partly Frozen;536 18.3.4;12.3.4 Surges of Polythermal Tidewater Glaciers;539 18.4;12.4 Surge Mechanisms;541 18.4.1;12.4.1 General Evidence Relevant to the Mechanism;541 18.4.2;12.4.2 The Mechanism for Temperate Glaciers;545 18.4.3;12.4.3 Polythermal Glaciers;549 18.5;12.5 Surging of Ice Sheets?;550 18.6;12.6 Ice Avalanches;551 19;Chapter 13. Ice Sheets and the Earth System;554 19.1;13.1 Introduction;554 19.2;13.2 Interaction of Ice Sheets with the Earth System;555 19.2.1;13.2.1 Processes Driving Ice S
heet Change;556 19.2.2;13.2.2 Feedback Processes;561 19.3;13.3 Growth and Decay of Quaternary Ice Sheets;568 19.3.1;13.3.1 Relation to Milankovitch Forcings;570 19.3.2;13.3.2 Climate Forcings at the LGM;574 19.3.3;13.3.3 Onset of Quaternary Cycles;576 19.3.4;13.3.4 Heinrich Events;576 19.4;13.4 Ice Sheet Evolution Models;578 19.4.1;13.4.1 Model Components;578 19.4.2;13.4.2 Model Calibration;582 19.4.3;13.4.3 Simulations of Quaternary Ice Sheets;582 19.5;Further Reading;587 20;Chapter 14. Ice, Sea Level, and Contemporary Climate Change;588 20.1;14.1 Introduction;588 20.1.1;14.1.1 Equivalent Sea Level;589 20.1.2;14.1.2 Recent Climate and Sea-level Change;590 20.2;14.2 Global Warming and Mountain Glaciers;591 20.2.1;14.2.1 History of Glacier Lengths;592 20.2.2;14.2.2 Worldwide Mass Balance of Mountain Glaciers and Small Ice Caps;595 20.2.3;14.2.3 Sea-level Forecasts: Mountain Glaciers and Small Ice Caps;599 20.3;14.3 The Ice Sheets and Global Warming;603 20.3.1;14.3.1 Greenland;603 20.3.2;14.3.2 Antarctica;608 20.3.3;14.3.3 Model Forecasts of Ice Sheet Contributions to Sea-level Change;614 20.3.4;14.3.4 Simple Approaches to Forecasts for the Century Ahead;617 20.4;14.4 Summary;620 20.4.1;14.4.1 Recent Sea-level Rise;620 20.4.2;14.4.2 The Twentieth Century;621 20.4.3;14.4.3 This Century;621 21;Chapter 15. Ice Core Studies;624 21.1;15.1 Introduction;624 21.1.1;15.1.1 Some Essential Terms and Concepts;625 21.1.2;15.1.2 Delta Notation;625 21.2;15.2 Relation Between Depth and Age;627 21.2.1;15.2.1 Theoretical Relations;627 21.2.2;15.2.2 Determination of Ages;635 21.2.3;15.2.3 Difference of Gas and Ice Ages;643 21.3;15.3 Fractionation of Gases in Polar Firn;643 21.4;15.4 Total Air Content;647 21.5;15.5 Stable Isotopes of Ice;649 21.5.1;15.5.1 Conceptual Model;649 21.5.2;15.5.2 Interpretation of Records;657 21.6;15.6 Additional Techniques of Temperature Reconstruction;663 21.6.1;15.6.1 Borehole Temperatures;663 21.6.2;15.6.2 Melt Layers;664 21.6.3;15.6.3 Thermal and Gravitati
onal Fractionation of Gases;665 21.7;15.7 Estimation of Past Accumulation Rates;665 21.8;15.8 Greenhouse Gas Records;667 21.8.1;15.8.1 Histories of Atmospheric Concentration;667 21.8.2;15.8.2 Isotopic Compositions of Greenhouse Gases;672 21.9;15.9 Gas Indicators of Global Parameters;672 21.9.1;15.9.1 Global Mean Ocean Temperature;672 21.9.2;15.9.2 Global Biological Productivity;673 21.10;15.10 Particulate and Soluble Impurities;673 21.10.1;15.10.1 Electrical Conductivity Measurement (ECM);675 21.10.2;15.10.2 Primary Aerosols;675 21.10.3;15.10.3 Secondary Aerosols;677 21.11;15.11 Examples of Multiparameter Records from Ice Sheets;680 21.11.1;15.11.1 Deglacial Climate Change;680 21.11.2;15.11.2 A Long Record of Climate Cycling;680 21.12;15.12 Low-latitude Ice Cores;683 21.13;15.13 Surface Exposures in Ablation Zones;685 21.14;Further Reading;687 22;Appendix A: A Primer on Stress and Strain;688 23;Index;696 24;Color Plates;714