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Calving of icebergs is an important component of mass loss from the polar ice sheets and glaciers in many parts of the world. Calving rates can increase dramatically in response to increases in velocity and/or retreat of the glacier margin, with important implications for sea level change. Despite their importance, calving and related dynamic processes are poorly represented in the current generation of ice sheet models. This is largely because understanding the 'calving problem' involves several other long-standing problems in glaciology, combined with the difficulties and dangers of field data collection. In this paper, we systematically review different aspects of the calving problem, and outline a new framework for representing calving processes in ice sheet models. We define a hierarchy of calving processes, to distinguish those that exert a fundamental control on the position of the ice margin from more localised processes responsible for individual calving events. The first-order control on calving is the strain rate arising from spatial variations in velocity (particularly sliding speed), which determines the location and depth of surface crevasses. Superimposed on this first-order process are second-order processes that can further erode the ice margin. These include: fracture propagation in response to local stress imbalances in the immediate vicinity of the glacier front; undercutting of the glacier terminus by melting at or below the waterline; and bending at the junction between grounded and buoyant parts of an ice tongue. Calving of projecting, submerged "ice feet" can be regarded as a third-order process, because it is paced by first- or second-order calving above the waterline. First-order calving can be represented in glacier models using a calving criterion based on crevasse depth, which is a function of longitudinal strain rate. Modelling changes in terminus position and calving rates thus reduces to the problem of determining the ice geometry and velocity distribution. Realistic solutions to the problem of modelling ice flow therefore depend critically on an appropriate choice of sliding law. Models that assume that basal velocities are controlled by basal drag can replicate much of the observed behaviour of calving glaciers with grounded termini, but an important limitation is that they cannot be used to model floating glacier termini or ice shelves. Alternative sliding laws that parameterise drag from the glacier margins provide more flexible and robust ways of representing calving in ice sheet models. Such models can explain a remarkable range of observed phenomena within a simple, unifying framework, including: downglacier increases in velocity and strain rates where basal and/or lateral drag diminishes; flow acceleration in response to thinning through time; the tendency for glaciers to stabilise at "pinning points" in relatively shallow water or fjord narrowings; the constraints on ice shelf stability; and the contrasts in calving rates between tidewater and freshwater calving glaciers. Many unresolved issues remain, however, including the role played by the removal of backstress in the acceleration of retreating calving glaciers, and the controls on melting at and below the waterline.
Glaciers and Glaciation is the classic textbook for all students of glaciation. Stimulating and accessible, it has established a reputation as a comprehensive and essential resource. In this new edition, the text, references and illustrations have been thoroughly updated to give today's reader an up-to-the minute overview of the nature, origin and behaviour of glaciers and the geological and geomorphological evidence for their past history on earth. The first part of the book investigates the processes involved in forming glacier ice, the nature of glacier-climate relationships, the mechanisms of glacier flow and the interactions of glaciers with other natural systems such as rivers, lakes and oceans. In the second part, the emphasis moves to landforms and sediment, the interpretation of the earth's glacial legacy and the reconstruction of glacial depositional environments and palaeoglaciology.
This updated and expanded version of the second edition explains the physical principles underlying the behaviour of glaciers and ice sheets. The text has been revised in order to keep pace with the extensive developments which have occurred since 1981. A new chapter, of major interest, concentrates on the deformation of subglacial till. The book concludes with a chapter on information regarding past climate and atmospheric composition obtainable from ice cores.
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
The principles of glacier physics are developed from basic laws in this up-to-date third edition for advanced students and researchers.
Measuring, monitoring, and modeling technologies and methods changed the field of glaciology significantly in the 14 years since the publication of the first edition of Fundamentals of Glacier Dynamics. Designed to help readers achieve the basic level of understanding required to describe and model the flow and dynamics of glaciers, this second edition provides a theoretical framework for quantitatively interpreting glacier changes and for developing models of glacier flow. See What’s New in the Second Edition: Streamlined organization focusing on theory, model development, and data interpretation Introductory chapter reviews the most important mathematical tools used throughout the remainder of the book New chapter on fracture mechanics and iceberg calving Consolidated chapter covers applications of the force-budget technique using measurements of surface velocity to locate mechanical controls on glacier flow The latest developments in theory and modeling, including the addition of a discussion of exact time-dependent similarity solutions that can be used for verification of numerical models The book emphasizes developing procedures and presents derivations leading to frequently used equations step by step to allow readers to grasp the mathematical details as well as physical approximations involved without having to consult the original works. As a result, readers will have gained the understanding needed to apply similar techniques to somewhat different applications. Extensively updated with new material and focusing more on presenting the theoretical foundations of glacier flow, the book provides the tools for model validation in the form of analytical steady-state and time-evolving solutions. It provides the necessary background and theoretical foundation for developing more realistic ice-sheet models, which is essential for better integration of data and observations as well as for better model development.
Calving remains one of the most important yet unresolved aspects of glacier and ice sheet flow. Providing better constraints on global mean sea level rise will depend on our ability to simulate the dynamic flow of ice as it is discharged into the oceans. The work of this dissertation focuses on the important role basal crevasses play in the discharge of ice from glaciers and ice streams and how we can better model the formation and development of these features, particularly with regard to ice rheology during failure. First we make use of a large amount of ice penetrating radar data to image and understand the geometry and location of these features along the grounding line of the Siple Coast, in Antarctica. These data motivate the use of a thin-elastic beam approximation to the stresses that promote failure there, and the model is applied to all grounding lines across Antarctica, producing order-of-magnitude predictions where basal crevasses have already been observed. The simplicity of this model leads to the development of a more complex numerical model capable of visco-elasto-plastic simulation, DynEarthSol3D (DES), which performs the only time-dependent benchmark test designed for higher-order Stokes models. DES performs reasonably well against purely viscous numerical models and executes several experiments with idealized geometries exploring the roles that ice thickness and grounding line curvature play in the formation of basal crevasses in elastoplastic ice. Finally, with the implementation of a ductile-brittle transition zone based on longitudinal strain rate, we model the development of grounding line basal crevasses using visco-elasto-plastic rheology. Here we explore the roles that ice thickness and basal melting play in the formation and development of basal crevasses in ice as it is advected from resting on bedrock to floating in the ocean. We find that the inclusion of an extra measure of weakening to simulate the infiltration of buoyant ocean water in the basal crevasses is a crucial mechanism in developing the failure pattern seen in the floating portions of Thwaites Glacier and other glaciers around the world. The features that we simulate are truly semi-brittle, in that they require both viscous and elastic components of stress and a failure mechanism to develop.
The present-day calving flux from Greenland and Antarctica is poorly known, and this accounts for a significant portion of the uncertainty in the current mass balance of these ice sheets. Similarly, the lack of knowledge about the role of calving in glacier dynamics constitutes a major uncertainty in predicting the response of glaciers and ice sheets to changes in climate and thus sea level. Another fundamental problem has to do with incomplete knowledge of glacier areas and volumes, needed for analyses of sea-level change due to changing climate. The authors proposed to develop an improved ability to predict the future contributions of glaciers to sea level by combining work from four research areas: remote sensing observations of calving activity and iceberg flux, numerical modeling of glacier dynamics, theoretical analysis of the calving process, and numerical techniques for modeling flow with large deformations and fracture. These four areas have never been combined into a single research effort on this subject; in particular, calving dynamics have never before been included explicitly in a model of glacier dynamics. A crucial issue that they proposed to address was the general question of how calving dynamics and glacier flow dynamics interact.
The earth’s cryosphere, which includes snow, glaciers, ice caps, ice sheets, ice shelves, sea ice, river and lake ice, and permafrost, contains about 75% of the earth’s fresh water. It exists at almost all latitudes, from the tropics to the poles, and plays a vital role in controlling the global climate system. It also provides direct visible evidence of the effect of climate change, and, therefore, requires proper understanding of its complex dynamics. This encyclopedia mainly focuses on the various aspects of snow, ice and glaciers, but also covers other cryospheric branches, and provides up-to-date information and basic concepts on relevant topics. It includes alphabetically arranged and professionally written, comprehensive and authoritative academic articles by well-known international experts in individual fields. The encyclopedia contains a broad spectrum of topics, ranging from the atmospheric processes responsible for snow formation; transformation of snow to ice and changes in their properties; classification of ice and glaciers and their worldwide distribution; glaciation and ice ages; glacier dynamics; glacier surface and subsurface characteristics; geomorphic processes and landscape formation; hydrology and sedimentary systems; permafrost degradation; hazards caused by cryospheric changes; and trends of glacier retreat on the global scale along with the impact of climate change. This book can serve as a source of reference at the undergraduate and graduate level and help to better understand snow, ice and glaciers. It will also be an indispensable tool containing specialized literature for geologists, geographers, climatologists, hydrologists, and water resources engineers; as well as for those who are engaged in the practice of agricultural and civil engineering, earth sciences, environmental sciences and engineering, ecosystem management, and other relevant subjects.