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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.
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.
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.
"Jakobshavn Isbræ, a fast-flowing outlet glacier in West Greenland, began a rapid retreat in the late 1990's. The glacier has since retreated over 15 km, thinned by tens of meters, and doubled its discharge into the ocean. The glacier's retreat and associated dynamic adjustment are driven by poorly-understood processes occurring at the glacier-ocean interface. These processes were investigated by synthesizing a suite of field data collected in 2007-2008, including timelapse imagery, seismic and audio recordings, iceberg and glacier motion surveys, and ocean wave measurements, with simple theoretical considerations. Observations indicate that the glacier's mass loss from calving occurs primarily in summer and is dominated by the semi-weekly calving of full-glacier-thickness icebergs, which can only occur when the terminus is at or near flotation. The calving icebergs produce long-lasting and far-reaching ocean waves and seismic signals, including 'glacial earthquakes'. Due to changes in the glacier stress field associated with calving, the lower glacier instantaneously accelerates by ~3% but does not episodically slip, thus contradicting the originally proposed glacial earthquake mechanism. We furthermore showed that the pre-dominance of calving during summer can be attributed to variations in the strength of the proglacial ice mélange (dense pack of sea ice and icebergs). Sea ice growth in winter stiffens the mélange and prevents calving; each summer the mélange weakens and calving resumes. Previously proposed calving models are unable to explain the terminus dynamics of Jakobshavn Isbræ (and many other calving glaciers). Using our field observations as a basis, we developed a general framework for iceberg calving models that can be applied to any calving margin. The framework is based on mass continuity, the assumption that calving rate and terminus velocity are not independent, and the simple idea that terminus thickness following a calving event is larger than terminus thickness at the event onset. Although the calving framework does not constitute a complete calving model, it provides a guide for future attempts to define a universal calving law"--Leaf iii.
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.
Snow and Ice-Related Hazards, Risks, and Disasters provides you with the latest scientific developments in glacier surges and melting, ice shelf collapses, paleo-climate reconstruction, sea level rise, climate change implications, causality, impacts, preparedness, and mitigation. It takes a geo-scientific approach to the topic while also covering current thinking about directly related social scientific issues that can adversely affect ecosystems and global economies. Puts the contributions from expert oceanographers, geologists, geophysicists, environmental scientists, and climatologists selected by a world-renowned editorial board in your hands Presents the latest research on causality, glacial surges, ice-shelf collapses, sea level rise, climate change implications, and more Numerous tables, maps, diagrams, illustrations and photographs of hazardous processes will be included Features new insights into the implications of climate change on increased melting, collapsing, flooding, methane emissions, and sea level rise
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.