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2009 | Buch

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Dynamics of Ice Sheets and Glaciers

verfasst von: Ralf Greve, Heinz Blatter

Verlag: Springer Berlin Heidelberg

Buchreihe : Advances in Geophysical and Environmental Mechanics and Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

Dynamics of Ice Sheets and Glaciers presents an introduction to the dynamics and thermodynamics of flowing ice masses on Earth. Based on an outline of general continuum mechanics, the different initial-boundary-value problems for the flow of ice sheets, ice shelves, ice caps and glaciers are systematically derived. Special emphasis is put on developing hierarchies of approximations for the different systems, and suitable numerical solution techniques are discussed. A separate chapter is devoted to glacial isostasy. The book is appropriate for graduate courses in glaciology, cryospheric sciences, environmental sciences, geophysics and related fields. Standard undergraduate knowledge of mathematics (calculus, linear algebra) and physics (classical mechanics, thermodynamics) provide a sufficient background for successfully studying the text.

Inhaltsverzeichnis

Frontmatter

1. Ice in the Climate System

Abstract

The frozen part of the terrestrial climate system is referred to as the cryosphere. The cryosphere consists of several subsystems, namely ice sheets, ice shelves, ice caps, glaciers, sea ice, lake ice, river ice, ground ice and snow. Ice sheets are ice masses of continental size (area greater than 50,000 km²) which rest on solid land, whereas ice shelves consist of floating ice nourished by the inflow from an adjacent ice sheet, typically stabilised by large bays. Extended land-based masses of ice covering less than 50,000 km² are termed ice caps, and smaller ice masses constrained by topographical features (for instance a mountain valley) are called glaciers. Sea ice floats on the ocean; however, in contrast to an ice shelf it forms directly by freezing sea water.

Ralf Greve, Heinz Blatter

2. Vectors, Tensors and Their Representation

Abstract

In mathematics, a vector is defined as an element of a vector space, and a vector space is a commutative (Abelian) group with a scalar multiplication. This is an abstract definition which has many possible realisations (numbers, functions, geometric objects and so on). For our purposes, it is sufficient to consider one of them, namely the geometric object of an arrow in the three-dimensional, Euclidian, physical space ε. Therefore, in our sense a vector a ∈ ε is an arrow which is characterised by a length and a direction. Physical quantities which can be described by such vectors are, for instance, velocity, acceleration, momentum and force. By contrast, scalars are simple numbers and characterise physical quantities without a direction, like mass, density, temperature etc.

Ralf Greve, Heinz Blatter

3. Elements of Continuum Mechanics

Abstract

Continuum mechanics is concerned with the motion and deformation of continuous bodies (for instance, a glacier). A body consists of an infinite number of material elements, called particles. For any time t, each particle is identified by a position vector x (relative to a prescribed origin O) in the physical space ε, and the continuous set of position vectors for all particles of the body is called a configuration κ of the body. If t is the actual time, the corresponding configuration is called the present configuration κ _t. In addition, we define a reference configuration κ _r which refers to a fixed (or initial) time t ₀.

Ralf Greve, Heinz Blatter

4. Constitutive Equations for Polycrystalline Ice

Abstract

The phase of H₂O ice which exists at pressure and temperature conditions encountered in ice sheets and glaciers is called ice Ih. It forms hexagonal crystals, that is, the water molecules are arranged in layers of hexagonal rings (Fig. 4.1). The plane of such a layer is called the basal plane, which actually consists of two planes shifted slightly (by 0.0923 nm) against each other. The direction perpendicular to the basal planes is the optic axis or c-axis, and the distance between two adjacent basal planes is 0.276 nm.

Ralf Greve, Heinz Blatter

5. Large-Scale Dynamics of Ice Sheets

Abstract

With the constitutive equations given in Sects. 4.3 and 4.4, we are now able to formulate the mechanical and thermodynamical field equations for the flow of ice in an ice sheet. Figure 5.1 shows the typical geometry (cross section) of a grounded ice sheet with attached floating ice shelf (the latter will be treated in Chap. 6), as well as its interactions with the atmosphere (snowfall, melting), the lithosphere (geothermal heat flux, isostasy) and the ocean (melting, calving). Also, a Cartesian coordinate system is introduced, where x and y lie in the horizontal plane, and z is positive upward. These coordinates are naturally associated with the set of basis vectors {e_x, e_y, e_z}. The free surface (ice-atmosphere interface) is given by the function z = h(x, y, t), the ice base by z = b(x, y, t) and the lithosphere surface by z = z _l(x, y, t).

Ralf Greve, Heinz Blatter

6. Large-Scale Dynamics of Ice Shelves

Abstract

Ice shelves are floating ice masses, which are connected to and nourished by a grounded ice sheet (see Fig. 5.1). Most ice shelves, like the three major ice shelves of Antarctica (Ross Ice Shelf, Filchner-Rønne Ice Shelf, Amery Ice Shelf), are confined by large embayments. Smaller ice shelves can also be unconfined. In the latter case, stabilisation typically results from the contact with small islands or grounding on shoals.

Ralf Greve, Heinz Blatter

7. Dynamics of Glacier Flow

Abstract

As mentioned in the introduction (Chapter 1), the size of land ice masses spans several orders of magnitude, from large ice sheets of a few thousand kilometres in diameter down to small glaciers of a few hundreds of metres in length. Consequently, the scaling given for ice sheets in Chapter 5 [Eqs. (5.5) and (5.102)] is not valid for smaller ice caps and glaciers, and needs to be modified. However, the Froude number (5.7) and Coriolis-force-to-pressure-gradient ratio (5.10) are always extremely small compared to unity, and therefore the Stokes flow problem formulated in Sect. 5.1 is applicable to land ice masses of all shapes and sizes. On the other hand, the applicability of the approximations defined in Sects. 5.2 to 5.4 is limited by the size of the ice masses.

Ralf Greve, Heinz Blatter

8. Glacial Isostasy

Abstract

The ice sheets on Earth have undergone very large changes over the glacial-interglacial cycles in the past. Today, ice sheets of significant size occur only in Antarctica and Greenland, whereas during the Last Glacial Maximum (LGM), 21,000 years ago, extended ice sheets also covered large parts of North America, northern Europe, etc. (see Chapter 1). These ice sheets, with typical thicknesses of several kilometres, impose therefore large, time-dependent loads on the crust of the Earth, to which the body of the Earth as a visco-elastic, multi-layer system reacts with a delayed, essentially vertical displacement.

Ralf Greve, Heinz Blatter

9. Advanced Topics

Abstract

While in the previous chapters relatively well-established aspects of ice dynamics have been treated, we now turn to some more advanced and demanding topics at the forefront of current research. The selection of the topics (induced anisotropy, compressible firn, polythermal glaciers) is strongly influenced by the authors’ own research interests and makes no claim to be complete. Other issues, such as subglacial hydrology, ice stream dynamics or calving mechanics, deserve equal attention, and we explicitly encourage the interested reader to follow these paths as well.

Ralf Greve, Heinz Blatter

10. Conclusions, Summary and Outlook

Abstract

In agreement with the scope of the series Advances in Geophysical and Environmental Mechanics and Mathematics (AGEM²), it is our intention that this book serves the purposes

Ralf Greve, Heinz Blatter

Erratum

Publisher

Backmatter

Titel: Dynamics of Ice Sheets and Glaciers
verfasst von: Ralf Greve
Heinz Blatter
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-03415-2
Print ISBN: 978-3-642-03414-5
DOI: https://doi.org/10.1007/978-3-642-03415-2