Forensic glaciology

The c-axis fabrics, grain sizes and shapes, bubble sizes and shapes, etc., of ice preserve a history of the ice flow and climatic conditions that produced these characteristics, over some 'memory' interval that depends on the active physical processes. In addition, some of these characteristics partially control the rate of ongoing deformation in response to applied stress and temperature. The study of these relations has been a special interest of ours over the years, but the efforts of many other glaciologists show the value of the subject, so we include it despite the possibility that it appears self-serving.

A fundamental difficulty remains that no one has successfully calculated the behaviours of ice physical properties from first principles. (For some idea of one of the many difficulties involved, see Miguel et al., 2001.) Some models (such as that for rotation of existing grains under nearest-neighbour influences; e.g. Azuma & Higashi, 1985; Alley, 1988; van der Veen & Whillans, 1994) have had some success, but are clearly not complete descriptions. Other key quantities, such as conditions for the onset of nucleation and growth of new, strain-free grains, or the rate of grain subdivision by polygonization, remain very poorly known (see review by Alley, 1992).

The 'obvious' solution, that of laboratory experiments, is quite unlikely to work for most of the ice on Earth. This was shown most clearly by the work of Jacka & Li (2000). A great range of experiments, under different stresses and temperatures and with different starting conditions, produced highly consistent results in terms of c-axis fabric, grain size, etc. (also see Budd & Jacka, 1989). All of these consistent results, however, came from experiments that shared the 'problem' of having higher strain rates (usually by order(s) of magnitude) than observed in most of the world's ice, either through higher temperature or stress. Jacka & Li (2000), however, conducted especially heroic experiments approaching strain rates of upper regions of ice sheets, and obtained a very different result: the onset of nucleation and growth of new grains was delayed, consistent with numerous field observations. High-deformation-rate situations develop grain sizes and c-axis fabrics that reflect the stress state over the last 10% strain or so; lower deformation rates allow the physical properties to integrate conditions over much longer times, to more than 100% strain (Alley, 1992).

A rather straightforward explanation is possible. Nucleation and growth of new, strain-free grains, with the attendant loss of 'memory' of earlier conditions and the attendant change in c-axis fabric, grain size, etc., are favoured by accumulation of 'damage' to ice-crystal lattices during deformation (dislocation tangles, etc.). The rate at which damage is produced increases as the deformation rate increases. Various diffusive processes remove or 'heal' damage (recovery). These are not driven by the stress directly, and some at least have a lower activation energy than does the accumulation of damage (grain-boundary versus volume diffusion), so the healing rate increases with increasing temperature more slowly than does the rate of damage accumulation. Above some temperature-stress threshold, the rate of recovery is inconsequential compared with the rate of damage accumulation. Accumulation of sufficient damage will drive nucleation and growth of new grains, and faster deformation simply speeds the attainment ofthe damage threshold for such nucleation. At slower deformation rates, however, the recovery rate is sufficient to delay onset of nucleation by removing some of the stored strain energy.

Because we lack the ability to calculate the key deformational fields from first principles, and because the natural deformation rates of most of the world's ice are largely out of reach for laboratory experiments, we are left with 'forensic glaciology'—we must look at the ice, and figure out what happened using clues from the situation, the known behaviour of ice and theory from other materials. Through sufficient measurements of ice-core physical properties with different histories of temperature and stress, different impurity loadings, etc., we should be able to work out the key thresholds, and make them available for further ice-core interpretation and ice-flow modelling.

Some possibility of failure exists (if we cannot learn enough from sufficient samples to make a useful 'inversion' for the unknown parameters), but we are optimistic. Early work such as that by Gow & Williamson (1976) points the way, and efforts such as Cuffey et al. (2000a) show how successful this can be.

Perhaps the most important step is generation of extensive new data sets, with improving standards of quality. Here, the advent of automatic c-axis-fabric analysers (reviewed by Wilen et al., 2003), of downhole logging and seismic techniques, and perhaps of additional frontiers such as c-axis analyses from radar (Matsuoka et al., 2003) offer the possibility of great advances.

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