Incorporation into models of icemass motion

The constitutive relation for ice forms the basic building block of all ice-flow models, many of which until recently adopted Glen's law with a spatially uniform value of n and a temperature-dependent value of A in Equation (3). However, ice-sheet models are increasingly adopting a two-layered structure, with a basal layer that is softer than the overlying ice (e.g. Huybrechts et al., 2000). This normally is achieved by introducing an additional multiplier, termed an enhancement factor, into Equation (3). This distinction, however, is only one among many potential spatial variations in ice softness, including, for example, those associated with down-glacier changes in crystal fabric and water content that remain unknown and, thus, unaccounted for in ice-sheet models.

Although the binary layering of polythermal ice masses is imperfect, the treatment is markedly better than that of temperate valley glaciers, models of which tend to include no spatial variability in ice softness. One exception is an evaluation of the potential significance of ionic variability within the ice cores recovered from Tsanfleuron Glacier (above). Here, Hubbard et al. (2003) (i) used measured ice bulk ionic concentrations to approximate the water content and ice softness of each of the ice zones identified in the cores; (ii) incorporated those rheologies and their host zone geometries (Fig. 67.1) within a two-dimensional firstorder flow model, and (iii) ran the model to compare the effects of a homogeneous (uniform rheology) glacier and a three-layered glacier. Results of the ice analysis indicated that the Lower Zone and Basal Zone ice are respectively 1.80 and 10.74 times softer than the Upper Zone ice. Modelling indicated that the imposition of a 75 m rise in equilibrum line altitude (ELA) resulted in a predicted homogeneous glacier that was 65% larger than the predicted layered glacier (Fig. 67.2).

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