Tidal bending of glaciers: a linear viscoelastic approach

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Abstract
In theoretical treatments of tidal bending of floating glaciers, the glacier is usually modelled as an elastic beam with uniform thickness, resting on an elastic foundation. With a few exceptions, values of the elastic (Young’s) modulus E of ice derived from tidal deflection records of floating glaciers are in the range 0.9–3 GPa. It has therefore been suggested that the elastic-beam model with a single value of E ≈ 1GPa adequately describes tidal bending of glaciers. In contrast, laboratory experiments with ice give E = 9.3 GPa, i.e. 3–10 times higher than the glacier-derived values. This suggests that ice creep may have a significant influence on tidal bending of glaciers. Moreover, detailed tidal-deflection and tilt data from Nioghalvfjerdsfjorden glacier, northeast Greenland, cannot be explained by elastic-beam theory. We present a theory of tidal bending of glaciers based on linear viscoelastic-beam theory. A four-element, linear viscoelastic model for glacier ice with a reasonable choice of model parameters can explain the observed tidal flexure data. Implications of the viscoelastic response of glaciers to tidal forcing are discussed briefly.