Relative magnitudes of shear and longitudinal strain rates in the inland Antarctic ice sheet, and response to increasing accumulation

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Abstract
An approximation common to vertically integrated and three-dimensional models used to simulate growth and retreat of ice sheets in response to changes in climate and sea level is that the component of the mean column velocity attributable to longitudinal strain rates is small relative to the component attributable to shear strain rates parallel to the gcoid, and can be neglected. We investigate the internal consistency of this sliallow-ice approximation by using a three-dimensional model of the Antarctic ice sheet to calculate the ratio of the horizontal shear strain rates, averaged through the lowest 10% of the ice depth, to the horizontal longitudinal strain rates, averaged through the total ice depth. This ratio is plotted for the regions of the ice sheet characterized by “inland ice-sheet flow”, i.e. where the surface elevations are above 1500 m in East Antarctica, and above 950 m in West Antarctica. These areas are generally inland of the ice streams. The areas where this ratio exceeds 10, 50 and 100 are delineated for the cases of (i) no basal motion, and (ii) “moderate” basal motion. The results generally support the validity of the shallow-ice approximation throughout most areas of the inland Antarctic ice sheet, although it breaks down, as expected, near flow divides and mountain ranges. The model is also employed to simulate the response of the ice sheet to linearly increasing accumula-tion rates, such that the present accumulation is doubled after 100 years and then held constant, using the surface kinematic equation. The results suggest that the accumulation increase in East Antarctica during recen t decades observed in widely spaced ice cores may be sufficient to account for a positive change in the time rate-of-change of the surface heights of up to 0.1 m a−1 during this time period, throughout the areas north of 72° S, if the accumulation increase has been widespread.

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