Frequency response of ice streams

Changes at the grounding line of ice streams have consequences for inland ice dynamics and hence sea level. Despite substantial evidence documenting upstream propagation of frontal change, the mechanisms by which these changes are transmitted inland are not well understood. In this vein, the frequency response of an idealized ice stream to periodic forcing in the downstream strain rate is examined for basally and laterally resisted ice streams using a one-dimensional, linearized membrane stress approximation. This reveals two distinct behavioural branches, which we find to correspond to different mechanisms of upstream velocity and thickness propagation, depending on the forcing frequency. At low frequencies (centennial to millennial periods), slope and thickness covary hundreds of kilometres inland, and the shallow-ice approximation is sufficient to explain upstream propagation, which occurs through changes in grounding-line flow and geometry. At high frequencies (decadal to sub-decadal periods), penetration distances are tens of kilometres; while velocity adjusts rapidly to such forcing, thickness varies little and upstream propagation occurs through the direct transmission of membrane stresses. Propagation properties vary significantly between 29 Antarctic ice streams considered. A square-wave function in frontal stress is explored by summing frequency solutions, simulating some aspects of the dynamical response to sudden ice-shelf change.