The Formation of Fjord Thresholds

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Abstract
The erosion rate of bedrock by glacier action is analyzed under conditions of constant-state radial convergent and divergent flow, assuming that the quarrying rate increases with increasing sliding velocity, and assuming a conventional power-function sliding law. Ice is modeled as a non-linear Glen material. Deviatoric stresses are computed but are shown to be negligible compared to the basal shear stress, provided that suitable restraints are placed on the ratio of channel radius of curvature to ice thickness. If the ice is sufficiently thick, radial divergent flow results in erosion rates which decrease in the down-stream direction This provides an explanation for the formation of the largest class of fjord thresholds which occur at channel widenings. In contrast, increased erosion rates are predicted at narrows which can explain the presence of deep troughs at gradual narrows. It is argued that the presence of pronounced thresholds in abrupt narrows can be explained by low quarryability or locally high roughness which reduces the sliding velocity. The origin of till overlying thresholds is explained as a natural consequence of a threshold being a position of relative stability for the terminus of a retreating tide-water glacier.