A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier

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Abstract
A time-dependent numerical model of temperate glacier flow without sliding is developed and applied to the quiescent phase of surge-type Variegated Glacier, Alaska. The model is based on a one-dimensional continuity equation but the transverse channel shape is explicitly included allowing the complex geometries of real glaciers to be modelled. Velocities and volume fluxes are calculated from the glacier geometry. Transverse stress is taken into account by shape factors which are fitted to measurements of geometry and velocity and are chosen to be insensitive to changes in geometry. Longitudinal stress gradients are taken into account by use of a large-scale surface slope. A Crank-Nicholson finite-difference approximation is used and it is unconditionally stable when a small contribution from the local slope is added to the average slope.Model parameters are fitted to extensive data collected on Variegated Glacier in 1973 and 1974. Predictions of the model over a four year interval agree well with field measurements. Predictions of the current quiescent phase (1965–84) indicate depth increases in the upper glacier of more than 75 m with a twenty-fold increase in the volume flux. During this interval the base shear stress increases 40% in the upper glacier and decreases 20% in the lower glacier. During the mid to late quiescent phase, ice motion becomes more important than mass balance in the redistribution of mass over the central region of the glacier. If normal flow were to persist, the predicted steady-state profile would be an average of 100 m deeper and 41% more voluminous than in 1973.The predicted base shear-stress gradient is never negative enough to satisfy Robin and Weertman’s (1973) condition for blockage of subglacial water flow. The annual rate of water production by dissipation of mechanical straining at the bed remains two orders of magnitude below that produced by summer surface melt. The predicted fractional increase in base stress during the quiescent phase is a maximum in the region believed to be the trigger zone of the surges.

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