Glacier Surge Mechanism Based on Linked Cavity Configuration of the Basal Water Conduit System

Abstract

Based on observations of the 1982–1983 surge of Variegated Glacier, Alaska, a model of the surge mechanism is developed in terms of a transition from the normal tunnel configuration of the basal water conduit system to a linked cavity configuration that tends to restrict the flow of water, resulting in increased basal water pressures that cause rapid basal sliding. The linked cavity system consists of basal cavities formed by ice-bedrock separation (cavitation), ∼1 m high and ∼10 m in horizontal dimensions, widely scattered over the glacier bed, and hydraulically linked by narrow connections where separation is minimal (separation gap ≲ 0.1 m). The narrow connections, called orifices, control the water flow through the conduit system; by throttling the flow through the large cavities, the orifices keep the water flux transmitted by the basal water system at normal levels even though the total cavity cross-sectional area (∼200 m^2) is much larger than that of a tunnel system (∼10 m^2). A physical model of the linked cavity system is formulated in terms of the dimensions of the "typical" cavity and orifice and the numbers of these across the glacier width. The model concentrates on the detailed configuration of the typical orifice and its response to basal water pressure and basal sliding, which determines the water flux carried by the system under given conditions. Configurations are worked out for two idealized orifice types, step orifices that form in the lee of downglacier-facing bedrock steps, and wave orifices that form on the lee slopes of quasisinusoidal bedrock waves and are similar to transverse "N channels." The orifice configurations are obtained from the results of solutions of the basal-sliding-with-separation problem for an ice mass constituting of linear half-space of linear rheology, with nonlinearity introduced by making the viscosity stress-dependent on an intuitive basis. Modification of the orifice shapes by melting of the ice roof due to viscous heat dissipation in the flow of water through the orifices is treated in detail under the assumption of local heat transfer, which guarantees that the heating effects are not underestimated. This treatment brings to light a melting-stability parameter Ξ that provides a measure of the influence of viscous heating on orifice cavitation, similar but distinct for step and wave orifices. Orifice shapes and the amounts of roof meltback are determined by Ξ. When Ξ ≳ 1, so that the system is "viscous-heating-dominated," the orifices are unstable against rapid growth in response to a modest increase in water pressure or in orifice size over their steady state values. This growth instability is somewhat similar to the jökulhlaup-type instability of tunnels, which are likewise heating-dominated. When Ξ ≲ 1, the orifices are stable against perturbations of modest to even large size. Stabilization is promoted by high sliding velocity ν, expressed in terms of a ν^(−½) and ν^(−1) dependence of Ξ for step and wave cavities. The relationships between basal water pressure and water flux transmitted by linked cavity models of step and wave orifice type are calculated for an empirical relation between water pressure and sliding velocity and for a particular, reasonable choice of system parameters. In all cases the flux is an increasing function of the water pressure, in contrast to the inverse flux-versus-pressure relation for tunnels. In consequence, a linked cavity system can exist stably as a system of many interconnected conduits distributed across the glacier bed, in contrast to a tunnel system, which must condense to one or at most a few main tunnels. The linked cavity model gives basal water pressures much higher than the tunnel model at water fluxes ≳1 m^(3/s) if the bed roughness features that generate the orifices have step heights or wave amplitudes less than about 0.1 m. The calculated basal water pressure of the particular linked cavity models evaluated is about 2 to 5 bars below ice overburden pressure for water fluxes in the range from about 2 to 20 m^(3/s), which matches reasonably the observed conditions in Variegated Glacier in surge; in contrast, the calculated water pressure for a single-tunnel model is about 14 to 17 bars below overburden over the same flux range. The contrast in water pressures for the two types of basal conduit system furnishes the basis for a surge mechanism involving transition from a tunnel system at low pressure to a linked cavity system at high pressure. The parameter Ξ is about 0.2 for the linked cavity models evaluated, meaning that they are stable but that a modest change in system parameters could produce instability. Unstable orifice growth results in the generation of tunnel segments, which may connect up in a cooperative fashion, leading to conversion of the linked cavity system to a tunnel system, with large decrease in water pressure and sliding velocity. This is what probably happens in surge termination. Glaciers for which Ξ ≲ 1 can go into surge, while those for which Ξ ≳ 1 cannot. Because Ξ varies as α^(3/2) (where α is surface slope), low values of Ξ are more probable for glaciers of low slope, and because slope correlates inversely with glacier length in general, the model predicts a direct correlation between glacier length and probability of surging; such a correlation is observed (Clarke et al., 1986). Because Ξ varies inversely with the basal shear stress τ, the increase of τ that takes place in the reservoir area in the buildup between surges causes a decrease in Ξ there, which, by reducing Ξ below the critical value ∼1, can allow surge initiation and the start of a new surge cycle. Transition to a linked cavity system without tunnels should occur spontaneously at low enough water flux, in agreement with observed surge initiation in winter.

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