Hydraulics of subglacial supercooling: Theory and simulations for clear water flows

Abstract

Glaciohydraulic supercooling is a mechanism for accreting ice and sediment to the base of glaciers. We extend existing models by reworking the Spring‐Hutter model for subglacial water flow in tubular conduits to allow for distributed water sheets. Our goal is to determine diagnostic features of supercooling relative to controlling variables. Results focus on along‐path water flow under time‐varying conditions, with attention to ice accretion in and along subglacial overdeepenings. We contrast simulations with constant recharge to diurnally‐varying recharge and expose behavior that cannot be inferred from simple models. For example, locations of simulated ice accretion differ from those found for steady state models, even though total ice accretion remains comparable to field estimates. Downstream accretion influences upstream effective pressures that then modify the hydraulic gradient that drives water flow. This modified gradient tends to inhibit additional accretion by increasing velocity and heat production via viscous dissipation. During diurnal cycles, accretion varies considerably: in daytime, viscous dissipation dominates the heat balance and ice melts. In morning and evening, when flow is rising or falling, viscous dissipation is lower and accretion can proceed. Over nighttime, the largest temperature depressions occur in the subglacial system, but water flux is lowest and accretion rates are negligible. We conclude by inferring that overdeepened glaciers with only clear water flows evolve toward stronger supercooling regimes rather than toward a dynamic equilibrium. Stabilizing feedbacks are unlikely to occur through glacier hydrology alone, and other processes, such as erosion, sedimentation, and sliding, must play an important role.