Constraints on melt-water flux through the West Greenland ice-sheet: modeling of hydro- fracture drainage of supraglacial lakes

Recent observations of rapid ice-flow acceleration following the onset of surface melting from Greenland suggest that ice-sheets may respond more rapidly and dramatically to climate change than previously believed. Melt- water may drain advectively through the ice-sheet, lubricating and warming the bed, and accelerate ice flow. Understanding the mechanisms and constraints on melt-water transport through ice-sheets is critical for incorporating these feedbacks into models of ice-sheet evolution and for estimating future rates of ice-sheet drawdown and sea-level change. We have investigated the viability of rapidly transporting melt-water from the ice- sheet's surface to its bed using a linear elastic fracture mechanics approach to model crack propagation in ice. Building on the work of Weertman (IASH, 1973), Alley et al. (Annal Glac, 2004) and van der Veen (GRL, 2007), who showed that only water filled crevasses will propagate through an ice-sheet, we model the size and shape of water-filled crevasses. In doing so, we place volumetric constraints on the amount of water necessary to keep water-filled crevasses propagating through 1-2 km of sub-freezing ice. This volume of water is then used to constrain the minimum lake sizes that can hydro-fracture to the bed. For example, in our study area there are over 1000 lakes that contain enough water (> 0.3-0.5 km in diameter) to keep a crevasse filled to the ice-bed interface (~1.5 km of ice). In addition, our calculations of the opening geometry of hydro-fractures demonstrate that the time scale for draining the largest known lakes through a single crevasse is on the order of 2-18 hrs, significantly faster than the time-scale for refreezing of crevasses in ice. These model-based results of crevasse geometry and water drainage are consistent with and supported by recent field observations of rapid lake drainage south of Jakobshavn Isbrae, Greenland.