A numerical model for meltwater channel evolution in glaciers

Meltwater channels form an integral part of the hydrological system of a glacier. Better understanding of how meltwater channels develop and evolve is required to fully comprehend supraglacial and englacial meltwater drainage. Incision of supraglacial stream channels and subsequent roof closure by ice deformation has been proposed in recent literature as a possible englacial conduit formation process. Field evidence for supraglacial stream incision has been found in Svalbard and Nepal. In Iceland, where volcanic activity provides meltwater with temperatures above 0 °C, rapid enlargement of supraglacial channels has been observed. Supraglacial channels provide meltwater through englacial passages to the subglacial hydrological systems of big ice sheets, which in turn affects ice sheet motion and their contribution to eustatic sea level change. By coupling, for the first time, a numerical ice dynamic model to a hydraulic model which includes heat transfer, we investigate the evolution of meltwater channels and their incision behaviour. We present results for different, constant meltwater fluxes, different channel slopes, different meltwater temperatures, different melt rate distributions in the channel as well as temporal variations in meltwater flux. The key parameters governing incision rate and depth are channel slope, meltwater temperature loss to the ice and meltwater flux. Channel width and geometry are controlled by melt rate distribution along the channel wall. Calculated Nusselt numbers suggest that turbulent mixing is the main heat transfer mechanism in the meltwater channels studied.