Parameterising the Melting of Marine Glacier Termini with Buoyant Meltwater Plumes in a Stratified Ocean

Abstract:

Melting of submerged marine glacier termini can impact the dynamics of ice flow, and hence provides a key control on the ocean forcing of ice sheets and potential sea-level rise. Melting rates are controlled by the supply of heat and salt to the ice-ocean interface, which depend on both the details of turbulence and the temperature and salinity conditions in the neighbouring ocean. One such feedback on ice melting comes from the buoyancy-driven flow of fresh meltwater rising along the ice face at a steep glacier terminus. The strength of this flow and resulting melting rates are sensitive to the vertical stratification of temperature and salinity in the neighbouring ocean. To build theoretical insight into the role of ocean stratification, we apply a plume model to describe buoyancy-driven flow along planar ice faces sitting in a stratified ocean. A range of background ocean temperature and salinity profiles are studied. Our plume model considers both persistent flows that rise to the ocean surface, or layered flows featuring multiple intrusions into the background ocean, with intrusions occurring after the plume density reaches a neutral buoyancy level compared to the background ocean density stratification. For flows with negligible subglacial discharge into a linear stratification, we theoretically derive approximate scaling laws for the dependence of melting rates on the temperature and salinity stratifications. The scaling laws are in good agreement with results from numerical simulations. Under appropriate conditions, these scaling laws may provide a computationally-efficient approximation to the rate of glacier terminus melting controlled by buoyancy-driven flows, in circumstances where the use of a more detailed ocean model proves impractical.