Brief communication: Representation of heat conduction into ice in marine ice shelf melt modelling

Basal melt of marine-terminating glaciers is a key uncertainty in predicting the future climate and the evolution of the Antarctic and Greenland ice sheets. Regional ocean circulation models rely on an approximated heat budget at the ice–ocean interface that includes turbulent heat flux from the ocean below, latent heat for phase transition, and heat conduction into the ice in order to parameterize melt rates. Here we review the formulations of Holland and Jenkins (1999) for the approximation of heat conduction into ice, utilizing three distinct observed ice temperature profiles. We show that the formulation accounting for constant vertical advection and vertical diffusion of heat into ice best represents the observed ice temperature profiles. Using idealized ocean simulations of a Greenlandic fjord and observed melt rates from Antarctica, we find a difference of up to 28 % (average of 12 %) in melt rates between the different approximations.