A comment on the Equation of State and the freezing point equation with respect to subglacial lake modelling

Abstract

The empirical Equation of State ( EoS) allows the calculation of the density of water in dependence of salinity, temperature, and pressure. Water density is an important quantity to determine the internal structure and flow regime of ocean and lakes. Hence, its exact representation in numerical models is of utmost importance for the specific simulation results. The three parameters namely salinity, temperature, and pressure have a complex interdependency on the EoS. Whether warmer water parcels sink or rise, therefore depends on the surrounding salinity and pressure. The empirical Equation of Freezing Point ( EoFP) allows to calculate the pressure- and salinity-dependent freezing point of water. Both equations are necessary to model the basal mass balance below Antarctic ice shelves or at the ice–water interface of subglacial lakes. This article aims three tasks: first we comment on the most common formulations of the EoS and the EoFP applied in numerical ocean and lake models during the past decades. Then we describe the impact of the recent and self-consistent Gibbs thermodynamic potential formulation of the EoS and the EoFP on subglacial lake modelling. Finally, we show that the circulation regime of subglacial lakes covered by at least 3000 m of ice, in principle, is independent of the particular formulation, in contrast to lakes covered by a shallower ice sheet, like e.g., Subglacial Lake Ellsworth. However, as modelled values like the freezing and melting patterns or the distribution of accreted ice at the ice–lake interface are sensitive to different EoS and EoFP, we present updated values for Subglacial Lake Vostok and Subglacial Lake Concordia.