Ice shelf-ocean interactions in a general circulation model : melt-rate modulation due to mean flow and tidal currents

Abstract

Interactions between the ocean circulation in sub-ice shelf cavities and the overlying ice shelf have received considerable attention in the context of observed changes in flow speeds of marine ice sheets around Antarctica. Modeling these interactions requires parameterizing the turbulent boundary layer processes to infer melt rates from the oceanic state at the ice-ocean interface. Here we explore two such parameterizations in the context of the MIT ocean general circulation model coupled to the z-coordinates ice shelf cavity model of Losch (2008). We investigate both idealized ice shelf cavity geometries as well as a realistic cavity under Pine Island Ice Shelf (PIIS), West Antarctica. Our starting point is a three-equation melt rate parameterization implemented by Losch (2008), which is based on the work of Hellmer and Olbers (1989). In this form, the transfer coefficients for calculating heat and freshwater fluxes are independent of frictional turbulence induced by the proximity of the moving ocean to the fixed ice interface. More recently, Holland and Jenkins (1999) have proposed a parameterization in which the transfer coefficients do depend on the ocean-induced turbulence and are directly coupled to the speed of currents in the ocean mixed layer underneath the ice shelf through a quadratic drag formulation and a bulk drag coefficient. The melt rate parameterization in the MITgcm is augmented to account for this velocity dependence. First, the effect of the augmented formulation is investigated in terms of its impact on melt rates as well as on its feedback on the wider sub-ice shelf circulation. We find that, over a wide range of drag coefficients, velocity-dependent melt rates are more strongly constrained by the distribution of mixed layer currents than by the temperature gradient between the shelf base and underlying ocean, as opposed to velocity-independent melt rates. This leads to large differences in melt rate patterns under PIIS when including versus not including the velocity dependence. In a second time, the modulating effects of tidal currents on melting at the base of PIIS are examined. We find that the temporal variability of velocity-dependent melt rates under tidal forcing is greater than that of velocity-independent melt rates. Our experiments suggest that because tidal currents under PIIS are weak and buoyancy fluxes are strong, tidal mixing is negligible and tidal rectification is restricted to very steep bathymetric features, such as the ice shelf front. Nonetheless, strong tidally-rectified currents at the ice shelf front significantly increase ablation rates there when the formulation of the transfer coefficients includes the velocity dependence. The enhanced melting then feedbacks positively on the rectified currents, which are susceptible to insulate the cavity interior from changes in open ocean conditions.