Buoyancy Feedbacks on Wave-Induced Melting of Icebergs

Icebergs play an important role in the climate system through their temporally and spatially distributed injection of freshwater into the ocean. Waterline melting from surface wave action accounts for a substantial amount of iceberg mass loss and drives iceberg fragmentation, yet it is poorly constrained and lacks physics-based model implementation, particularly in considering the ice-ocean boundary layer. Here we develop a hierarchy of models that couple wave-induced iceberg melt with the ice-ocean interfacial boundary layer, an approach traditionally used in modeling the ocean-driven melting of ice shelves. We find that the flux of meltwater from wave-induced ice loss into the proximal ocean acts to lower further wave-induced melting by 10-20\%. Depth-averaged wave-induced melting increases sublinearly with increasing wave height and wavelength, and approximately linearly with respect to far-field ocean temperatures. Furthermore, the most widely used wave erosion parameterizations overestimate depth-average melt rates by a factor greater than two compared to the models developed here. We derive an analytical solution for wave-induced melt rate that more accurately represents thermal forcing and wave-driven heat transfer at the ice boundary, and which can be readily applied in future modeling studies. Furthermore, numerical solutions of box models developed here for wave-induced melting and meltwater plume transport can model sub-grid near-ice mixing and can be used in larger-scale ocean models simulating icebergs. We conclude by proposing the modification of a traditionally used simple power-law function describing wave-driven melt rates to more accurately model bulk iceberg mass loss.