LABORATORY AND THEORETICAL INVESTIGATION INTO WAVE-INDUCED EROSION OF ICE CLIFFS

Abstract

Wave erosion is one of the dominant deterioration mechanisms for icebergs in the open ocean, while also contributing to the ablation of ice shelves and marine-terminating glacier fronts. Oscillatory wave action around the waterline of any vertical ice cliff efficiently erodes a notch into the ice wall, over time resulting in calving of both the undercut ice overhang and the submerged protrusion/foot—a consequence that makes wave erosion especially effective at rapidly breaking down large bodies of ice. However, despite being widely considered a key driver of ice melting and breakup, few studies have sought to thoroughly investigate this mechanism either experimentally or theoretically. The current wave erosion parameterization is based on only a handful of empirical works (and one theoretical attempt) from decades ago, and has been incorporated in numerous ice sheet, ocean, and climate models since its publication. This presents a persistent and significant source of uncertainty for ice melting parameterizations, and a clear call to be re-addressed in order to improve projections of future climate change impacts, as freshwater and heat fluxes to the ocean associated with ice melt have crucial feedbacks with global climate. Here, we report on several laboratory experiments dedicated to wave erosion of ice, along with a new theoretical approach to understanding what exactly might control the ability of surface waves to enhance waterline melting of vertical ice cliffs. The theory begins with dimensional analysis of the problem, postulating that the wave steepness, wave Reynolds number, Stefan number, Eckert number, and the square root of the water thermal diffusivity times the wave angular frequency will be influential in setting the melt rate. Then, we derive a novel equation for the wave-induced melt rate based on heat transport across a boundary layer for waves reflected off a vertical wall, coupled with a Stefan Problem to account for the phase change that occurs at the moving ice-water interface. On the experimental side, seven ice blocks were melted in a room-temperature flume subject to incident wave amplitudes between 0.3 and 2.0 cm and freshwater (zero salinity) temperatures from 22°C (room temperature) down to 10°C. Data from three ultrasonic wave gauge sensors were used to characterize the incident wave conditions and the reflection coefficient of the initially-vertical ice face, while quantitative image analysis was performed to estimate the maximum melt rate in the wavecut notch. The resulting melt rates are visualized as functions of wave steepness and water temperature, and compared with multiple theoretical predictions. The overarching goal of this thesis work is to aid in the development of a more physically-sound and observationally-robust parameterization of wave erosion that can be incorporated into models of ice, ocean, and climate interactions.