Mathematical modelling of ice-sheet surface melt

Thesis

Shortwave radiation penetrating beneath an ice-sheet surface can cause internal melting and the formation of a near-surface porous layer known as the weathering crust. The weathering crust is a dynamic hydrological system that provides home to impurities and microbial life. It grows and decays in response to changing weather and climate conditions, affecting the albedo, the melt rate, and the transport of meltwater and nutrients across the ice-sheet surface. We develop a mathematical model, incorporating thermodynamics, water flow and population dynamics, for the evolution of such layers. The model accounts for conservation of mass and energy, for internal and surface-absorbed radiation, for water flow governed by Darcy's law, and for logistic growth of a microbial species mediated by nutrients that are sourced from the melting ice. Existing models have accounted for only one or two of these processes, so our model is valuable in providing a more complete picture. In this thesis, we use a one-dimensional reduction of the model to explore (1) the effect of the weathering crust on near-surface melt, (2) the response of the weathering crust to changing weather conditions, and (3) the potential of microbes to enhance melting via a feedback between the weathering crust, albedo and melting. Idealised steadily-melting and time-dependent solutions both with and without meltwater flow provide physical insight into the evolution of the weathering crust, the effect of microbes, and the conditions that favour growth and decay. Our model demonstrates the importance of accounting for the weathering crust and subsurface melt processes, and agrees well with observations of surface lowering, porosity and temperature when forced with weather data from the Greenland ice sheet. The model therefore provides a useful tool for exploring the response of the weathering crust to climate change, and hence the resulting consequences for surface albedo, melting and runoff.

Authors: Woods, T

• DOI: 10.5287/ora-e9gpppbm8
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: population dynamics; weathering crust; microbes; ice sheet; enthalpy method; porous media; phase change
• Subjects: Fluid dynamics; Glaciology