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Tim Hill | Applied Mathematics, University of Waterloo
Mathematical modelling of supraglacial meltwater production and drainage
Mountain glaciers and the polar ice sheets exert a critical control on water resource availability, drive sea level change, and impact global ocean circulation. These and other impacts are controlled by surface meltwater that flows through the glacier hydrologic system to the base of the ice and drives seasonal and long-term changes in ice flow velocity. This thesis presents numerical models for the production and transport of meltwater runoff across the surface of melting glaciers and ice sheet.
First, a surface energy balance model is developed that improves on existing models by utilizing high resolution satellite data to capture spatial variations in surface melt. The model is applied to Kaskawulsh Glacier and Nàłùdäy (Lowell) Glacier in the St. Elias Mountains, Yukon, Canada using six years of in-situ meteorological data. By validating model outputs against in-situ measurements, it is shown that modelled seasonal melt agrees with observations within 9% across a range of elevations.
In order to determine how surface meltwater is transported through moulins, we develop the Subaerial Drainage System (SaDS) model. SaDS is a physics-based, finite-volume numerical model that calculates supraglacial runoff in both a distributed sheet and through supraglacial channels. The benefit of this approach is that a connected network of supraglacial channels and lakes naturally emerges without using prior information about the channel network, for example from satellite-derived maps. In synthetic settings and when applied to the Greenland Ice Sheet, model outputs show realistic and varied moulin flux rates, and modelled supraglacial lake and channel locations match those mapped from satellite images. These results demonstrate that SaDS is a promising tool to provide moulin inputs for subglacial and ice dynamic studies.
These models represent significant steps forward in their respective domains. Together, these tools will be valuable components of future modelling work, including for studies that aim to constrain how climatic variables control sea level contributions from glaciers and ice sheets.