Modelling Ice-Dammed Lake Drainage

The drainage of ice-dammed lakes produces floods that can pose hazards, waste water resources and modulate ice flow. In this thesis I investigate several aspects of ice-dammed lake drainage through the development and analysis of mathematical models.
After an introduction in the first chapter and a description of the mathematical background to the thesis in the second, the third chapter investigates the mechanisms behind observed variability in the size and timing of subglacial floods from ice-dammed lakes. In particular, I examine how environmental controls like the weather and the shape of glaciers affect floods.
In the next chapter, I quantify how well simple models can predict the dates of floods from an ice-marginal lake in Kyrgyzstan. I find that incorporating environmental controls into models improves their prediction ability.
Next I investigate the coupling between subglacial drainage and glacier motion during ice-dammed lake drainage by developing and analysing a model which couples a marginal lake, glacier sliding, subglacial drainage through a channel and subglacial drainage through a distributed system of cavities. I show how changes in lake level cause the rate at which a glacier slides to increase during the first half of floods and decrease during the second half.
The next two chapters are concerned with two lake-drainage scenarios that involve water flowing as an open stream: firstly, the subglacial open-channel flow that occurs after a marginal lake drains completely during a flood, and secondly, the drainage of supraglacial lakes across the surface of ice sheets.
I end the thesis with a summary of my findings and some suggestions of theoretical and field-based investigations that are worthwhile pursing in the future.