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

Widespread movement of meltwater onto and across Antarctic ice shelves

Surface meltwater drains across ice sheets, forming melt ponds that can trigger ice-shelf collapse acceleration of grounded ice flow and increased sea-level rise. Numerical models of the Antarctic Ice Sheet that incorporate meltwater’s impact on ice shelves, but ignore the movement of water across the ice surface, predict a metre of global sea-level rise this century in response to atmospheric warming. To understand the impact of water moving across the ice surface a broad quantification of surface meltwater and its drainage is needed. Yet, despite extensive research in Greenland and observations of individual drainage systems in Antarctica, we have little understanding of Antarctic-wide surface hydrology or how it will evolve. Here we show widespread drainage of meltwater across the surface of the ice sheet through surface streams and ponds (hereafter ‘surface drainage’) as far south as 85° S and as high as 1,300 metres above sea level. Our findings are based on satellite imagery from 1973 onwards and aerial photography from 1947 onwards. Surface drainage has persisted for decades, transporting water up to 120 kilometres from grounded ice onto and across ice shelves, feeding vast melt ponds up to 80 kilometres long. Large-scale surface drainage could deliver water to areas of ice shelves vulnerable to collapse, as melt rates increase this century. While Antarctic surface melt ponds are relatively well documented on some ice shelves, we have discovered that ponds often form part of widespread, large-scale surface drainage systems. In a warming climate, enhanced surface drainage could accelerate future ice-mass loss from Antarctic, potentially via positive feedbacks between the extent of exposed rock, melting and thinning of the ice sheet

Musical memories of Nigeria

Most of the instruments I heard were percussive. There were the ordinary tomtom and drum, and some extraordinary drums carved for juju ceremonial. There were logs of wood hollowed out through a slot, with one “cheek” thinner than the other and thus giving a higher note when struck. Then there was the Ilu or dundun drum. The wooden part is shaped like an hour glass; there is a skin head at each end, the skins being joined together all round by thonging. You hold it under your left arm and strike the upper head with a drumstick curved like a crane’s bill; by squeezing and relaxing the arm pressure on the thongs, you can raise or lower the pitch of the note. The result is an intriguing “pop pop pop” running with great mobility up and down over a range of a full fifth. This instrument is used also as a “talking drum” for conveying messages. Rattles? All sorts. One like a pepper pot containing seeds. One a gourd or calabash covered with a bead net which rattles beautifully when shaken. Or a species of nut shells strung together, which make an almost deafening row. Then there are gongs: round, square or flat, of iron or brass. Every senior Chief has his private band, which plays perpetually; also a bard to sing his praises. There are traditional songs for every occasion: birth, initiation, marriage, death, the propitiation of ancestors, and so on. Cult groups have their own songs; and different kinds of song are sung with a different quality of voice

Chaotic dynamics of a glaciohydraulic model

A model subglacial drainage system, coupled to an ice-dammed reservoir that receives a time-varying meltwater input, is described and analysed. In numerical experiments an ice-marginal lake drains through a subglacial channel, producing periodic floods, and fills with meltwater at a rate dependent on air temperature, which varies seasonally with a peak value of Tm. The analysis reveals regions of Tm parameter space corresponding to ‘mode locking’, where flood repeat time is independent of Tm; resonance, where decreasing Tm counter-intuitively increases flood size; and chaotic dynamics, where flood cycles are sensitive to initial conditions, never repeat and exhibit phase-space mixing. Bifurcations associated with abrupt changes in flood size and timing within the year separate these regions. This is the first time these complex dynamics have been displayed by a glaciohydraulic model and these findings have implications for our understanding of ice-marginal lakes, moulins and subglacial lakes

Antarctic surface hydrology and impacts on ice-sheet mass balance

Melting is pervasive along the ice surrounding Antarctica. On the surface of the grounded ice sheet and floating ice shelves, extensive networks of lakes, streams and rivers both store and transport water. As melting increases with a warming climate, the surface hydrology of Antarctica in some regions could resemble Greenland’s present-day ablation and percolation zones. Drawing on observations of widespread Antarctica surface water and decades of study in Greenland, we consider three modes by which meltwater could impact Antarctic mass balance: increased runoff, meltwater injection to the bed, and meltwater-induced ice-shelf fracture, all of which may contribute to future ice sheet mass loss from Antarctica

Ice‐Shelf Basal Melt Channels Stabilized by Secondary Flow

Ice-shelf basal channels form due to concentrated submarine melting. They are present in many Antarctic ice shelves and can reduce ice-shelf structural integrity, potentially destabilizing ice shelves by full-depth incision. Here, we describe the viscous ice response to a basal channel - secondary flow - which acts perpendicular to the channel axis and is induced by gradients in ice thickness. We use a full-Stokes ice-flow model to systematically assess the transient evolution of a basal channel in the presence of melting. Secondary flow increases with channel size and reduces the rate of channel incision, such that linear extrapolation or the Shallow-Shelf Approximation cannot project future channel evolution. For thick ice shelves (> 600 m) secondary flow potentially stabilizes the channel, but is insufficient to significantly delay breakthrough for thinner ice (< 400 m). Using synthetic data, we assess the impact of secondary flow when inferring basal-channel melt rates from satellite observations

Modelling the coupling of flood discharge with glacier flow during jökulhlaups

We explore a mathematical model that couples together a thermomechanically evolving subglacial channel, distributed cavity drainage, and basal sliding along a subglacial flood path fed by a jökulhlaup lake. It allows water transfer between channel and cavities and a migrating subglacial water divide or 'seal' to form between floods. Notably, it accounts for full coupling between the lake and subglacial drainage in terms of both discharge and pressure, unlike models that neglect the pressure coupling by imposing a known history of lake discharge at the channel inlet. This means that flood hydrographic evolution and its impact on glacier motion are consistently determined by our model. Numerical simulations for a model alpine lake yield stable limit cycles simulating repeating jökulhlaups, with the channel drawing water from the cavities at a varying rate that modulates basal sliding during each flood. A wave of fast sliding propagates down-glacier at flood initiation, followed by deceleration as the growing channel sucks water from the cavities. These behaviours cannot be correctly simulated without the full coupling. We show that the flood's peak discharge, its initiation threshold and the magnitude of the 'fast sliding' wave decrease with the background water supply to the cavities