Instability of ice sheets and ice shelves
Dr. Sam Pegler (firstname.lastname@example.org)
Dr. Stephen Griffiths (email@example.com)
School of Mathematics, University of Leeds
Continental ice sheets, and their adjoining ice shelves which float upon coastal seas, play a central role in determining the Earth’s climate, ocean circulation, and sea levels. In the present day, there are ice sheets in Antarctica and Greenland, but they were generally much more widespread over the past 100,000 years. For example, 26,000 years ago at the Last Glacial Maximum, the Laurentide Ice Sheet covered much of North America whilst the Fenno-Scandian Ice Sheet covered much of northern Europe, as shown in Figure 1. Over the past 100,000 years, the ice sheets have undergone periodic oscillations in their total mass, in which the ice sheets lose and subsequently gain considerable amounts of ice every few thousand years. However, the reasons for these variations are not well understood, presenting a major open question in climate science. This project will develop and analyse mathematical models describing the mechanisms of ice-sheet–ocean interactions that control the mass balance of the past, present and future ice sheets on Earth.
Understanding the processes controlling the mass balance of ice sheets and ice shelves, i.e., their flow rates, growth and decay, and any movements of the grounding line where the ice sheets turns into an ice shelf, is of vital importance for climate science, and of major humanitarian importance in regard to future sea-level changes. Of particular interest is the possibility of instability, in which either the ice shelves break up, or the ice sheets rapidly advance or retreat. A recent example, from 2001, was the collapse of the Larsen B ice shelf in Antarctica, which led to the formation of a convoy of icebergs and acceleration of the grounded ice streams that fed it . Changes in ice sheets have global implications for weather and climate (for example, by reflecting incoming solar radiation), atmospheric and oceanic circulations (via freshwater input from melting ice at high latitudes), and sea level.
Perhaps the most famous examples of ice-sheet instability occurred as part of so-called Heinrich events, which apparently occurred about every 7,000 years over recent glaciations, and are associated with rapid climate change . Heinrich events are thought to involve massive discharges of ice from the Laurentide Ice Sheet via Hudson Strait; the resulting icebergs carried rock fragments across the North Atlantic, leading to a record in sediment cores. There is evidence for similar millennial-scale episodic instability of the Antarctic ice sheets , although data from the Southern Oceans is much sparser than that from the North Atlantic. There are many theories for the causes of episodic Heinrich events . One intriguing idea that has emerged in recent years is that large-amplitude ocean tides could be responsible for the ice-sheet instabilities underlying Heinrich events, based upon modelling results that predict the existence of unusually large tides in certain polar oceans (including the Labrador Sea, adjoining Hudson Strait) during recent glaciations [4, 5, 6, 7]. Although tides are known to cause small fluctuations in present-day ice-sheets , how they could lead to such a large-scale instability remains unknown. The present vague theories call for some sort of ‘preconditioning’ for other instabilities , or appeal to a critical tidal flexure of ice-shelves  with the resulting fractures triggering shelf break-up (cf. ). However, following an ice-shelf break up, the loss of buttressing they provide could potentially trigger ice sheets to expel ice at a faster rate over a relatively short period of time . This effect could be a key source of additional mass loss needed to explain Heinrich events, an open question that can be explored as part of this project.
This PhD project will involve detailed modelling of interactions between ice sheets, ice shelves, and ocean tides, with the aim of testing whether or not tides can lead to episodic instabilities of ice sheets, and, if so, whether these instabilities have the characteristics of Heinrich events. A series of investigations will be required.
What are the two-way interactions between ocean tides and overlying floating ice shelves, on short time scales? How large do the tides need to become in order to lead to significant fracturing, crevassing, rifting or softening  of the floating ice shelves? Can elastic flexing near the grounding line suppress tidal displacements? These will be treated as problems in elasticity or viscoelasticity of thin sheets, using a combination of theoretical development, analytical methods and numerical simulation.
If tides can indeed lead to the break up of ice shelves, what are the implications for the stability of the now unbuttressed ice sheet? Will it retreat? Will the ice shelf regrow? If so, what are the timescales? These problems can be treated using shallow-layer viscous flow approximations, of the sort commonly used in theoretical glaciology, with both analytical and numerical work required.
For appropriate continental shelf widths and depths, ocean tides will change substantially with the location of the ice-sheet grounding line. Does this feedback with the ice sheets allow for periodic instability events, without the need for external (climate or orbital) forcing? If so, what are the implied oscillation timescales, and ice discharges? Are these consistent with Heinrich events?
The existence of such periodic instabilities is likely to depend upon a special geometrical configuration, with the width and depth of the continental shelf key for the ocean tides, and the basin geometry key for the ice dynamics  (due to buttressing, pinning, etc.). How special are these configurations? Using topographic reconstructions of recent glaciations (such as ICE-5G of Figure 1, and its successors), along with appropriate results from global tidal models (cf. [5, 6]), what locations (if any) are candidates for such periodic instabilities? There would be a natural focus on Labrador Sea and Hudson Strait, as the source of Heinrich events (cf. ).
Potential for high-impact outcomes:
The origin of Heinrich events remains a topic of major importance in the paleoclimate community. The implied understanding of ice-sheet stability also has possible implications for understanding the dynamics of the present-day Antarctic ice sheets. The dynamics of these ice sheets (albeit under climate forcing) is of considerable importance, particularly with sea level in mind. Understanding the conditions for paleo-ice-sheet collapse will thus elucidate the conditions for future stability of present-day ice sheets.
The work will be performed in the Astrophysical and Geophysical Fluid Dynamics research group within the Department of Applied Mathematics. This is one of the leading research groups of its type in the country, with expertise in mathematical and numerical modelling of fluid dynamics in settings varying from the Earth (core, cryosphere, ocean and atmosphere), to our solar system (solar and planetary interiors), and beyond. Group members have the opportunity to take part in weekly discussion meetings, seminars in fluid dynamics, and seminars in applied mathematics. In addition to learning analytical, computational and writing skills during their research, our PhD students will enrol in taught graduate-level modules. These might be taught at Leeds (e.g., Advanced Geophysical Fluid Dynamics, Advanced Mathematical Methods) or taken as part of the UK-wide MAGIC distributed learning network (e.g., Nonlinear Waves, Numerical Methods in Python). The Panorama NERC DTP provides additional cohort-wide research training.
This PhD project would be well suited to somebody with a background in applied mathematics or theoretical physics/geophysics. Highly desirable would be expertise in one or more of fluid dynamics, solid mechanics, glaciology, asymptotic methods, and partial differential equations. Experience with computer programming, or the willingness to learn, is essential.
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