Theses and Dissertations Collection

Despite rapid advances in ice sheet modeling, uncertainty in sea-level rise projections is growing. Thisis largely due to an increasingly refined understanding of inherently complex ice dynamical processes, especially at the ice-ocean interface. As more and more of this complexity is brought into ice sheet models, it is critical not only that we continue to advance our process-based understanding of ice dynamics, but also that the mathematical tools we use to develop that knowledge be well communicated among modelers. This dissertation provides a range of perspectives on these tools, from the critical analysis of a historical analytic model to the development and application of finite element schemes.

Historically, the equations governing the flow of glacier ice were solved by analytic methods. One ofthe most enduring analytic models in glaciology is the “Thomas model,” which describes the extending flow of an unconfined ice shelf. Despite its deep history and continued use in theory-building, there remain persistent miscommunications regarding the role of vertical shear stress in the Thomas model. Specifically, vertical shear is often interpreted as negligible – an interpretation at odds with the modern approach to constructing the model. We show that vertical shear stress should not be considered negligible even in simple analytic models, and we provide guidance on how to correctly calculate its value.

Analytic methods, however, are too simplistic to address many of the problems faced by glaciologiststoday. Instead, numerical methods are typically employed to solve glacier flow approximations of various levels of sophistication. We develop a finite element scheme for the hydrostatic approximation, which permits slightly more complexity than the approximations to the Stokes equations that are usually solved in glaciology. Besides introducing a new numerical tool with which glacier dynamics can be studied, our finite element scheme for the hydrostatic approximation reduces to familiar schemes for lower-order approximations. Thus, we provide a unifying framework for several finite element schemes at once.

We then provide a process-based explanation for a long-observed, but often overlooked, ice shelfrifting mechanism. Using the finite element software package icepack, we demonstrate that, where floating ice shelves detach from rigid lateral boundaries (“detachment zones”), the flow regime spatially transitions from confined to unconfined shelf flow, and we show that this transition can produce tension strong enough to fracture a shelf’s full thickness. Because the lateral contact between ice shelves and rigid boundaries is critical in suppressing instability feedbacks, the damage accrued in detachment zones may trigger those instabilities. We suggest that the rifting behaviour in detachment zones may be an important indicator of the vulnerability of coupled ice shelf/ice sheet systems to rapid glacier retreat and increased ice discharge.