The effect of buttressing on grounding line dynamics

Determining the position and stability of the grounding line of a marine ice sheet is a major challenge for ice-sheet models. Here, we investigate the role of lateral shear and ice-shelf buttressing in grounding line dynamics by extending an existing boundary layer theory to laterally confined marine ice sheets. We derive an analytic expression for the ice flux at the grounding line of confined marine ice sheets that depends on both local bed properties and non-local ice-shelf properties. Application of these results to a laterally confined version of the MISMIP 1a experiment shows that the boundary condition at the ice-shelf front (i.e. the calving law) is a major control on the location and stability of the grounding line in the presence of buttressing, allowing for both stable and unstable grounding line positions on downwards sloping beds. These results corroborate the findings of existing numerical studies that the stability of confined marine ice sheets is influenced by ice-shelf properties, in contrast to unconfined configurations where grounding line stability is solely determined by the local slope of the bed. Consequently, the marine ice-sheet instability hypothesis may not apply to buttressed marine ice sheets

The role of subtemperate slip in thermally driven ice stream margin migration

The amount of ice discharged by an ice stream depends on its width, and the widths of unconfined ice streams such as the Siple Coast ice streams in West Antarctica have been observed to evolve on decadal to centennial timescales. Thermally driven widening of ice streams provides a mechanism for this observed variability through melting of the frozen beds of adjacent ice ridges. This widening is driven by the heat dissipation in the ice stream margin, where strain rates are high, and at the bed of the ice ridge, where subtemperate sliding is possible. The inflow of cold ice from the neighboring ice ridges impedes ice stream widening. Determining the migration rate of the margin requires resolving conductive and advective heat transfer processes on very small scales in the ice stream margin, and these processes cannot be resolved by large-scale ice sheet models. Here, we exploit the thermal boundary layer structure in the ice stream margin to investigate how the migration rate depends on these different processes. We derive a parameterization of the migration rate in terms of parameters that can be estimated from observations or large-scale model outputs, including the lateral shear stress in the ice stream margin, the ice thickness of the stream, the influx of ice from the ridge, and the bed temperature of the ice ridge. This parameterization will allow the incorporation of ice stream margin migration into large-scale ice sheet models

Englacial Pore Water Localizes Shear in Temperate Ice Stream Margins

The margins of fast‐moving ice streams are characterized by steep velocity gradients. Some of these gradients cannot be explained by a temperature‐dependent viscosity alone. Laboratory data suggest that water in the ice‐grain matrix decreases the ice viscosity; we propose that this causes the strong localization of shear in temperate ice stream margins. However, the magnitude of weakening and its consequences for ice stream dynamics are poorly understood. Here we investigate how the coupling between temperate ice properties, ice mechanics, and drainage of melt water from the ice stream margin alters the dynamics of ice streams. We consider the steady‐state ice flow, temperature, water content, and subglacial water drainage in an ice stream cross section. Temperate ice dynamics are modeled as a two‐phase flow, with gravity‐driven water transport in the pores of a viscously compacting and deforming ice matrix. We find that the dependence of ice viscosity on meltwater content focuses the temperate ice region and steepens the velocity gradients in the ice stream margin. It provides a possible explanation for the steep velocity gradients observed in some ice stream shear margins. This localizes heat dissipation there, which in turn increases the amount of meltwater delivered to the ice stream bed. This process is controlled by the permeability of the temperate ice and the sensitivity of ice viscosity to meltwater content, both of which are poorly constrained properties

Response of Marine‐Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics

Recent observations indicate that many marine‐terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long‐term trends in climate forcing. In this study, we describe a simple two‐stage model that accurately emulates the response to external forcing of marine‐terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine‐terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine‐terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state

Oscillatory subglacial drainage in the absence of surface melt

The presence of strong diurnal cycling in basal water pressure records obtained during the melt season is well established for many glaciers. The behaviour of the drainage system outside the melt season is less well understood. Here we present borehole observations from a surge-type valley glacier in the St Elias Mountains, Yukon Territory, Canada. Our data indicate the onset of strongly correlated multi-day oscillations in water pressure in multiple boreholes straddling a main drainage axis, starting several weeks after the disappearance of a dominant diurnal mode in August 2011 and persisting until at least January 2012, when multiple data loggers suffered power failure. Jökulhlaups provide a template for understanding spontaneous water pressure oscillations not driven by external supply variability. Using a subglacial drainage model, we show that water pressure oscillations can also be driven on a much smaller scale by the interaction between conduit growth and distributed water storage in smaller water pockets, basal crevasses and moulins, and that oscillations can be triggered when water supply drops below a critical value. We suggest this in combination with a steady background supply of water from ground water or englacial drainage as a possible explanation for the observed wintertime pressure oscillations

Response of Marine‐Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics

Recent observations indicate that many marine‐terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long‐term trends in climate forcing. In this study, we describe a simple two‐stage model that accurately emulates the response to external forcing of marine‐terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine‐terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine‐terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state

Thermal controls on ice stream shear margins

Ice stream discharge responds to a balance between gravity, basal friction and lateral drag. Appreciable viscous heating occurs in shear margins between ice streams and adjacent slow-moving ice ridges, altering the temperature-dependent viscosity distribution that connects lateral drag to marginal strain rates and ice stream velocity. Warmer ice deforms more easily and accommodates faster flow, whereas cold ice supplied from ice ridges drives advective cooling that counteracts viscous heating. Here, we present a two-dimensional (three velocity component), steady-state model designed to explore the thermal controls on ice stream shear margins. We validate our treatment through comparison with observed velocities for Bindschadler Ice Stream and verify that calculated temperatures are consistent with results from previous studies. Sweeping through a parameter range that encompasses conditions representative of ice streams in Antarctica, we show that modeled steady-state velocity has a modest response to different choices in forcing up until temperate zones develop in the shear margins. When temperate zones are present, velocity is much more sensitive to changes in forcing. We identify key scalings for the emergence of temperate conditions in our idealized treatment that can be used to identify where thermo-mechanical feedbacks influence the evolution of the ice sheet

Modelling the migration of ice stream margins

The Siple Coast ice streams are long, narrow bands of ice within the Antarctic ice sheet. They move significantly faster than the surrounding ice ridges, and therefore discharge significantly more ice. Observations suggest that their fast flow is due to sliding along a water-saturated bed, while the bed of the neighbouring ridges generally appears to be frozen. The ice stream velocities and widths vary on decadal to centennial time scales, and these variations include the migration of the ice stream margins, where the fast flow slows down to the speed of the surrounding ice. In this thesis I show that conventional thin film models, which are used to calculate the evolution of ice sheets on continental scales, are only able to reproduce the inwards migration of ice stream margins and the subsequent shutdown of an ice stream. These processes are the result of an insufficient heat dissipation and freezing at the bed. Conversely, I find that the widening of ice streams into regions where the bed is frozen can only be modelled by taking small-scale heat transfer processes in the ice stream margin into account. Previous research has shown that ice stream widening results from an interplay of heating through lateral shearing in the ice stream margin and inflow of cold ice from the adjacent ridges. However, the relative importance of the different effects on the migration speed has not yet been quantified. To account for these processes, I derive a new boundary layer model for ice stream margins. The numerical solution of this model provides the margin migration speed as a function of large-scale ice stream properties such as ice stream width, ice thickness, and geothermal heat flux. The influence of different basal boundary conditions and temperate ice properties on the margin migration velocity is also investigated. To derive a parameterization of ice stream widening that can be used in continental-scale models, I consider asymptotic solutions with high heat production rates and high advection velocities, a limit that likely applies in real ice stream margins.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat

Ice streams

Non UBCUnreviewedAuthor affiliation: University of OxfordPostdoctora

Effects of calving and submarine melting on steady states and stability of buttressed marine ice sheets

Mass loss from ice shelves is a strong control on grounding-line dynamics. Here we investigate how calving and submarine melt parameterizations affect steady-state grounding-line positions and their stability. Our results indicate that different calving laws with the same melt parameterization result in more diverse steady-state ice-sheet configurations than different melt parameterizations with the same calving law. We show that the backstress at the grounding line depends on the integrated ice-shelf mass flux. Consequently, ice shelves are most sensitive to high melt rates in the vicinity of their grounding lines. For the same shelf-averaged melt rates, different melt parameterizations can lead to very different ice-shelf configurations and grounding-line positions. If the melt rate depends on the slope of the ice-shelf draft, then the positive feedback between increased melting and steepening of the slope can lead to singular melt rates at the ice-shelf front, producing an apparent lower limit of the shelf front thickness as the ice thickness vanishes over a small boundary layer. Our results illustrate that the evolution of marine ice sheets is highly dependent on ice-shelf mass loss mechanisms, and that existing parameterizations can lead to a wide range of modelled grounding-line behaviours