Colin R. Meyer

The Path-Independent M Integral Implies the Creep Closure of Englacial and Subglacial Channels

Drainage channels are essential components of englacial and subglacial hydrologic systems. Here we use the M integral, a path-independent integral of the equations of continuum mechanics for a class of media, to unify descriptions of creep closure under a variety of stress states surrounding drainage channels. The advantage of this approach is that the M integral around the hydrologic channels is identical to same integral evaluated in the far-field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g. involving antiplane shear as well as overburden pressure. We start by analyzing the axisymmetric case and show that the Nye solution for the creep closure of the channels is implied by the path-independence of the M integral. We then examine the effects of superimposing antiplane shear. We show that the creep closure of the channels acts as a perturbation in the far-field, which we explore analytically and numerically. In this way, the creep closure of channels can be succinctly written in terms of the pathindependent M integral and understanding the variation with applied shear is useful for glacial hydrology models.

Inversion of a glacier hydrology model

ABSTRACT The subglacial hydrologic system exerts strong controls on the dynamics of the overlying ice, yet the parameters that govern the evolution of this system are not widely known or observable. To gain a better understanding of these parameters, we invert a spatially averaged model of subglacial hydrology from observations of ice surface velocity and outlet stream discharge at Kennicott Glacier, Wrangell Mountains, AK, USA. To identify independent parameters, we formally non-dimensionalize the forward model. After specifying suitable prior distributions, we use a Markov-chain Monte Carlo algorithm to sample from the distribution of parameter values conditioned on the available data. This procedure gives us not only the most probable parameter values, but also a rigorous estimate of their covariance structure. We find that the opening of cavities due to sliding over basal topography and turbulent melting are of a similar magnitude during periods of large input flux, though turbulent melting also exhibits the greatest uncertainty. We also find that both the storage of water in the englacial system and the exchange of water between englacial and subglacial systems are necessary in order to explain both surface velocity observations and the relative attenuation in the amplitude of diurnal signals between input and output flux observations.

Formation of ice eddies in subglacial mountain valleys

Radar data from both Greenland and Antarctica show folds and other disruptions to the stratigraphy of the deep ice. The mechanisms by which stratigraphy deforms are related to the interplay between ice flow and topography. Here we show that when ice flows across valleys or overdeepenings, viscous overturnings called Moffatt eddies can develop. At the base of a subglacial valley, the shear on the valley sidewalls is transferred through the ice, forcing the ice to overturn. To understand the formation of these eddies, we numerically solve the non-Newtonian Stokes equations with a Glens law rheology to determine the critical valley angle for the eddies to form. When temperature is incorporated into the ice rheology, the warmer basal ice is less viscous and eddies form in larger valley angles (shallower slopes) than in isothermal ice. We also show that when ice flow is not perpendicular to the valley orientation, complex 3D eddies transport ice down the valley. We apply our simulations to the Gamburtsev Subglacial Mountains and solve for the ice flow over radar-determined topography. These simulations show Moffatt eddies on the order of 100 meters tall in the deep subglacial valleys.

A Model for the Downstream Evolution of Temperate Ice and Subglacial Hydrology Along Ice Stream Shear Margins

15 Antarctic mass balance and contribution to sea level rise are dominated by the flow of ice 16 through narrow conduits called ice streams. These regions of relatively fast flow drain over 17 90% of the ice sheet and generate significant amounts of frictional heat at the ice stream mar18 gins where there is a transition to slow flow in the ridge. This heat can generate temperate 19 ice and a sharp transition in flow speed between the stream and the ridge. Within zones of 20 temperate ice, meltwater is produced and drains to the bed. Here we model the downstream 21 development of a temperate zone along an ice stream shear margin and the flow of meltwa22 ter through temperate ice into a subglacial hydrologic system. The hydrology sets the basal 23 effective pressure, defined as the difference between ice overburden and water pressure. Us24 ing the Southern shear margin of Bindschadler Ice Stream as a case study, our model results 25 indicate an abrupt transition from a distributed to channelized hydrologic system within a 26 few ice thicknesses of the point where the temperate zone initiates. This transition leads to a 27 strengthening of the till due to reduced pore pressure because the water pressure in the chan28 nel is lower than in the distributed system, a potential mechanism by which hydrology can 29 prevent lateral migration of shear margins. 30