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Glacial erosional systems exhibit a complex, highly scaledependent phenomenology. Some aspects of modelling the development of glacial erosional landforms in response to glacial erosional processes acting over a wide range of scales are considered. The physics of ice at the glacier sole is discussed. A simple ice-water mixture theory is proposed. A method for finding the solution of the equations of motion of ice at the glacier sole based on the finite element velocities-pressure formulation is shown, which includes novel formulations for the sliding boundary condition, compression of ice and flow of water between ice and bedrock. These finite element formulations are used to simulate flows at the ice-rock interface. The use of the Laplace equation in simulating uni-axial flow is also considered, and further simulations are carried out using this equation. The results from these finite element simulations are used to consider erosional processes occurring at the glacier bed. The processes of abrasion are considered, and previous models are shown to be physically inconsistent. Cavitation, transiency and heterogeneity are shown to have an effect on clast-bed contact forces, and the local viscosity of ice is identified as being a further controlling variable on abrasion. These results are used to consider the likely development of hummocks of bedrock. A mass-balance analysis of basal debris is carried out and shown to have an important effect on erosional patterns. The equations describing the movement of a surface normal to itself are considered. Various solution techniques for these equations are tested, and requirements for the persistence of form under lowering are given. The modelling strategy used in this thesis is a nested hierarchy, with the various hierarchical levels corresponding to different scales. The effect of this hierarchisation on the modelling is discussed with respect to the generic properties of the systems, explanation and testability.

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This thesis considers the use of Interferometric Synthetic Aperture Radar (InSAR) for surveying temporal fluctuations in the velocity of glaciers in the Arctic region. The aim of this thesis is to gain a broader understanding of the manner in which the flow of both land- and marine-terminating glaciers varies over time, and to asses the ability of InSAR to resolve flow changes over timescales which provide useful information about the physical processes that control them. InSAR makes use of the electromagnetic phase difference between successive SAR images to produce interference patterns (interferograms) which contain information on the topography and motion of the Earth's surface in the direction of the radar line-of-sight. We apply established InSAR techniques (Goldstein et al., 1993) to (i) the 925 km2 LangjÖkull Ice Cap (LIC) in Iceland, which terminates on land (ii) the 8 500 km2 Flade Isblink Icecap (FIIC) in Northeast Greenland which has both land- and marine-terminating glaciers and (iii) to a 7 000 km2 land-terminating sector of the Western Greenland Ice Sheet (GrIS). It is found that these three regions exhibit velocity variations over contrasting timescales. At the LIC, we use an existing ice surface elevation model and dual-look SAR data acquired by the European Remote Sensing (ERS) satellite to estimate ice velocity (Joughin et al., 1998) during late-February in 1994. A comparison with direct velocity measurements determined by global positioning system (GPS) sensors during the summer of 2001 shows agreement (r2 = 0.86), suggesting that the LIC exhibits moderate seasonal and inter-annual variations in ice flow. At the FIIC, we difference pairs of interferograms (Kwok and Fahnestock, 1996) formed using ERS SAR data acquired between 15th August 1995 and 3rd February 1996 to estimate ice velocity on four separate days. We observe that the flow of 5 of the 8 outlet glaciers varies in latesummer compared with winter, although flow speeds vary by up to 20 % over a 10 day period in August 1995. At the GrIS, we use InSAR (Joughin et al., 1996) and ERS SAR data to reveal a detailed pattern of seasonal velocity variations, with ice speeds in latesummer up to three times greater than wintertime rates. We show that the degree of seasonal speedup is spatially variable and correlated with modeled runoff, suggesting that seasonal velocity changes are controlled by the routing of water melted at the ice sheet surface. The overall conclusion of this work is that the technique of InSAR can provide useful information on fluctuations in ice speed across a range of timescales. Although some ice masses exhibit little or no temporal flow variability, others show marked inter-annual, seasonal and even daily variations in speed. We observe variations in seasonality in ice flow over distances of ~ 10 km and over time periods of ~10 days during late-summer. With the aid of ancillary meteorological data, we are able to establish that rates of flow in western Greenland are strongly moderated by the degree of surface melting, which varies seasonally and secularly. Although the sampling of our data is insufficiently frequent and spans too brief a period for us to derive a general relationship between climate and seasonality of flow, we show that production of meltwater at the ice surface and its delivery to the ice bed play an important role in the modulation of horizontal flow speeds. We suggest that a similarly detailed investigation of other ice masses is required to reduce the uncertainty in predictions of the future Arctic land-ice contribution to sea level in a warming world.

The influence of seasonal influx of supraglacial meltwater on basal water pressures and consequent changes in ice surface velocity has been a focus of research spanning over three decades. With a need to better include glacial hydrology within models of ice sheet evolution, the ability to predict where and when meltwater reaches the subglacial system is paramount for understanding the dynamics of large Arctic ice masses. The response of ice velocities to melt production suggests efficient transmission of meltwater from the supraglacial to subglacial hydrologic systems, and it has been shown that build-ups of stored meltwater in supraglacial lakes can force crevasse penetration through hundreds of metres of ice. This thesis presents a new modelling routine for prediction of moulin formation and delivery of meltwater to the ice-bed interface. Temporal and spatial patterns of moulin formation and drainage of supraglacial lakes are presented, and quantitative controls on crevasse propagation are investigated through a series of sensitivity tests. _J .' . The model is applied to two glacial catchments: the Croker Bay catchment of the Devon Ice Cap in High Arctic Canada; and the Leverett glacier catchment of the Greenland Ice Sheet. Through model application to these sites, sensitivities to crevasse surface dimensions, ice tensile strength, ice fracture toughness and air temperatures are investigated. Model predictions of moulin formation and melt transfer are compared with field observations and remotely sensed data, including ice surface velocities, proglacial discharge, dynamic flow regimes, and visible surface features. The inclusion of spatially distributed points of meltwater delivery to the 'subglacial system is imperative to fully understand the behaviour of the subglacial drainage system. Furthermore, dynamic response to future climatic change and melt scenarios, and the evolution of ice masses, cannot be fully understood without first understanding the glacial hydrologic processes driving many of these changes.