Thesis - University of Nottingham. / Fold map in v.l. Errata leaves inserted in v.l. Bibliography: v. 2., p. 464-476.

Recent interest in climatic change and ice .sheet variations points out the need for accurate and numerically stable models of time-dependent ice masses. Little attention has been paid to this topic by the glaciological community, and there is good reason to believe that much of the published literature on numerical modelling of the flow of glaciers and ice sheets is quantitatively incorrect. In particular, the importance of the nonlinear instability has not been widely recognized. The purposes of this thesis are to develop and to verify a new numerical model for glacier flow, compare the model to another widely accepted model, and to demonstrate the model in several glaciologically interesting applications. As in earlier work, the computer model solves the continuity equation together with a flow law for ice. Thickness profiles along flow lines are obtained as a function of time for a temperate ice mass with arbitrary bed topography and mass balance. A set of necessary tests to be satisfied by any numerical model of glacier flow is presented. The numerical solutions are compared with analytical solutions; these include a simple thickness-velocity relation to check terminus mobility, and Burgers* equation to check continuity and dynamic behaviour with full nonlinearity. An attempt has been made to verify the accuracy of the computer model of Budd and Mclnnes (1974), Rudd (1975) and Mclnnes (unpublished). These authors have reported problems with numerical instability. If the existing documentation is accurate, the Budd-Mclnnes model appears to suffer from mass conservation violations both locally and globally. The new numerical model developed in this thesis can be used to reconstruct the velocity field within the glacier at each time step; this velocity field satisfies continuity and Glen's flow law for ice. Integration of this velocity field yields the trajectories of individual ice elements flowing through the time-varying ice mass. The trajectories and velocity field are checked by comparison with an analytical solution for a steady state ice sheet (Nagata, 1977). The model in this thesis is not restricted to steady state, and it avoids the violations of mass conservation, and the approximations about the velocity field found in some published trajectory models. The feasibility of using stable isotopes to investigate prehistoric surging of valley glaciers has been studied with a model simulating the Steele Glacier, Yukon Territory. A sliding < velocity and surge duration were specified, based on the observations of the 1966-67 surge. A surge period of roughly 100 years gave the most realistic ice thickness throughout the surge cycle. By calculating ice trajectories and using two plausible relationships between 6(01B/016) and position or height, longitudinal sections and surface profiles of 6 were constructed for times before, during, and after a surge. Discontinuities of up to 0.8°/Oo were found across several surfaces dipping upstream into the glacier. Each of these surfaces is the present location of the ice which formed the ice-air interface at the time a previous surge began. It may be difficult to observe these surfaces on the Steele Glacier due to the large and poorly-understood background variability of 6. The generation of wave ogives has been examined following the theory of Nye (I958[b])r wherein waves are caused by a combination of seasonal variation in mass balance and plastic deformation in an icefall. The wave train generated on a glacier is shown in this thesis to be a convolution of the velocity gradient with an integral of the mass balance function. This integral is the impulse response of the glacier surface to a step in the velocity function. Spatial variations in the glacier width and mass balance also contribute to the wave train. This formulation is used to explain why many icefalls do not generate wave ogives in spite of large seasonal balance variations and large plastic deformations. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

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Thesis (Ph. D.) in Physics--University of Maine, 2003. / Includes vita. Includes bibliographical references (leaves 111-116).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

Several aspects of impulse radar echo sounding of small glaciers are investigated. First, the ranges of values expected for conductivity and relative dielectric permittivity of glacier ice, glacier bed materials and mixtures of ice and rock are established. These parameters, and the fundamentals of electromagnetic wave propagation, are employed in a modelling scheme that examines the reflection of pulses from planar reflectors within the glacier. The glacier bed can be modelled as solid rock or unconsolidated debris and as either frozen or wet. A layer of mixed ice and rock between the glacier ice and bed can also be included. Signal enhancement, especially using multi-channel principal component analysis, is discussed. Discussion of practical application of the technique begins with the description of a portable microprocessor-controlled instrument capable of recording digitized echograms. Then results from experiments on Trapridge Glacier, Yukon Territory are presented. Surveys up to half a kilometer long with soundings at 1 to 20 m intervals were conducted. Bed topography is presented and locally anomalous sections are examined. Smaller-scale parameters such as the attenuation constant of ice and reflector properties are also extracted from the data. Subglacial and englacial temporal variations were studied by automatically recording echoes at one location every 20 minutes over a three-day period. Such experiments are to be used in the future in conjunction with other, concurrent, geophysical and hydrological investigations. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

In order to increase coverage, mass balance changes of the world’s ice sheets are increasingly derived from surface elevation changes measured via satellite. Across the percolation zone of the Greenland Ice Sheet, meltwater, percolation and refreezing cause a re-distribution of mass through densification which may result in elevation change with no associated mass loss. Therefore, densification processes need to be quantified, spatially and temporally, and accounted for in mass balance measurements. This thesis investigates the relationships between patterns of elevation change and temporally and spatially variable accumulation and densification processes. In doing so, it provides an important contribution to the validation of the European Space Agency’s CryoSat-2 mission by placing error bars on the accuracy to which changes in satellite-measured ice-mass surface elevation represent real changes in ice mass. Temporal variability in near-surface (<10 m) snowpack and firn density and structure was measured in snowpits, shallow cores and using a neutron probe in the spring and autumn of 2004 at ~1945 m elevation (T05, 69o 51N, 47o 15W) in the percolation zone of the Greenland Ice Sheet. Results show that average snowpack density increased by 26% from spring to autumn, with a 5% (7.6 cm) increase in elevation, and a corresponding 32% increase in mass. Spatial variability was investigated at 11 sites along two transects at spatial scales of 1 m – 10 km. Whilst there was little variability in small scale (1 - 100 m) density changes, ‘seasonal densification’ increased at lower elevations, rising to 47% 10 km closer to the ice sheet margin at 1860 m a.s.l. The spatial variability in seasonal densification was further investigated in spring 2006 at seven sites located at ~10 km intervals along a 57 km transect spanning a 350 m elevation range. Snowpits and shallow cores reveal no significant variation in spring (prior to melt) snowpack density but following summer melt and refreezing cycles, seasonal densification decreased with increasing elevation at 32 kg m-3 per 100 m. Measurements at three sites ranging in elevation from 1860 – 2015 m and spanning three melt-seasons show inter-annual variation in the seasonal densification gradient. In order to obtain a longer time series of mass balance, a 17 m core retrieved in spring 2004 was analysed for stratigraphy, density and ionic and isotopic concentrations to identify annual layers. Unfortunately, the seasonal melt cycle (whereby on average 10% of the snowpack undergoes melt), results in a complex stratigraphy and density and ionic concentrations that cannot be resolved into a seasonal signature. However, the δ18O and δ D isotopes show clear sinusoidal fluctuations, which have been used to derive annual mass balance from 1986 to 2003. These show a mean annual accumulation of 53.7 cm w.e. (s.d. 12.9 cm w.e.) although the accuracy of these measurements is compromised by the percolation of meltwater through more than more year’s snowpack. These findings confirm that estimates of mass balance cannot be calculated solely from observed changes in surface elevation. However, predicting spatial and temporal variations in densification is not straightforward because of the complex inter-annual variations in the processes of accumulation, melt, percolation and refreezing.

Hydrology is recognised as an important component of the glacial system in alpine environments. In particular, the subglacial drainage of surface meltwaters is known to exert a strong influence on the motion of glaciers and on their capacity to erode the underlying bedrock. This thesis examines the more poorly understood drainage system of the Greenland Ice Sheet, with specific focus on Leverett Glacier, a landterminating outlet glacier on the ice sheet’s western margin. Because of the vast size of the ice sheet, the influence of the drainage system could have wide ranging implications, most notably for sea level rise and continental scale landscape evolution. The thesis commences with an investigation into the morphology of the drainage system of the lower 14 km of Leverett Glacier. This is undertaken using a variety of field methods, including dye tracing and the monitoring of proglacial discharge, englacial water levels, surface melt rates and glacier motion. The data reveal that the drainage system of the glacier closely resembles that of alpine glaciers, undergoing an evolution from distributed to channelised drainage morphologies as the melt season progresses. Another aspect of the field data, the suspended sediment load evacuated from the subglacial system in the emerging proglacial river, is then examined to investigate the impact that this drainage system morphology has on the interaction between the glacier and the underlying bedrock or substrate. This demonstrates that the presence of large, efficient subglacial drainage channels allows for the removal of vast quantities of basal debris during much of the melt season, facilitating an erosion rate 1-2 orders of magnitude greater than previously proposed for ice sheet settings. The thesis then focuses on the relationship between discharge, water pressure and ice motion. Observations from Greenlandic and alpine glaciers demonstrate that glaciers generally decelerate through the melt season following a maximum velocity induced by the onset of melt in the spring. The data indicate that the evolution of the drainage system from a distributed to a channelised morphology occurs rapidly and so can only explain this trend in ice velocity during the early part of the melt season. Beyond this period, ice velocity patterns can instead be explained primarily by transient fluctuations in water pressure within the channelised drainage system. These transient pressure fluctuations result from the lag between changes to the rate of meltwater input to the glacier and the subsequent adjustment of channel cross section. This indicates that it is crucial to consider temporal variability in melt rate when seeking to link climate with the dynamics of ice sheets and glaciers. This process can be simulated, which is demonstrated by using the proglacial discharge record to model subglacial water pressure and ice velocity. In the following chapter, this model is built upon by considering how these variations in water pressure, originating in discrete subglacial channels, control sliding velocities across large areas of the glacier. Detailed examination of high-resolution ice velocity records from Leverett Glacier reveals that, in keeping with theory, horizontal ice velocity is dependent on both the volume of subglacial cavities and the rate-of-change of this volume. A simple model of subglacial water movement is then used to demonstrate how these changes in the cavity system could be driven by the pressure fluctuations predicted within the channelised drainage system. This enables a system scale model of glacier hydrology to be developed, which is presented in the final chapter, linking variations in surface melt rate to channel pressure, cavity volume and ultimately ice motion. In summary, this research has helped to illuminate the morphology and functioning of the drainage system of Leverett Glacier. This has improved our understanding of how hydrology influences both the motion of the Greenland Ice Sheet and its impact on the underlying topography, and enabled better prediction of how these processes are influenced by changes in climate.

In this thesis, I present results from a two-year study of strain-rate variations along a flow line on the western margin of the Greenland ice sheet. I used baseline network solutions to investigate variations in longitudinal strain rates over the 2006 and 2007 melt seasons. Analyses revealed high-magnitude, short-duration events of increased longitudinal strain early in the melt season coincident with a high melt year, suggesting a link between melt production and its effects on seasonal ice flow. Results from 2006 data show that longitudinal strain rates became variable shortly after the onset of melt (day 186) changing up to ~ 15 x 10-4 a-1 within 24 hours. The onset of melting occurred earlier in 2007 (day 153) and was also followed closely by strain-rate deviation from background rates calculated prior to melting. The data revealed rapid (hours to days), high-magnitude (two to ten times greater than background rates) changes in longitudinal strain rates (hereafter referred to as ‘high-strain’ events) that occurred both on the small-scale (affecting 1-4 baselines) and on the large-scale (affecting 5 or more baselines). Large-scale high-strain events were infrequent, on the order of two events per season. Events were likely caused by drainage of supraglacial meltwater that penetrated to the bed of the glacier raising the basal water pressure. The increase in pressure reduced the basal resistive stress, and allowed rapid local acceleration. The basal stress reduction was transmitted to areas of higher stress which resulted in longitudinal compression of the ice down glacier and longitudinal extension up glacier. The evolution of high-strain events altered longitudinal strain rates more than 15 km along flow from the site of initiation. I estimated the origin and spatial extent of highstrain events by assessing the magnitude of the strain-rate variations in various baselines, and observing whether the altered strain regime was extensive or compressive. Magnitude and timing of changes in strain suggest that high-strain events originated in the ablation zone, the equilibrium zone, and inland of the equilibrium zone, and indicate that short-term altered stress conditions are not confined to the ablation zone. The background strain-rate for 2007 (~ -7 x 10-4 a-1 for a 37 km longitudinal baseline) was similar to the 2006 longitudinal background rate. When extrapolating the 2006 background rate over the melt season, the expected change in baseline length (~ 11 m) was similar to the observed change (~ 9 m). In contrast, when extrapolating the 2007 background rate over the melt season, the expected shortening was ~ 6 m, but the observed shortening was less than 1 m. This result suggests that seasonal high-strain events have the ability to alter longitudinal baseline length, allowing a greater ice flux to lower elevations where melting occurs for a larger portion of the year. However, the cumulative seasonal effects of both large-scale and small-scale strain events are modest, and indicate that seasonal changes in strain rates have a minor effect on the overall stability of the ice sheet. Nevertheless, it is possible that over much longer timescales these seasonal changes may become more important with increasing temperatures and available melt. Results from this study may also be useful in making broader inferences regarding the response of grounded portions of the ice sheet to seasonal changes in basal resistive stress.