Modelling glacial erosional landform development

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

Draping or overriding: The effect of horizontal stress gradients on internal layer architecture in ice sheets

Internal isochronic layers in ice sheets sensed by radar show two characteristic relationships to the basal topography: Either they override it, with layers above the crests of rises lying essentially flat, or they drape over it, with the layers following rises and falls in basal topography. A mechanical theory is presented which shows that overriding is the expected behavior when topographic wavelengths are comparable with or less than the ice thickness, while draping occurs at longer wavelengths. This is shown with analytical perturbation solutions for Newtonian fluids, numerical perturbation solutions for nonlinear fluids, and finite element solutions for nonlinear fluids and large-amplitude variations. Bed variation from topography and changes in the basal boundary condition are considered, for fixed bed and sliding beds, as well as three-dimensional flows and thermomechanically coupled flows. In all cases, the dominant effect on draping/overriding is the wavelength of the topography or variation in basal boundary conditions. Results of these full mechanical system calculations are compared with those from the shallow ice approximation and the longitudinal stress approximation. Some calculations are carried out for zero accumulation, where the age of the ice and therefore isochrone geometry is not defined. It is shown that there is a close relationship between isochrones and streamlines, and that they behave similarly when bed wavelength divided by the ice thickness is small compared with the ratio of ice velocity and accumulation rate, which is a useful approximation. Numerical comparisons of isochrones and streamlines show them to be virtually coincident

On the Reconstruction of Palaeo-Ice Sheets: Recent Advances and Future Challenges

Reconstructing the growth and decay of palaeo-ice sheets is critical to understanding mechanisms of global climate change and associated sea-level fluctuations in the past, present and future. The significance of palaeo-ice sheets is further underlined by the broad range of disciplines concerned with reconstructing their behaviour, many of which have undergone a rapid expansion since the 1980s. In particular, there has been a major increase in the size and qualitative diversity of empirical data used to reconstruct and date ice sheets, and major improvements in our ability to simulate their dynamics in numerical ice sheet models. These developments have made it increasingly necessary to forge interdisciplinary links between sub-disciplines and to link numerical modelling with observations and dating of proxy records. The aim of this paper is to evaluate recent developments in the methods used to reconstruct ice sheets and outline some key challenges that remain, with an emphasis on how future work might integrate terrestrial and marine evidence together with numerical modelling. Our focus is on pan-ice sheet reconstructions of the last deglaciation, but regional case studies are used to illustrate methodological achievements, challenges and opportunities. Whilst various disciplines have made important progress in our understanding of ice-sheet dynamics, it is clear that data-model integration remains under-used, and that uncertainties remain poorly quantified in both empirically-based and numerical ice-sheet reconstructions. The representation of past climate will continue to be the largest source of uncertainty for numerical modelling. As such, palaeo-observations are critical to constrain and validate modelling. State-of-the-art numerical models will continue to improve both in model resolution and in the breadth of inclusion of relevant processes, thereby enabling more accurate and more direct comparison with the increasing range of palaeo-observations. Thus, the capability is developing to use all relevant palaeo-records to more strongly constrain deglacial (and to a lesser extent pre-LGM) ice sheet evolution. In working towards that goal, the accurate representation of uncertainties is required for both constraint data and model outputs. Close cooperation between modelling and data-gathering communities is essential to ensure this capability is realised and continues to progress

Bedmap2: improved ice bed, surface and thickness datasets for Antarctica

We present Bedmap2, a new suite of gridded products describing surface elevation, ice-thickness and the seafloor and subglacial bed elevation of the Antarctic south of 60° S. We derived these products using data from a variety of sources, including many substantial surveys completed since the original Bedmap compilation (Bedmap1) in 2001. In particular, the Bedmap2 ice thickness grid is made from 25 million measurements, over two orders of magnitude more than were used in Bedmap1. In most parts of Antarctica the subglacial landscape is visible in much greater detail than was previously available and the improved data-coverage has in many areas revealed the full scale of mountain ranges, valleys, basins and troughs, only fragments of which were previously indicated in local surveys. The derived statistics for Bedmap2 show that the volume of ice contained in the Antarctic ice sheet (27 million km3) and its potential contribution to sea-level rise (58 m) are similar to those of Bedmap1, but the mean thickness of the ice sheet is 4.6% greater, the mean depth of the bed beneath the grounded ice sheet is 72 m lower and the area of ice sheet grounded on bed below sea level is increased by 10%. The Bedmap2 compilation highlights several areas beneath the ice sheet where the bed elevation is substantially lower than the deepest bed indicated by Bedmap1. These products, along with grids of data coverage and uncertainty, provide new opportunities for detailed modelling of the past and future evolution of the Antarctic ice sheets

Bedmap2: improved ice bed, surface and thickness datasets for Antarctica

We present Bedmap2, a new suite of gridded products describing surface elevation, ice-thickness and the seafloor and subglacial bed elevation of the Antarctic south of 60° S. We derived these products using data from a variety of sources, including many substantial surveys completed since the original Bedmap compilation (Bedmap1) in 2001. In particular, the Bedmap2 ice thickness grid is made from 25 million measurements, over two orders of magnitude more than were used in Bedmap1. In most parts of Antarctica the subglacial landscape is visible in much greater detail than was previously available and the improved data-coverage has in many areas revealed the full scale of mountain ranges, valleys, basins and troughs, only fragments of which were previously indicated in local surveys. The derived statistics for Bedmap2 show that the volume of ice contained in the Antarctic ice sheet (27 million km3) and its potential contribution to sea-level rise (58 m) are similar to those of Bedmap1, but the mean thickness of the ice sheet is 4.6% greater, the mean depth of the bed beneath the grounded ice sheet is 72 m lower and the area of ice sheet grounded on bed below sea level is increased by 10%. The Bedmap2 compilation highlights several areas beneath the ice sheet where the bed elevation is substantially lower than the deepest bed indicated by Bedmap1. These products, along with grids of data coverage and uncertainty, provide new opportunities for detailed modelling of the past and future evolution of the Antarctic ice sheets

Characterizing ice sheets during the Pliocene: evidence from data and models

The Pliocene (c. 5.3 - 1.8 Myr BP) was the last epoch of geological time in which global temperatures were generally higher than modern. It is important if we are to understand the dynamics of warm climates. This is particuarly true of the interaction of climate and cryosphere, where the Pliocene may represent the first epoch in which ice sheets, at least on Antarctica, were a permanent feature. In this paper, we review the available evidence for the state of ice sheets during the Pliocene as well as previous attempts to model them. We then present new models and sensitivity studies of the mid-Pliocene East Antarctic Ice Sheet (EAIS) and consider the implications for the debate on ice-sheet stability during the Pliocene. These new reconstructions suggest that the mid-Pliocene EAIS was significantly smaller than modern, but the modelled average mid-Pliocene climate is not sufficient to cause the widespread deglaciation suggested by Sirius Group diatom evidence

Stochastic perturbation of divide position

Perturbation of divide position is considered by a linearization about the Vialov-Nye solution and also about related solutions with 0(1) relief. Relaxation times of one-sixteenth the fundamental thickness/accumulation-rate time-scale are found for the Vialov-Nye configuration, while substantial basal topography can halve the rate of relaxation. Steady divide position is most sensitive to anti-symmetric accumulation-rate distributions near the divide, but transient divide motion is most strongly excited by anti-symmetric accumulation rate variations halfway between the margin and the divide. Relaxation times for the Antarctic Peninsula divide position are estimated to be around 200 years, while the larger Greenland ice sheet has a divide-position relaxation time of around 600 years. Modelling accumulation rate as a white-noise process permits analysis of divide perturbation as a (stochastic) Ornstein-Uhlenbeck process, where the standard deviation of the response is proportional to the standard deviation of the forcing. If observed accumulation-rate variability in the Antarctic Peninsula were antisymmetric about the divide, it would be sufficient to force the divide position to fluctuate with standard deviation 10-20 times the depth of the ice sheet. There appears to be sufficient noise to cause Raymond bumps to be spread significantly. More data on the statistical variation of accumulation with position are needed. Random forcing will increase the complexity of any fold structures created in the divide region and in particular the number of such structures intersecting any borehole