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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.

The relationships between teleconnection patterns the Pacific/North American (PNA) index, North Atlantic Oscillation (NAO) and the El Nino/Southern Oscillation (ENSO)—and lake-effect snowfall are examined. Bivariate and partial correlations are used over seasonal and semi-seasonal periods for stations within the Lake Erie snowbelt to link teleconnection phases to snowfall increases. Significant negative correlations were seen throughout the entire winter between NAO and snowfall. Relationships between PNA and ENSO on snowfall were less evident, with significant correlations during the mid-winter months between a positive PNA and snowfall and significant correlations during the late winter in the western zone between a negative ENSO and snowfall. / Department of Geography

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Observational and modelling studies show that the warming of the Arctic is leading to shrub expansion. This shift in vegetation cover is expected to significantly alter the distribution of snow across the landscape and the interactions between the land surface and the atmosphere. Shrubs capture wind-blown snow, increasing snow depth and decreasing winter water loss through sublimation, and bend beneath the weight of snow, affecting albedo. Snow is highly insulative and affects the soil hydrological and thermal properties. Therefore, as the snow-vegetation-soil interactions is expected to be at the core of feedback loops leading to further shrub expansion, there is a need for models to be able to simulate these processes accurately. Initially using the community land surface model JULES (Joint UK Land Environment Simulator) this study investigates the effects of shrub-tundra on snow and runoff. Alternative formulations of soil processes are proposed, which are better adapted to the representation of subgrid heterogeneity in cold regions than the current model formulation, and evaluated over the Abisko and Torne-Kalix river basins. In addition, a high resolution shrub bending model, which calculates the exposed winter shrub fraction, is developed and parameterised for use alongside the snow cover parameterisation in JULES in order to provide a better representation of shrub-specific processes. This revised JULES more than doubles the efficiency coefficient and halfs the negative bias between modelled and observed runoff in the shrub-tundra Abisko basin. However, the current structure of the model is found to be inadequate for use in investigating the effect of shrub-tundra expansion because it calculates a single energy balance for the snow-free and the snow-covered areas. To address this issue, a distributed three-source (snow-shrub-ground) model (D3SM) is developed. D3SM is evaluated against snow and energy ux measurements from a shrub-tundra basin in the Yukon, Canada, and is found to reproduce snowmelt energetics well. The effects of shrub expansion on the energy balance of the basin during snowmelt are then investigated by increasing the vegetation fraction and canopy height of the current shrub distribution, which is found to be positively correlated with topography. D3SM shows that the most significant effects of shrub expansion in the basin are to reduce the spatial variability of snow depth and to increase the sensible heat flux from the surface to the atmosphere.