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Title: Numerical modelling of glaciers : moving meshes and data assimilation
Author: Partridge, Dale
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2013
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In this thesis we consider the solution to dynamical ice flow equations using a combination of a moving mesh method and data assimilation. We show that by moving the mesh the approximation to the ice thickness profile is improved, and the location of the domain boundary is significantly better estimated. The method used is derived by utilising a relative mass conservation principle to define a net deformation velocity comprising of the internal diffusion of ice and the effect of accumulation or ablation. We use a finite difference numerical approximation in one-dimension and a finite element approximation in two-dimensions to demonstrate the ability of the methods to simulate different aspects of ice flow. In particular we focus on the accurate representation of the moving front of the glacier without the need for an interpolation procedure. Results are shown to compare favourably to exact, steady state solutions, while demonstrating improvements over traditional fixed grid methods. The impact of the internal diffusion of the ice on the movement of the glacier front is analysed, and a condition on the local profile near the boundary is constructed to determine when the front is moving as a result of diffusion rather than the accumulation or ablation. We utilise the technique of data assimilation to combine the moving mesh method with observational information to get a statistically best estimate of the ice thickness profile. In a moving mesh environment there are differences to the scheme that we detail, in both one and two dimensions. We introduce an extension to our data assimilation scheme to directly include the numerical mesh within the update. This allows for the potential inclusion of observations of key features such as the location of the boundary. We demonstrate the improvement that this extension has on our prediction of the domain in one dimension and discuss the challenges encountered when applying this extension to two dimensions.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available