Data assimilation problems in glaciology
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Rising sea levels due to mass loss from Greenland and Antarctica threaten to inun- date coastal areas the world over. For the purposes of urban planning and hazard mitigation, policy makers would like to know how much sea-level rise can be antici- pated in the next century. To make these predictions, glaciologists use mathematical models of ice sheet flow, together with remotely-sensed observations of the current state of the ice sheets. The quantities that are observable over large spatial scales are the ice surface elevation and speed, and the elevation of the underlying bedrock. There are other quantities, such as the viscosity within the ice and the friction co- efficient for sliding over the bed, that are just as important in dictating how fast the glacier flows, but that are not observable at large scales using current meth- ods. These quantities can be inferred from observations by using data assimilation methods, applied to a model of glacier flow. In this dissertation, I will describe my work on data assimilation problems in glaciology. My main contributions so far have been: computing the bed stress underneath the three biggest Greenland outlet glaciers; developing additional tools for glacier modelling and data assimi- lation in the form of the open-source library iceack; and improving the statistical methodology through the user of total variation priors.
- Applied mathematics