Characterization of the small scale ice sheet topography of Antarctica and Greenland

In this dissertation I analyze and model the characteristics of small-scale, dynamically supported topography. I develop a method for mapping spatial variations in the Fourier spectra of ice-sheet surfaces from elevation data measured along linear tracks. I find that there are characteristic patterns in these spectra, and that the shape of the spectra is largely determined by the local ice thickness, while the overall spectral amplitude is determined by the local surface slope and by bed roughness. I explain the broad features of the spectra and their variation with a model that describes the ice-sheet bed as isotropic red noise, and describes the ice flow dynamics with a perturbation analysis of flow of a viscous, Newtonian fluid. I further develop this model to take into account variations in the viscosity of the ice due to the nonlinear viscosity of flowing ice, and find that the patterns of surface topography are broadly consistent with expected variations in viscosity. Next, I analyze map-view variations in ice-sheet surface slopes, and find that there is a characteristic anisotropic pattern in surface slope variations that is common to Antarctica and Greenland. These variations are also consistent with a perturbation model of ice flow, which I use to show that the pattern of surface slopes may be useful in identifying areas where the ice is sliding rapidly at the bed. Finally, I analyze a two-year time-series of elevation measurements from the Ross Embayment in West Antarctica, detecting small but significant rates of elevation change throughout the region, with unexpectedly large rates of change in a few areas.