Quantifying subglacial roughness and its link to glacial geomorphology and ice speed

The shape of subglacial bed topography, termed its roughness, is a recognised control on basal ice-flow. Although glaciologists have observed patterns of variations in ice speed over beds with different roughness values, the strength of this relationship has rarely been quantified, and measurements of roughness are based on just a few methods. Moreover, the shape of topography can vary in a number of ways, but how this influences roughness and the quantification of roughness is largely unknown. This project investigates methods of measuring roughness, and how such measurements might be related to spatial patterns in ice speed in both contemporary and palaeo-settings. Roughness of ice-sheet beds has traditionally been summarised using spectral analysis. The first part of this projected was aimed at reviewing this method. The influence of the number of data points was explored by developing a new technique for re-digitising radio-echo sounding records, which remain the most extensive source of bed data from Antarctica. This yielded measurements with a resolution (c.250 m) eight-times higher than those used in previous work, and allowed assessment of roughness over short window lengths. Significantly, subjective decisions about, for example, the choice of window length can lead to differing results using spectral analysis. The second part of this project was, therefore, to identify and evaluate 36 alternative methods of quantifying roughness, many of which had never before been used to analyse subglacial beds. The project looked at the broader approach to quantifying roughness, exploring the benefits of 2D versus 3D techniques for investigating subglacial data. The relationship between roughness and ice speed was tested using these alternative techniques in isolation, but also in a combination. Indeed, the use of generalised linear models (GLMs) allowed the strength of this relationship to be quantified for the first time, and permitted the roughness variables most related to ice speed to be identified. Testing the agreement between patterns in roughness in ice speed for the Siple Coast showed a pattern of increasing ice speed as roughness decreased. Modelling revealed a 98% fit between ice speed and roughness for the MacAyeal Ice Stream indicating that roughness is a strong control on basal ice flow. It was revealed that the measures of roughness most related to ice speed were those that summarised changes in the vertical height of the surface, rather than the shape or wavelength of the features. It was also found that the lateral margin of the MacAyeal Ice Stream corresponds with an area of high bed roughness. Analysis of formerly glaciated areas of Britain showed that the size and frequency of subglacial bedforms influence parameter results as do subtle changes in the orientation of 2D profiles across bedform fields. It was demonstrated how this might be used to identify subglacial features beneath contemporary ice sheets. In conclusion, alternative roughness parameters were found to be less restrictive and arguably more informative than spectral analysis, because they have the advantage of allowing differing characteristics of the topography to be measured. Conversely, this meant that no single parameter could provide a complete summary. Thus, a key conclusion of this work is that the most suitable approach to quantifying roughness is to use a suite of roughness parameters, designed to summarise a range of variables that are most relevant to the specific investigation.