Characterization of subglacial landscapes by a two-parameter roughness index

Previous studies using Fourier transformation (FT) methods to analyze subglacial roughness have shown promise for distinguishing between different types of subglacial landscape from raw subglacial elevation data. We derive a two-parameter FT roughness index {xi, eta}, where xi is based on the FT of elevation (as previously considered in isolation), and eta is based on both the FT of elevation and the FT of bed-slope profile. In this way, we take account of both vertical and horizontal irregularities in subglacial surfaces. We demonstrate the statistical veracity of using {xi, eta} to consider roughness in terms of obstacle amplitudes and spacing, and consider the use of {xi, eta} in studies of ice dynamics and subglacial geomorphological interpretation. We show that {xi, eta} can be linked to basal sliding rates on the metre scale, and can be used to differentiate further than single-parameter roughness indices between different classes of subglacial landscape, in particular between erosional and depositional settings.