Articles | Volume 11, issue 3
The Cryosphere, 11, 1247–1264, 2017
The Cryosphere, 11, 1247–1264, 2017

Research article 24 May 2017

Research article | 24 May 2017

Self-affine subglacial roughness: consequences for radar scattering and basal water discrimination in northern Greenland

Thomas M. Jordan1, Michael A. Cooper1, Dustin M. Schroeder2, Christopher N. Williams1, John D. Paden3, Martin J. Siegert4, and Jonathan L. Bamber1 Thomas M. Jordan et al.
  • 1Bristol Glaciology Centre, School of Geographical Sciences, University of Bristol, Bristol, UK
  • 2Department of Geophysics, Stanford University, Stanford, California, USA
  • 3Center for Remote Sensing of Ice Sheets, University of Kansas, Lawrence, Kansas, USA
  • 4Grantham Institute and Department of Earth Science and Engineering, Imperial College, London, UK

Abstract. Subglacial roughness can be determined at a variety of length scales from radio-echo sounding (RES) data either via statistical analysis of topography or inferred from basal radar scattering. Past studies have demonstrated that subglacial terrain exhibits self-affine (power law) roughness scaling behaviour, but existing radar scattering models do not take this into account. Here, using RES data from northern Greenland, we introduce a self-affine statistical framework that enables a consistent integration of topographic-scale roughness with the electromagnetic theory of radar scattering. We demonstrate that the degree of radar scattering, quantified using the waveform abruptness (pulse peakiness), is topographically controlled by the Hurst (roughness power law) exponent. Notably, specular bed reflections are associated with a lower Hurst exponent, with diffuse scattering associated with a higher Hurst exponent. Abrupt waveforms (specular reflections) have previously been used as a RES diagnostic for basal water, and to test this assumption we compare our radar scattering map with a recent prediction for the basal thermal state. We demonstrate that the majority of thawed regions (above pressure melting point) exhibit a diffuse scattering signature, which is in contradiction to the prior approach. Self-affine statistics provide a generalised model for subglacial terrain and can improve our understanding of the relationship between basal properties and ice-sheet dynamics.

Short summary
Using radio-echo sounding data from northern Greenland, we demonstrate that subglacial roughness exhibits self-affine (fractal) scaling behaviour. This enables us to assess topographic control upon the bed-echo waveform, and explain the spatial distribution of the degree of scattering (specular and diffuse reflections). Via comparison with a prediction for the basal thermal state (thawed and frozen regions of the bed) we discuss the consequences of our study for basal water discrimination.