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.