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 topographicscale 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.

Abstract. The subglacial environment of the Greenland Ice Sheet (GrIS) is poorly constrained both in its bulk properties, for example geology, the presence of sediment, and the presence of water, and interfacial conditions, such as roughness and bed rheology. There is, therefore, limited understanding of how spatially heterogeneous subglacial properties relate to ice-sheet motion. Here, via analysis of 2 decades of radio-echo sounding data, we present a new systematic analysis of subglacial roughness beneath the GrIS. We use two independent methods to quantify subglacial roughness: first, the variability in along-track topography – enabling an assessment of roughness anisotropy from pairs of orthogonal transects aligned perpendicular and parallel to ice flow and, second, from bed-echo scattering – enabling assessment of fine-scale bed characteristics. We establish the spatial distribution of subglacial roughness and quantify its relationship with ice flow speed and direction. Overall, the beds of fast-flowing regions are observed to be rougher than the slow-flowing interior. Topographic roughness exhibits an exponential scaling relationship with ice surface velocity parallel, but not perpendicular, to flow direction in fast-flowing regions, and the degree of anisotropy is correlated with ice surface speed. In many slow-flowing regions both roughness methods indicate spatially coherent regions of smooth beds, which, through combination with analyses of underlying geology, we conclude is likely due to the presence of a hard flat bed. Consequently, the study provides scope for a spatially variable hard- or soft-bed boundary constraint for ice-sheet models.

Abstract. There is widespread, but often indirect, evidence that a significant fraction of the bed beneath the Greenland Ice Sheet is thawed (at or above the pressure melting point for ice). This includes the beds of major outlet glaciers and their tributaries and a large area around the North-GRIP borehole in the ice-sheet interior. The ice-sheet scale distribution of basal water is, however, poorly constrained by existing observations. In principle, airborne radio-echo sounding (RES) en-5 ables the detection of basal water from bed-echo reflectivity, but unambiguous mapping is limited by uncertainty in signal attenuation. Here we introduce a new RES diagnostic for basal water that is associated with wet to dry transitions in bed material: bed-echo reflectivity variability. Importantly, this diagnostic is demonstrated to be attenuation-insensitive and the technique enables combined analysis of over a decade of Operation IceBridge survey data. 10The basal water predictions are compared with existing analyses for the basal thermal state (frozen and thawed beds) and geothermal heat flux. In addition to the outlet glaciers, we demonstrate widespread water storage in the northern and eastern interior. Notably, we observe a quasi-linear 'corridor' of basal water extending from NorthGRIP to Petermann glacier that spatially correlates with elevated heat flux predicted by a recent magnetic model. Finally, with a general aim to stim-15 ulate regional and process specific investigations, the basal water predictions are compared with bed topography, subglacial flow paths, and ice-sheet motion. The basal water distribution, and its relationship with the basal thermal state, provides a new constraint for numerical models. 1The Cryosphere Discuss., https://doi

Abstract. Bed topography is a critical boundary for the numerical modelling of ice sheets and ice-ocean interactions. A persistent issue with existing topography products for the bed of the Greenland Ice Sheet and surrounding sea floor is the poor representation of coastal bathymetry, especially in regions of floating ice and near the grounding line. Sparse data coverage, and the resultant coarse resolution at the ice/ocean boundary, poses issues in our ability to model ice flow advance and retreat from the present position. In addition, as fjord bathymetry is known to exert strong control on ocean circulation and ice-ocean forcing, the lack of bed data leads to an inability to model these processes adequately. Since the release of the last complete Greenland bed topography-bathymetry product, new observational bathymetry data have become available. These data can be used to constrain bathymetry, but many fjords remain completely unsampled and therefore poorly resolved. Here, as part of the development of the next generation of Greenland bed topography products, we present a new method for constraining the bathymetry of fjord systems in regions where data coverage is sparse. For these cases, we generate synthetic fjord geometries using a method conditioned by surveys of terrestrial glacial valleys as well as existing sinuous feature interpolation schemes. Our approach enables the capture of the general bathymetry profile of a fjord in North West Greenland close to Cape York, when compared to observational data. We validate our synthetic approach by demonstrating reduced over-estimation of depths compared to past attempts to constrain fjord bathymetry. We also present an analysis of the spectral characteristics of fjord centrelines using recently acquired bathymetric observations, demonstrating how a stochastic model of fjord bathymetry could be parameterised and used to create different realisations.