Subglacial bedforms reveal an exponential size-frequency distribution

Subglacial bedforms preserved in deglaciated landscapes record characteristics of past ice-sediment flow regimes, providing insight into subglacial processes and ice sheet dynamics. Individual forms vary considerably, but they can often be grouped into coherent fields, typically called flow-sets, that reflect discrete episodes of ice flow. Within these, bedform size-frequency distributions (predominantly height, width and length) are currently described by several statistics (e.g., mean, median, and standard deviation) that, arguably, do not best capture the defining characteristics of these populations. This paper seeks to create a better description based upon semi-log plots, which reveal that the frequency distributions of bedform dimensions (drumlin, mega-scale glacial lineation, and ribbed moraine) plot as straight lines above the mode (φ). This indicates, by definition, an exponential distribution, for which a simple and easily calculated, yet statistically rigorous, description is designed. Three descriptive parameters are proposed: gradient (λ; the exponent, characterising bedforms likely least affected by non-glacial factors), area-normalised y-intercept (β; quantifying spatial density), and the mode (φ). Below φ, small features are less prevalent due to i) measurement: data, sampling and mapping fidelity; ii) possible post-glacial degradation; or iii) genesis: not being created sub-glacially. This new description has the benefit of being insensitive to the impact of potentially unmapped or degraded smaller features and better captures properties relating to ice flow. Importantly, using λ, flow sets can now be more usefully compared with each other across all deglaciated regions and with the output of numerical ice sheet models. Applications may also exist for analogous fluvial and aeolian bedforms. Identifying the characteristic exponential and that it is typical of 'emergent' subglacial bedforms is a new and potentially powerful constraint on their genesis, perhaps indicating that ice-sediment interaction is fundamentally stochastic in nature. © 2013 Elsevier B.V

An ice-sheet scale comparison of eskers with modelled subglacial drainage routes

Eskers record a time-integrated signature of channelised meltwater drainage during deglaciation providing vital information on the nature and evolution of subglacial drainage. In this paper, we compare the spatial pattern of eskers beneath the former Laurentide Ice Sheet with subglacial drainage routes diagnosed at discrete time intervals from the results of a numerical icesheet model. Perhaps surprisingly, we show that eskers predominantly occur in regions where modelled subglacial water flow is low. Eskers and modelled subglacial drainage routes were found to typically match for lengths <10 km, and most eskers show a better agreement with the routes close to the ice margin just prior to deglaciation. This supports a time-transgressive esker pattern, with formation in short (<10 km) segments of conduit close behind a retreating ice margin, and probably associated with thin, stagnant or sluggish ice. Esker forming conduits were probably dominated by supraglacially fed meltwater inputs. We also show that modelled subglacial drainage routes containing the largest concentrations of meltwater show a close correlation with palaeo-ice stream locations. The paucity of eskers along the terrestrial portion of these palaeo-ice streams and meltwater routes is probably due to the prevalence of distributed drainage and the high erosion potential of fast-flowing ice