Spatial organisation of drumlins

Ice-sheets flowing over soft sediments produce undulations in the bed, typically of metres in relief, of which drumlins are the most abundant and widely investigated. Consensus regarding their mechanism of formation has yet to be achieved. In this paper we examine the spatial organisation of drumlins in order to provide an improved description of the phenomenon and to guide hypotheses of their formation. We review the literature highlighting contradictory findings regarding drumlin spatial organisation and then use this to motivate our study based on a large sample (42,488) of drumlins from Canada, Britain and Norway. Are there typical arrangements in drumlin positioning and are they organised in a regular spatial manner (patterned) or are they distributed randomly? We recognise that drumlin fields are inherently patchy and therefore apply inhomogeneous spatial statistics in order to study their distribution. This shows that whilst drumlins are occasionally randomly placed, their main state is non- random. They exhibit a strong and statistically significant signal of regularity across lengths scales of 100 – 1200 m. We conclude that patterning is a near ubiquitous property of drumlins. This finding of regularity demonstrates spatial self-organisation in the bedforming process with drumlins as an emergent manifestation of subglacial sediment mobility. Kilometre-scale interactions between drumlins must occur as they evolve, or interactions may arise as a consequence of growth or migration. Hypotheses or models are required that can explain the regular spacing of drumlins. We highlight three suggestions for such self-organisation: instability in the coupling of ice flow - sediment flux - bed shape; local feedback between sediment mobility and relief; and coarsening by growth or migration.