Spatial organization 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 organization 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 organization 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 organized in a regular spatial manner (patterned) or are they distributed randomly? We recognize 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 to 1200 m. We conclude that patterning is a near ubiquitous property of drumlins. This finding of regularity demonstrates spatial self-organization in the bedforming process with drumlins as an emergent manifestation of sub-glacial 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-organization: instability in the coupling of ice flow–sediment flux–bed shape; local feedback between sediment mobility and relief; and coarsening by growth or migration