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Subglacial bedforms reveal an exponential size-frequency distribution

Hillier, J.K.; Smith, M.J.; Clark, C.D.; Stokes, C.R.; Spagnolo, M.

Subglacial bedforms reveal an exponential size-frequency distribution Thumbnail


J.K. Hillier

M.J. Smith

C.D. Clark

M. Spagnolo


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 (β0; 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.


Hillier, J., Smith, M., Clark, C., Stokes, C., & Spagnolo, M. (2013). Subglacial bedforms reveal an exponential size-frequency distribution. Geomorphology, 190, 82-91.

Journal Article Type Article
Publication Date May 1, 2013
Deposit Date Apr 12, 2013
Publicly Available Date May 8, 2013
Journal Geomorphology
Print ISSN 0169-555X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 190
Pages 82-91
Keywords Subglacial, Bedform, Exponential, Stochastic, Flow-set, Fluvial.


Accepted Journal Article (645 Kb)

Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Geomorphology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Geomorphology, 190, 2013, 10.1016/j.geomorph.2013.02.017

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