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Sedimentary bed evolution as a mean‐reverting random walk: Implications for tracer statistics
Author(s) -
Martin Raleigh L.,
Purohit Prashant K.,
Jerolmack Douglas J.
Publication year - 2014
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2014gl060525
Subject(s) - random walk , flume , tracer , geology , sediment transport , erosion , bed load , hydrology (agriculture) , stochastic process , sediment , statistics , geomorphology , mechanics , mathematics , geotechnical engineering , physics , flow (mathematics) , nuclear physics
Sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates. Tracer trajectories are dominated by periods of immobility (“waiting times”) as they are buried and reexcavated in the stochastically evolving river bed. Here we model bed evolution as a random walk with mean‐reverting tendency (Ornstein‐Uhlenbeck process) originating from the restoring effect of erosion and deposition. The Ornstein‐Uhlenbeck model contains two parameters, a and b , related to the particle feed rate and range of bed elevation fluctuations, respectively. Observations of bed evolution in flume experiments agree with model predictions; in particular, the model reproduces the asymptotic t −1 tail in the tracer waiting time exceedance probability distribution. This waiting time distribution is similar to that inferred for tracers in natural gravel streams and avalanching rice piles, indicating applicability of the Ornstein‐Uhlenbeck mean‐reverting model to many disordered transport systems with tracer burial and excavation.