Streamwise and Vertical Dispersal of Tracer Stones in an Equilibrium Bed

Enrica Viparelli, Amanda Balkus, Daniel Vázquez-Tarrío, Kimberly M. Hill, Michal Tal, Juan Fedele

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Modeling transport, erosion, and deposition of nonuniform sediment over temporal intervals that are short compared to those characterizing channel bed aggradation and degradation remains an open problem due to the complex quantification of the sediment fluxes between the bed material load and the alluvial deposit. Parker, Paola, and Leclair in 2000 proposed a morphodynamic (PPL) framework to overcome this problem. This framework is used here to model the dispersal of a patch of gravel tracers in three different settings, a laboratory flume, a mountain creek, and a braided river. To simplify the problem, (a) the bed slope, bedload transport rate, and bed configuration are assumed to be constant in space and time (equilibrium), (b) sediment entrainment and deposition are modeled with a constant step length formulation, and (c) the PPL framework is implemented in a one-dimensional (laterally averaged) model. Model validation against laboratory experiments suggests that, as the transport capacity of the flow increases, the maximum elevation-specific density of sediment entrainment may migrate downward in the deposit. The comparison between model results and field data shows that the equilibrium solution can reasonably capture tracer dispersal. The equilibrium model can also reproduce subdiffusion and superdiffusion of a patch of tracers in the streamwise direction, depending on the magnitude of the short-term bed level changes. Finally, the average tracer elevation in a cross-section decreases in time because particles that are buried deep in the deposit are only rarely reentrained into bedload transport.

Original languageEnglish (US)
Article numbere2022WR033137
JournalWater Resources Research
Issue number11
StatePublished - Nov 2022
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank Miguel Wong who provided the data many years ago, Guillaume Brousse and Guillaume Fantino for providing the raw data of the RFID tags he introduced into the Buëch in 2018 as part of his thesis work, Nate Bradley for providing information on the variability of bed elevations and a picture of the Halfmoon Creek field site, G. Parker and two anonymous reviewers for comments and suggestions that helped to improve the manuscript. This work was partially supported by an Exxon Mobil grant. Amanda Balkus was supported with a REU supplement to the NSF Grant CBET 1751926.

Publisher Copyright:
© 2022. The Authors.


  • bedload transport
  • gravel bed river
  • probabilistic morphodynamics
  • tracer stones


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