Extended Einstein's parameters to include vegetation in existing bedload predictors

José A. Bonilla-Porras, Aronne Armanini, Alessandra Crosato

Research output: Contribution to journalArticleScientificpeer-review


Observations show that instream vegetation has a strong impact on bedload transport. However, there is a scarcity of sediment transport predictors that directly account for the effects of plants, and existing methods, based on re-calculation of roughness coefficients, may present some inconsistencies. The approach herein proposed extends Einstein's parameters to include the effects of vegetation on sediment transport for implementation in existing bedload predictors of the form Φ = f(Ψ). The new formulations are applicable in presence of submerged and emergent vegetation and reduce to the original Einstein's parameters if vegetation is absent. Calibration is based on laboratory data. For this purpose, an extensive experimental program was carried out on a tilting glass-walled flume with medium-sand bed and plants represented by aluminum cylinders. Validation is based on published bedload measurements from the literature. The results show a much better agreement between measurements and predictions when applying the extended parameters compared to using Einstein's original ones. Predicted bedload rates have, on average, the same order of magnitude of the measured ones, and quantitative agreement is substantially increased. Clear improvements were also observed when comparing the results with the bedload predictions of Baptist's (2005) method, which is based on the re-calculation of bed roughness in the presence of vegetation.

Original languageEnglish
Article number103928
Pages (from-to)1-13
Number of pages13
JournalAdvances in Water Resources
Publication statusPublished - 2021


  • Aquatic vegetation
  • Bedload predictor
  • Einstein's sediment transport parameters
  • Flume experiments


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