Regime equations for natural meandering cobble and gravel bed rivers

Stephanie Kenston Davidson, Richard D. Hey

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Data obtained from 48 stable reaches of upland rivers in the UK were stratified by stream-type in order to develop regime equations specifically for natural meandering cobble- and gravel-bed rivers: C3 and C4 stream-types according to the Rosgen classification. Multiple regression models were applied to derive equations for reach-averaged values of bankfull width, mean depth, slope, meander arc length and sinuosity in terms of bankfull discharge and associated bed material load, the calibre of the bed material, bank vegetation density and valley slope. The equations show that their cross-sectional dimensions are primarily determined by the bankfull discharge, bank vegetation and bed material size whereas their profile and plan form are also very strongly influenced by the valley gradient. Although bankfull bed material load only appears to have a minor influence on channel morphology, its effect is implicit in the value of bankfull discharge as this corresponds to the flow that transports most bed material load. Explanations are given for these results, based on the processes affecting channel geometry. Comparisons with the regime equations derived more than twenty years ago by Hey and Thorne from the same UK dataset, indicate that stratification by stream-type generates equations that are more consistent, for example bank vegetation affects all aspects of channel morphology rather than simply channel width, and provide significantly better explanations for channel slope and sinuosity due to the inclusion of valley slope as an independent variable. Their potential for designing river restoration schemes is evaluated against North American data. The equations prove to be comparable to the Hey and Thorne equations for predicting width and depth, but provide a significant improvement for the determination of slope and sinuosity. Although bed material load was shown, statistically, to influence channel dimensions, numerically its influence is trivial. Removing it from the analysis generates equations that provide the best practical point estimates of channel morphology. Predictions with the simplified regime equations are shown to be comparable to the full equations
Original languageEnglish
JournalJournal of Hydraulic Engineering
Issue number9
Early online date19 Feb 2011
Publication statusPublished - 2011


  • channel design
  • river morphology
  • regime equations
  • river restoration


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