Flow resistance equations without explicit estimation of the resistance coefficient for coarse-grained rivers

Abstract

The uncertainty and subjectivity inherent in estimating the resistance coeffi-cient is one of the main sources of error in the application of flow resistance equations tonatural channels. Various studies have shown that it is possible to relate discharge suc-cessfully with variables related to the hydraulic flow geometry without the need for anindependent estimate of the resistance coefficient. The aim of this paper is to calibrateand validate three models, previously proposed by other researchers, using an extensiveempirical base, made up of 904 data from over 400 reaches of gravel-bed rivers and moun-tain streams from various regions of the world.Thanks to the cross validation procedure, the three models were calibrated using thefull database, which allowed the fitted equations to be based on the maximum numberof observations. There are no important differences between the three models calibratedwith regard to their explanatory power. These models show that the exponent of thehydraulic radius is greater than 2/3 and that the exponent of the slope is closer to 1/4than 1/2 in gravel-bed rivers and mountain streams. Validation confirmed the precisionof the fitted equations, by reaching predictive power values comparable with those fromcalibration. The fitted equations can be successfully applied in reaches of gravel-bed riv-ers and mountain streams (for non-sinuous, un-vegetated and hydraulically-wide channelsand for flow higher than 0.1 m3/s and lower or equal to bankfull discharge) for which thereis no specific detailed information about flow resistance available.