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

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