Flow resistance estimation in mountain streams

The quantification of flow resistance in complex natural channels continues to be a key source of uncertainty in basic research, engineering, and environmental management. This paper describes a meta-analysis of data compiled from a wide range of sources and flow conditions in mountain streams that compares the accuracy of equations developed by Jarrett (1984), Hey (1979), Bathurst (1985) and Bathurst (2002), with a new empirical model. The regression algorithm that was used to develop the model involved a four – fold cross validation procedure, with stratification of the compiled dataset by friction slope (Sf) values, to arrive at a dimensionless piecewise, nonlinear equation for Darcy–Weisbach friction factor. The new model is a function of Sf and relative submergence (ratio of hydraulic radius R to D84) for streams <8% in slope, and relative submergence and ratio of D84 to D50 for streams with Sf ≥8%. Mean square error values, discrepancy ratios, and coefficients of determination indicate that the new model predicts friction factor better than the existing models that were tested, especially for mountain streams with large bed material and Sf values greater than 4%.