Sampling variability in estimates of flow characteristics in coarse-bed channels: Effects of sample size

Adequate description of hydraulic variables based on a sample of field measurements is challenging in coarse-bed streams, a consequence of high spatial heterogeneity in flow properties that arises due to the complexity of channel boundary. By applying a resampling procedure based on bootstrapping to an extensive field data set, we have estimated sampling variability and its relationship with sample size in relation to two common methods of representing flow characteristics, spatially averaged velocity profiles and fitted probability distributions. The coefficient of variation in bed shear stress and roughness length estimated from spatially averaged velocity profiles and in shape and scale parameters of gamma distribution fitted to local values of bed shear stress, velocity, and depth was high, reaching 15-20% of the parameter value even at the sample size of 100 (sampling density 1 m^-2). We illustrated implications of these findings with two examples. First, sensitivity analysis of a 2-D hydrodynamic model to changes in roughness length parameter showed that the sampling variability range observed in our resampling procedure resulted in substantially different frequency distributions and spatial patterns of modeled hydraulic variables. Second, using a bedload formula, we showed that propagation of uncertainty in the parameters of a gamma distribution used to model bed shear stress led to the coefficient of variation in predicted transport rates exceeding 50%. Overall, our findings underscore the importance of reporting the precision of estimated hydraulic parameters. When such estimates serve as input into models, uncertainty propagation should be explicitly accounted for by running ensemble simulations.