Sampling Interval Analysis and CDF Generation for Grain-Scale Gravel Bed Topography

Abstract

In river hydraulics, there is a continuing need for characterizing bed elevations to arrive at quantitative roughness measures that can be used in flow depth calculations and for improved prediction of fine-sediment transport over and through coarse beds. Recently published prediction methods require a method for estimating the cumulative distribution function (CDF) of bed elevations. Representing the distribution of elevations for rough beds requires a correct choice for the number and spacing of measurement locations. Laboratory experiments over a screeded flat gravel bed with sand having median diameter D5=35 mm were used to determine the number and spatial coverage of measurements needed to define the elevation field for a range of uncertainty levels. Approximately 1,–5, randomly collected single elevation measurements were needed to quantify the distribution of elevations for the gravel bed. Relative error in estimating the standard deviation of elevations was insensitive to the number and spacing of elevation measurements when the spacing exceeded D5 (35 mm). The standard deviation of bed elevations was found to be proportional to the median bed material size for several different gravel beds. A method is presented for generating a CDF for bed elevations using the elevation-distribution standard deviation with a randomly sampled distribution function.