The size sorting and shape sorting of gravel bedload by running water often is investigated using identifiable tracer grains that represent the grains within the riverbed. A new, robust, and reproducible method is described for the objective selection of three-dimensional shapes that are representative of the variety of shape within any whole sample. Widespread adoption of the method would ensure comparability between the shape-sorting results of different experiments. The approach identifies average and extreme grain shapes from natural gravel samples. Importantly, tracer dimensions are derived that form shapes with equal volume, thus ensuring that the shape of the tracers is the only transport variable. The method is tested on seven gravel samples from a range of fluvial, beach, and scree-slope environments as well as different sieve sizes.
Initially, measurements of the short (S), intermediate (I), and long (L) orthogonal axes of clasts are made from selected sieve intervals that represent the spread in the size distribution of the natural gravel. Shapes are identified to be within the realms of the observed shapes of the sampled population: four extreme shapes are identified (a blade, a rod, a spheroid, and a discoid) as well as a median form. The starting points of the analysis are the Zingg ratios S/I and I/L. However, these quantities require polar coordinate transformation to be useful in shape selection. The polar coordinate quantities form a joint probability density function that is the product of the marginal distributions of the new shape indices and the axes of the shape diagram. Utilizing and combining extreme percentiles of these latter distributions identifies the required shapes. A reverse transformation returns these selected quantities back into Zingg indices. Finally, using the intermediate axial dimensions and the volume ratio, the final tracer dimensions are found.