The hyperbolic shape triangle as a tool for discriminating populations of sediment samples of closely connected origin

This paper describes a new method for discriminating populations of sediment samples of closely connected origin. It provides a dynamical interpretation to grain size data. The descriptive modelling power of the hyperbolic distribution, the hyperbolic shape triangle and the population concept have been applied to several hundred beach sand samples from the Mediterranean coast of southern Israel. The investigated samples are from a 60 km stretch of beach, from Rafah to Ashqelon, and represent an autumn storm profile. The domain of variation of the hyperbolic shape parameters χ and ξ is a triangle referred to as the hyperbolic shape triangle. The distribution of the estimated (χ, ξ) shape positions in the hyperbolic shape triangle was studied graphically and statistically using the newly developed tools described here to present, evaluate and compare hyperbolic shape position data for analysed grain size populations. The graphical methods of contouring the scatter diagrams of the samples in the domain of the hyperbolic shape triangle and chi‐squared tests are demonstrated. They were performed on two sedimentary environments normal to the beach, namely inshore and mid‐swash zone. The qualitative and quantitative estimated changes in the populations (χ, ξ) shape positions in the shape triangle suggest that they are subjected mainly to ε erosion‐deposition processes. Their modes are located along one of the upper ‘hammock’curves in the shape triangle. The location and scale invariant hyperbolic shape parameter ρ indicates a change of the grain size distribution across the left part of the hyperbolic shape triangle, which is the domain of predominantly depositional processes. However, the mid‐swash zone sediments reflect that they are subjected more to depositional processes and the inshore sediments more to erosional ones.