Erosion, Deposition and Size Distributions of Sand

A mathematical-physical model for erosion and deposition of sand is formulated and related to the logarithmic hyperbolic distributional form of mass-size distributions. The location-scale invariant parameters χ and ξ of the hyperbolic distribution express, respectively, the skewness and the kurtosis of that distribution, and the triangular domain of variation of these two parameters is referred to as the hyperbolic shape triangle. The erosion-deposition model implies that erosion will tend to move the (χ, ξ)-position of a given sediment to the right-hand part of the shape triangle and that deposition will move the (χ, ξ)-position towards the left part of the triangle, along specified curves. This is confirmed by sediments from a variety of natural environments. An empirically determined curve bisecting the shape triangle is found to separate the samples from predominantly depositional environments as compared with the samples from predominantly erosional environments. The hyperbolic shape triangle is also found to discriminate well between samples of different but closely related origins.