An extreme value model for expressing grain size and bed thickness as functions of the spatial variation of grain frequency

An extreme value model is developed for the situation where a cloud of sediment particles moves away from the boundary of a defined source area while undergoing constant depletion due to deposition of the larger particles. Taking the particles deposited at distance xfrom the source boundary to represent a distribution of largest extremes derived from a parent distribution of smallest extremes, it is possible to express the mean size of the deposited sediment in terms of the parameters of the original distribution at the source area. Thickness functions can be obtained as the product of expected diameter and particle frequency. If the spatial distribution f(x)of particle frequency along a linear transect can be inferred from a physical process, then this provides sufficient information for the construction of particle size and bed thickness prediction equations. Alternatively, the model places some restrictions on distribution selection if an empirical choice of f(x)is necessary. Some generalizations are obtained for trends in the mean and variance of the deposited particles on the basis of the hazard function of f(x).