Wave Runup Distributions on Natural Beaches

Abstract

Runup distributions were measured on a wide spectrum of sandy beaches on the coast of New South Wales, Australia. The data indicates that the Rayleigh distribution is a reasonable statistical model for the maximum level reached by individual waves. The vertical scale of the best-fit distribution is proportional to the wave height times the surf similarity parameter for the steeper beaches in accordance with Hunt's formula for runup of regular waves on structures. For flat beaches, however, the vertical scale of the distribution is independent of the beach slope. The base level for the best-fit distribution (i.e. the highest level transgressed by all incoming wave crests) is indistinguishable from the still water level on the steep beaches but significantly lower on flat beaches. The demarcation between "steep" and "flat" beaches in these respects is at a beach face slope of approximately 0.10. The level of the shoreline relative to the runup distribution is a decreasing function of the beach slope.