Statistical characterisation of extreme overtopping wave volumes

The starting point for this paper is the recently developed formula for the shape parameter of the Weibull distribution of overtopping wave volumes at a coastal defence. This shape factor b increases with decreasing relative freeboard and was developed strictly for smooth and impermeable structures like a dike or levee. Data on overtopping wave volumes are available for rubble mound structures, but the distributions of the volumes have never been analysed jointly with smooth-slope distributions and have never been compared with the new formula for smooth and impermeable dikes. This paper describes the analysis of the Weibull b-value for conventional rubble mound breakwaters as well as for low crested structures with the crest at or just above the water level. These data are then compared with the trend for smooth structures. It is concluded that rubble mound structures show more scatter in the b-value than smooth impermeable structures, but the same trend is found. The combined data make even more sense if the b-value is related to relative discharge instead of relative freeboard because the effects of slope angle and wave steepness are implicitly included. An improved prediction formula is proposed representing permeable and impermeable structures.