The joint probability of waves and water levels in coastal engineering design

On coasts with high tidal ranges, or subject to high surges, both still water levels and waves can be important in assessing flood risk; their relative importance depends on location and on the type of sea defence. The simultaneous occurrence of large waves and a high still water level is therefore important in estimating their combined effect on sea defences. Wave period can also be important in assessing fun-up and overtopping, and so it is useful also to have information on the joint distribution of wave height and period. Unless the variables are either completely independent or completely dependent, multivariate extremes are difficult to predict directly from observational data, as there may be too few events of the relevant type amongst the observations. In the past, the fitting and extrapolation of the dependence functions between the variables has often involved complicated and/or subjective approaches. This paper presents a method for joint probability analysis, using a Monte Carlo simulation approach, based on distributions fitted to water level, wave height and wave steepness, and to the dependence between them.