Probability distributions for wave runup on beaches

Measured probability distributions of shoreline elevation, swash height (shoreline excursion length) and swash maxima and minima from a wide range of beach types are compared to theoretical probability distributions. The theoretical distributions are based on assumptions that the time series are weakly steady-state, ergodic and a linear sum of random variables. Despite the swash process being inherently non-linear, results indicate that these assumptions are not overly restrictive with respect to modeling exceedence statistics in the upper tail of the probability distribution. The RMS-errors for a range of exceedence level statistics (50, 10, 5, 2, and 1%) were restricted to < 10 cm (and often < 5 cm) for all of the swash variables that were investigated. The results presented here provide the basis for further refinement of coastal inundation modeling as well as stochastic-type morphodynamic modeling of beach response to waves. Further work is required, however, to relate the parameters of swash probability distributions to wave conditions further offshore.