Predicting wave runup on composite beaches

Abstract

Empirical formulae for predicting wave runup (the maximum elevation reached by the water on a wave-by-wave basis) have not been widely tested on composite beaches, which have a characteristic cross-shore boundary in sediment size and slope. Using video-derived runup observations from two natural composite beaches in Oregon, U.S.A during both berm collision and inundation, the performance of existing empirical runup formulae was examined. The tested formulae were developed for sandy beaches, cobble beaches, and composite beaches. The sandy beach formulae showed good correlation with composite beach observations, however all but one tended to overpredict observations by 1–2 m. The overprediction depended in part on the definition used for beach slope, and is likely also a function of swash zone position and berm sediment characteristics. One sandy beach formula (that of Medellin et al., 2016; https://doi.org/10.5194/nhess-16-167-2016) and a modified version of a cobble beach formula (from Poate et al., 2016; https://doi.org/10.1016/j.coastaleng.2016.08.003) were found to show good performance, with root mean squared errors (RMSE) of 0.55 m and 0.63 m, respectively (26 % and 30 % compared to the mean $R_{2\%}$ of 2.09 m), when the average of the beach and berm slopes was used. The only existing composite beach formulae were found to fit our observations during berm collision poorly, though performed more strongly for observations during berm inundation. Since those formulae were developed for the case of berm inundation, and the observations used here encompassed both berm collision and inundation, the results suggest that a more general formula encompassing both impact regimes is needed. By deconstructing the sources of error in the existing composite beach runup formulae, we identified parameterizations for wave setup and swash excursion to fit the present dataset of berm collision and inundation. The newly developed formula performs similarly though slightly worse than the existing composite beach formulae for a limited set of inundation observations, however across all observations (inundation and collision) the new formula obtains RMSE = 0.48 m (23 % of average observed $R_{2\%}$) when the average of the beach and berm slopes is used, less than half of the existing composite beach formulae and lower than any other tested formula.