Empirical Estimation of Wave Height Over Reef Based on Boussinesq Wave Model

Abstract

In coral reefs around the Okinawa Islands and Pacific Islands, waves are gentle by wave breaking caused by sudden change in water depth at the edge of coral reefs; therefore, coral reefs are called natural breakwaters. On the other hand, it has also been reported that wave overtopping damage occurred due to high waves behind coral reefs, when typhoons approach or pass through. Thus, it is necessary to understand the wave transformation characteristics on coral reefs in the design of wave overtopping countermeasures. The wave height change and wave setup are usually calculated using empirical formula proposed by the experiment (Takayama et al., 1977), the observation (Egashira et al., 1985), or the design manual (1999) and the guidebook (2003) for the fisheries infrastructures. Although in order to apply the empirical formula to various coral reefs, coastal topography and slope gradient should also be considered, present empirical formula are insufficient for considering the unique characteristics of the coral reef coasts. This study proposes an empirical formula of wave height estimation on coral reefs and the coefficients in the formula are determined using simulated results by Boussinesq wave model which can simulate wave transformation in shallow sea. The reef slope and gradient are not considered in the previous studies, but those were considered in the coefficients in this study. The applicability of proposed formula was confirmed through comparison with the observations and the simulated results by the other nonlinear wave model (KP wave model). The proposed equation agreed well with the results by the KP wave model when the wave height was high. When the wave height is small, the attenuation at the edge of reef is slightly overestimated, but the reproducibility of wave height over the reef was good. The accuracy of the estimated wave height on the reef by the present formula was higher than estimations by the other existing formulas. The proposed empirical formula can apply for estimation of design wave heights at arbitrary location over reefs.