Explicit wave-runup formula for beaches fronted by coral reefs using tree-based models

Fast and accurate estimation of wave runup is needed for coral-reef islands, but most of the existing formulae are not applicable in this context. Tree-based models were applied to the comprehensive numerical database of Pearson et al. (J. Geophys. Res. Oceans. 122, 10099–10117) to identify the essential predictor parameters for runup in coral-reef environments and classify different runup regimes on which a set of runup formulae was developed. It was found that, wave conditions, reef roughness, and reef-flat length are generally crucial for predicting runup, while the importance of forereef and beach slopes depends on the relative reef submergence (reef submergence normalized by off-reef wave height). The forereef slope is more important than the beach slope when waves mainly break over the forereef at low relative reef submergences but less important when waves mainly break over the reef flat and the beach at middle and high relative reef submergences. The proposed formula set was validated against data from laboratory and field coral reefs, which implies that the formula set has the potential for fast prediction of runup along coral-reef islands at broad scales for flooding assessment.