A Semi-Analytical Model on Wave-Induced Setup over Fringing Reefs with a Shallow Reef Crest

The vulnerability of low-lying reef-fringed atolls to coastal inundation in extreme wave events is of increasing concern in the context of global sea level rise. Wave-induced setup is an important component of wave runup along reef shorelines. We improved a semi-analytical model to investigate wave-induced setup over fringing reefs crested by a shallow reef. Using mass balance and hydraulics, we developed the model based on flow around reef crest kinematics. We proposed a scaling factor to account for flow unsteadiness and reef-crest shape effects. Our solution showed that wave setup on the reef flat is a function of both offshore wave steepness and the wave refection coefficient. Validation of the model by laboratory data shows that the model reproduces the maximum wave-induced setup on the reef flat in the presence of a reef crest with diffident crest widths. Applying the model to experimental data under various reef configurations and wave conditions were also successful. We found that the scaling factor in the model increased with increasing fore-reef slope but was insensitive to variations in reef-crest width. A key requirement for the model to do is that the reef-crest submergence must be small enough or nearly emergent so that an approximate critical flow condition exists.