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Predicting wave runup on reef-fringed coasts using phase-resolving modelings suffers from uncertainty induced by wave randomness, spectral-width determination, and reef-surface-roughness reproduction. A multi-layer non-hydrostatic model SWASH was first validated against two physical experiments and then applied to simulate runup over coral reefs. Simulations with different wave sequences for the same wave condition indicated that infragravity swash (R IGW) variability was the main contributor to the extreme runup (R 2 %) uncertainty. R IGW was positively correlated to the off-reef incident-wave groupiness factor and the average number of waves per wave group, suggesting that prior knowledge of incident group structure could help in reducing the uncertainty of runup prediction. In ensembles with 100 simulations of different random wave sequences, the ratio of R 2 % with 5% exceedance level to R 2 % with 95% exceedance level decreased with increasing number of spectral components and approached to 1.15–1.3 with over 600 components. Runup uncertainty induced by randomly phasing did not significantly vary with spectral widths and reef-surface roughness. Runup uncertainty due to arbitrarily specifying reef-surface roughness was much more significant than the uncertainty induced by wave randomness and spectral width, suggesting that accurate reproduction of reef surface roughness has a high priority in physical and numerical modelings. • Uncertainty in runup prediction is considerable over fringing reefs. • Variability in infragravity-frequency swash is a primary source for the uncertainty. • The uncertainty reduces with incident waves generated using more frequency bins. • Incident wave-group height and length affect the infragravity-frequency swash height. • Accurate reproduction of reef surface roughness has a high priority. [ABSTRACT FROM AUTHOR]

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. • Four regimes of wave runup over reef-lined beaches are identified. • An explicit runup formula set corresponding to the four regimes is derived. • The formula set is validated against data of laboratory and field coral reefs. • Beach slope is more important than forereef slope at high water levels. [ABSTRACT FROM AUTHOR]

Long waves are amplified as short-wave groups shoal and break over reefs, therefore, having significant impacts on coastal inundation, structure stability, and sediment transport. This study investigated the cross-reef variation of long-wave energy exchange with short-wave group over a reef using fully nonlinear analysis of simulation results by the non-hydrostatic model SWASH. The objective was to elucidate the mechanisms of long-wave transformation under nonlinear short-wave group forcing over a reef, and to assess the consequences of simplifications in linear and weakly nonlinear analyses in this problem. The energy transfer between short and long waves is the work done by radiation stress on long-wave velocity. Unlike conventional linear and weakly nonlinear analysis, the Stokes transport and long-wave modulation of local water depth are included in the fully nonlinear analysis. It was found that only the long-wave energy flux gradient given by the fully nonlinear analysis was balanced by the work done by wave radiation stress over a shallow reef. The fully nonlinear analysis showed that strict mass conservation has to be used to extract long wave velocity properly. In contrast, in linear and weakly nonlinear analysis, the long-wave velocity is extracted from single-point velocity measurements. The fully nonlinear analysis demonstrated that the generation and growth of incoming breakpoint-forced long waves overcame the dissipation of bound long waves in the surf zone, leading to amplification of incoming long-wave energy flux. This phenomenon occurred even when short waves mainly broke over the horizontal reef flat with large submergence, indicating that long-wave evolution is not locally controlled but dependent on wave spatial evolution history. Outgoing breakpoint-forced long waves were dissipated considerably during de-shoaling over the forereef due to substantial energy transfer to incoming short waves, though both of them are free waves. The consistent phase coupling between outgoing long waves and incoming short-wave groups at all frequencies was found to be the primary driving mechanism for the energy transfer. According to the fully nonlinear analysis, the reef-flat submergence may affect the long wave in a complex fashion, i.e. , reducing the submergence may enhance the energy transfer from short waves to long waves or suppress long-wave growth by increasing its frictional dissipation at the same time. • Long-wave energy balance is achieved with fully nonlinear analysis. • Strict mass conservation has to be used to extract long-wave velocity properly. • Long wave amplitude is dependent on short-wave spatial evolution history. • Radiation stress does positive work on incoming long waves in surf zone. • Free outgoing long waves transfer energy to incoming short waves in shoaling zone. [ABSTRACT FROM AUTHOR]

Widespread flooding of reef-fringed islands demonstrates the insufficient protection provided by reef topographies and suggests the necessity of artificial structures for hazard prevention and mitigation. As an indicator of the structural protection efficiency, the wave overtopping rate is difficult to estimate in reef environments because hydrodynamics over reefs violate the application conditions of standard overtopping formulas. A combined physical and numerical modeling was performed to investigate wave transformations over reefs of different topographies and overtopping at vertical seawalls on the reefs. Results showed that, in addition to the off-reef wave height and still water level, the off-reef wave period also played significant roles. The intensity of short-wave motions and the level of wave setup near the seawall were positively correlated with the off-reef wave period, and the intensity of infragravity-wave motions depended largely on it. Steeper fore-reef slopes would lead to more intensive wave motions and higher setup on reef flats and, consequently, higher overtopping rates. Furthermore, the overtopping rate exponentially decreased with the distance between the seawall and reef edge, primarily due to the decay of short waves in the surf zone. • A laboratory experiment on random wave transformation and overtopping in reef environments was conducted. • The ability of SWASH model was validated against the experimental data. • Installation of a seawall on a reef flat could significantly modify the wave field. • Influences of hydrodynamic and reef topography on the physical drivers of flooding were studied. [ABSTRACT FROM AUTHOR]