Coupled wave action and shallow-water modelling for random wave runup on a slope

Wave runup statistics on beaches, dunes and coastal structures are needed for coastal management and engineering designs. Spectral wave energy-action models are widely used to predict wave propagation in deep and shallow water, incorporating the effects of refraction, bed friction, breaking and wave-wave interactions. To calculate nearshore runup or overtopping, wave-by-wave or phase-resolving modelling is necessary as spectral, phase-averaged models only give the spectral evolution and wave-induced setup. Herein, unidirectional wave propagation up a uniform slope predicted by the Simulating WAves Nearshore (SWAN) model is compared with experimental data. The surface elevation time series near the breaking position is then created from the predicted nearshore spectra and input to a non-linear shallow-water equation solver to give statistical runup predictions which are also compared with experimental data. Sensitivity to the offshore position for wave input is investigated. Runup statistics are shown to be reasonably well predicted.