Estimating runup with limited bathymetry

Wave runup estimates are used in erosion and overtopping models, and in coastal structure design. However, runup depends on often incompletely known surf and swash bathymetry. The many existing runup parameterizations characterizing bathymetry with only the foreshore (swash zone) beach slope beta(f) are necessarily of limited accuracy. Here, an empirical model relating runup to incident wave spectra is extended to include an effective, mid-surfzone slope, beta(eff), that depends on the cross-shore location of the midpoint of breaking-wave dissipation. The empirical model is trained using numerical simulations (SWASH) of 138 hindcast historical storm waves, two different offshore infragravity wave boundary conditions, and 24 representative eroded beach bathymetries from a Southern California beach. The model is tuned for the swell waves and concave up (sometimes barred) depth profiles characteristic of the study region. Consistent with their generation by surfzone-wide processes, setup and infragravity runup depend more strongly on surfzone beta(eff) than on foreshore beta(f). In contrast, sea-swell runup depends more strongly on shoreline processes, and beta(f) is more important than beta(eff). Empirical model accuracy is improved by including both beta(eff) and beta(f).

Automated summary

Wave runup estimates are crucial in erosion and overtopping models, but are often limited by incomplete knowledge of surf and swash bathymetry. This study extends an empirical model relating runup to wave spectra by including an effective mid-surfzone slope, beta(eff), and finds that setup and infragravity runup depend more strongly on beta(eff) than on foreshore beta(f). By considering both beta(eff) and beta(f), the accuracy of the empirical model is improved.