Effect of wave frequency and directional spread on shoreline runup

Abstract

Wave breaking across the surf zone elevates the mean water level at the shoreline (setup), and drives fluctuations about the mean (runup). Runup often is divided into sea‐swell (0.04–0.3 Hz) and lower frequency infragravity (0.00–0.04 Hz) components. With energetic incident waves, runup is dominated by infragravity frequencies, and total water levels (combined setup and runup) can exceed 3 m, significantly contributing to coastal flooding and erosion. Setup and runup observations on sandy beaches are scattered about empirical parameterizations based on near‐shoreline beach slope and deep water wave height and wavelength. Accurate parameterizations are needed to determine flooding and erosion risk to coastal ecosystems and communities. Here, numerical simulations with the Boussinesq wave model funwaveC are shown to statistically reproduce typical empirical setup and runup parameterizations. Furthermore, the model infragravity runupRs(ig) strongly depends on the incident wave directional and frequency spread (about the mean direction and peak frequency). Realistic directional spread variations change Rs(ig) equivalent to a factor of two variation in incident wave height. The modeled Rs(ig)is shown to vary systematically with a new, non‐dimensional spreading parameter that involves peak frequency, frequency spread, and directional spread. This suggests a new parameterization forRs(ig) potentially useful to predict coastal flooding and erosion.