Effect of wave frequency and directional spread on shoreline runup

TLDR

Wave breaking in the surf zone raises shoreline mean water level (setup) and causes runup fluctuations, which are typically divided into sea‑swell and infragravity components and empirically parameterized by beach slope, deep‑water wave height, and wavelength. The study aims to develop accurate parameterizations to assess coastal flooding and erosion risk to ecosystems and communities. Numerical simulations with the Boussinesq funwaveC model reproduce empirical setup and runup parameterizations and reveal that infragravity runup is strongly influenced by wave directional and frequency spread, with a new non‑dimensional spreading parameter enabling a promising new parameterization for predicting coastal flooding and erosion.

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 runup R s (ig) strongly depends on the incident wave directional and frequency spread (about the mean direction and peak frequency). Realistic directional spread variations change R s (ig) equivalent to a factor of two variation in incident wave height. The modeled R s (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 for R s (ig) potentially useful to predict coastal flooding and erosion.