Field observations of wave-driven setdown and setup

Wave-driven setdown and setup observed for 3 months on a cross-shore transect between the shoreline and 5 m water depth on a barred beach are compared with a theoretical balance between cross-shore gradients of the mean water level and the wave radiation stress. The observed setdown, the depression of the mean water level seaward of the surf zone, is predicted well when radiation stress gradients are estimated from the observations using linear theory at each location along the transect. The observed setdown also agrees with analytical predictions based on offshore wave observations and the assumption of linear, dissipationless, normally incident waves shoaling on alongshore homogeneous bathymetry. The observed setup, the superelevation of the mean water level owing to wave breaking, is predicted accurately in the outer and middle surf zone, but is increasingly underpredicted as the shoreline is approached. Similar to previous field studies, setup at a fixed cross-shore location increases with increasing offshore wave height and is sensitive to tidal fluctuations in the local water depth and to bathymetric changes. Numerical simulations and the observations suggest that setup near the shoreline depends on the bathymetry of the entire surf zone and increases with decreasing surf zone beach slope, defined as the ratio of the surf zone-averaged water depth to the surf zone width. A new empirical formula for shoreline setup on nonplanar beaches incorporates this dependence.