Geometric Roughness Estimates of Surf-Zone Wave-Breaking Foam

Measurements of small-scale [O (mm)] geometric roughness length (\( k_{\text{f}} \)) associated with surface foam generated by depth-limited breaking waves were obtained within the surf zone on a sandy beach. The parameter \( k_{\text{f}} \) is described using the vertical standard deviation of the sea surface elevation for a foamy area as estimated from stereo imagery. A waterproof two-camera system with self-logging and internal power was developed for collecting stereo images using commercial off-the-shelf components and commercial software for operations 1 m above the sea surface within the middle of the surf zone. The surf-zone foam had a mean \( k_{\text{f}} \) value of 3.2 mm, ranging from 1.7 to 6.3 mm. Using an empirical land-based relationship results in a mean aerodynamic roughness length for surf-zone foam of 0.82 mm, with a range from 0.4 to 1.6 mm, which provides a reasonable estimate of the surf-zone drag coefficient compared with field measurements.