On the Dependence of Sea Surface Roughness on Wave Development

Abstract

The aerodynamic roughness of the sea surface, z₀, is investigated using data from Lake Ontario, from the North Sea near the Dutch coast, and from an exposed site in the Atlantic Ocean off the coast of Nova Scotia. Scaling z₀ by rms wave height gives consistent results for all three datasets, except where wave heights in the Atlantic Ocean are dominated by swell. The normalized roughness depends strongly on wave age: younger waves (traveling slower than the wind) are rougher than mature waves. Alternatively, the roughness may be normalized using the friction velocity, u_*, of the wind stress. Again, young waves are rougher than mature waves. This contradicts some recent deductions in the literature, but the contradiction arises from attempts to describe z₀ in laboratory tanks and in the field with a single simple parameterization. Here, it is demonstrated that laboratory waves are inappropriate for direct comparison with field data, being much smoother than their field equivalents. In the open ocean there is usually a mixture of swell and wind-driven sea, and more work is needed before the scaling of surface roughness in these complex conditions can be understood.