On the Consistent Parametric Description of the Wave Age Dependence of the Sea Surface Roughness

The wind drag on the sea surface is characterized by the aerodynamic roughness of the sea surface, z0, which is regulated by surface wind waves. Many studies have related the dimensionless form of z0 to the wave age parameter estimated from spectral peak information. These parametric relationships have been well developed for the wind-driven sea but not for mixed seas. Based on an analysis using observations from a fixed platform in the northern South China Sea, the deficiency of the spectral peak information in the parametric description z0 when swells dominate is indicated. Instead, a consistent parametric description of z0 can be obtained by using the wave age estimated from the mean wave period, and normalizing z0 by the mean wavelength. Normalizing z0 by the significant wave height introduces a spurious residual dependence of z0 on the wave steepness. A parametric relationship is developed between the dimensionless z0 (normalized by the mean wavelength) and the wave age from the mean wave period. A comparison of this new relationship to the wind speed-only formulation in COARE 3.5 is provided.