Drag Coefficient,Dynamic Roughness and Reference Wind Speed

Surface waves are the roughness element of the ocean surface. The parameterization of the drag coefficient of the ocean surface is simplified by referencing to wind speed at an elevation proportional to the characteristic wavelength. The dynamic roughness is analytically related to the drag coefficient. Under the assumption of fetch limited wave growth condition, various empirical functions of the dynamic roughness can be converted to equivalent expressions for comparison. For datasets covering a wide range of the dimensionless frequency (inverse wave age), it is important to account for the variable rate of wave development at different wave ages. As a result, the dependence of the Charnock parameter on wave age is nonmonotonic. Finally, the analysis presented here suggests that the significant wave steepness is a sensitive property of the ocean surface and a single variable normalization of the dynamic roughness using a wavelength or wave height parameter actually produces more robust functions than bi-variable normalizations using wave height and wave slope.