The Dependence of Sea Surface Roughness on the Height and Steepness of the Waves

Abstract
It is proposed that the sea surface roughness zo can be predicted from the height and steepness of the waves, zo/Hs = A(Hs/Lp)B, where Hs and Lp are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A = 1200, B = 4.5. The proposed formula is shown to predict well the magnitude and behavior of the drag coefficient as observed in wave tanks, lakes, and the open ocean, thus reconciling observations that previously had appeared disparate. Indeed, the formula suggests that changes in roughness due to limited duration or fetch are of order 10% or less. Thus all deep water, pure windseas, regardless of fetch or duration, extract momentum from the air at a rate similar to that predicted for a fully developed sea. This is confirmed using published field data for a wide range of conditions over lakes and coastal seas. Only for field data corresponding to extremely young waves (U10/cp > 3) were there appreciable differences betwe... Abstract It is proposed that the sea surface roughness zo can be predicted from the height and steepness of the waves, zo/Hs = A(Hs/Lp)B, where Hs and Lp are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A = 1200, B = 4.5. The proposed formula is shown to predict well the magnitude and behavior of the drag coefficient as observed in wave tanks, lakes, and the open ocean, thus reconciling observations that previously had appeared disparate. Indeed, the formula suggests that changes in roughness due to limited duration or fetch are of order 10% or less. Thus all deep water, pure windseas, regardless of fetch or duration, extract momentum from the air at a rate similar to that predicted for a fully developed sea. This is confirmed using published field data for a wide range of conditions over lakes and coastal seas. Only for field data corresponding to extremely young waves (U10/cp > 3) were there appreciable differences betwe...