The dependence of sea surface roughness on the height and steepness of thewaves

It is proposed that the sea surface roughness z(o) can be predicted from th e height and steepness of the waves, z(o)/H-s = A(H-s/L-p)(B), where H-s an d L-p 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 beh avior of the drag coefficient as observed in wave tanks, lakes, and the ope n ocean, thus reconciling observations that previously had appeared dispara te. Indeed, the formula suggests that changes in roughness due to limited d uration or fetch are of order 10% or less. Thus all deep water, pure windse as, regardless of fetch or duration, extract momentum from the air at a rat e similar to that predicted for a fully developed sea. This is confirmed us ing published field data for a wide range of conditions over lakes and coas tal seas. Only for field data corresponding to extremely young waves (U-10/ C-p> 3) were there appreciable differences between the predicted and observ ed roughness values, the latter being larger on average. Significant change s in roughness may be caused by shoaling or by swell. A large increase in r oughness is predicted for shoaling waves if the depth is less than about 0. 2L(p). The presence of swell in the open ocean acts, on average, to signifi cantly decrease the effective wave steepness and hence the mean roughness c ompared to that for a pure windsea. Thus the predicted open ocean roughness is, at most wind speeds, significantly less than is observed for pure wind waves on lakes. Only at high wind speeds, such that the windsea dominates the swell, do the mean open ocean values reach those for a fully developed sea.