It is proposed that the sea surface roughness z o can be predicted from the height and steepness of the waves, z o /H s ϭ A(H s /L p ) B , where H s and L p are the significant wave height and peak wavelength for the combined sea and swell spectrum; best estimates for the coefficients are A ϭ 1200, B ϭ 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 (U 10 /c p Ͼ 3) were there appreciable differences between the predicted and observed roughness values, the latter being larger on average. Significant changes in roughness may be caused by shoaling or by swell. A large increase in roughness 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 significantly decrease the effective wave steepness and hence the mean roughness compared 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.

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The concept of an “equivalent surface roughness” over the ocean is useful in understanding the relation between wind speed (at some height) and the net momentum flux from air to sea. The relative performance of different physics-motivated scalings for this roughness can provide valuable guidance as to which mechanisms are important under various conditions. Recently, two quite different roughness length scalings have been proposed. Taylor and Yelland presented a simple formula based on wave steepness, defined as the ratio of significant wave height to peak wavelength, to predict the surface roughness. A consequence of this formula is that roughness changes due to fetch or duration limitations are small, an order of 10%. The wave steepness formula was proposed as an alternative to the classical wave-age scaling first suggested by Kitaigorodskii and Volkov. Wave-age scaling, in contrast to steepness scaling, predicts order-of-magnitude changes in roughness associated with fetch or duration. The existence of two scalings, with different roughness predictions in certain conditions, has led to considerable confusion among certain groups. At several recent meetings, including the 2001 World Climate Research Program/Scientific Committee on Oceanic Research (WCRP/SCOR) workshop on the intercomparison and validation of ocean–atmosphere flux fields, proponents of the two scalings met with the goal of understanding the merits and limitations of each scaling. Here the results of these efforts are presented. The two sea-state scalings are tested using a composite of eight datasets representing a wide range of conditions. In conditions with a dominant wind-sea component, both scalings were found to yield improved estimates when compared with a standard bulk formulation. In general mixed sea conditions, the steepness formulation was preferred over both bulk and wave-age scalings, while for underdeveloped “young” wind sea, the wave-age formulation yields the best results. Neither sea-state model was seen to perform well in swell-dominated conditions where the steepness was small, but the steepness model did better than the wave-age model for swell-dominated conditions where the steepness exceeded a certain threshold.

Wind velocity and air-sea turbulent flux measurements made from shipborne instruments are biased due to the effect of the ship on the flow of air to the instruments. The presence of the ship causes the airflow to a particular instrument site to be either accelerated or decelerated, displaced vertically, and sometimes deflected slightly in the horizontal. Although recognized for some time, it is only recently that the problem has been addressed using three-dimensional computational fluid dynamics (CFD) models to simulate the flow over particular ships, quantify the effects of flow distortion, and hence correct the ship-based measurements. It has previously been shown that this improves the calculated momentum fluxes by removing disparities between data from different ships, or from instruments in different locations on the same ship. This paper provides validation of the CFD model simulations. Two research ships were instrumented with multiple anemometers located in both well-exposed and badly exposed sites. Data are compared to the results of model simulations of the flow at various relative wind directions and wind speeds. Except when the anemometers are in the wake of an upwind obstruction, the model and the in situ wind speed estimates typically agree to within 2%. Direct validation of the model-derived estimates of the vertical displacement of the flow was not possible due to the extreme difficulty of obtaining such measurements in the field. In this study, simulations of flows at 0Њ and 90Њ from the bow of the ship were made and displacements of about 1 and 5 m were found, respectively. These results were used to correct the in situ momentum flux data. In one case, the application of the different bow-on and beam-on corrections for vertical displacement successfully removed the disparity seen in the uncorrected data. In a second case, the beam-on vertical displacement overcorrected the flux results. This overcorrection could be caused either by uncertainties in the in situ estimate of the relative wind direction or by partial adjustment of the turbulence during the vertical displacement. The effects of flow distortion are found to vary only slightly with wind speed, but are very sensitive to the relative wind direction and, if uncorrected, can cause large biases in ship-based meteorological measurements (up to 60% for the drag coefficient). Model results are given for bow-on flows over 11 research ships (American, British, Canadian, French, and German).