On sea state parameterisations of sea surface roughness

Recently, two quite different sea state parameterisations of roughness length have been proposed. Taylor and Yelland (2001) 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, of order 10%. The wave steepness formula was proposed as an alternative to the classical wave age scaling first suggested by Kitaigorodskii and Volkov (1965). 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 rather different roughness predictions in certain conditions, has led to considerable confusion among certain groups. Here we present the results of recent efforts to understanding the merits and limitations of each scaling. The two sea state scalings are tested using a composite of eight data sets representing a wide range of conditions. In conditions with a dominant wind sea component, both scalings were found to yield improved estimates compared to 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.