A Note on the Ocean Surface Roughness Spectrum*

Abstract In a recent study, the dimensionless surface roughness spectrum has been empirically parameterized as a power-law function of the dimensionless wind speed expressed as the ratio of wind friction velocity and phase speed of the surface roughness wave component. The wave-number-dependent proportionality coefficient, A, and exponent, a, of the power-law function are derived from field measurements of the short-wave spectrum. To extend the roughness spectrum model beyond the wavenumber range of field data, analytical functions are formulated such that A and a approach their asymptotic limits: A0 and a0 toward the lowest wavenumber, and A∞ and a∞ toward the highest wavenumber. Of the four asymptotic values, A∞ is considered most questionable for the lack of reference information. When applied to the normalized radar cross-section (NRCS) computation, the results are in good agreement (within about 2 dB) with field data or geophysical model functions (GMFs) for incidence angles between 20° and 40° but significant underestimation occurs for higher incidence angles. The comparison study of NRCS computation offers helpful guidelines for adjusting the asymptotic factors, especially the numerical value of A∞. Improved agreement between the computed NRCS (vertical polarization) using the new roughness spectrum with GMF is expanded to incidence angles between 20° and 60°. The wind speed range of good agreement between calculation and GMF is below about 15 m s−1 for Ku band and about 30 m s−1 for C band.