Full-range sea surface spectrum in nonfully developed state for scattering calculations

A new form for the spectrum of the ocean surface vertical displacements is derived for the case of nonfully developed states. The gravity range is expressed as a function of the fetch x and the significant slope ∮ as well. The capillary-gravity range is assumed dependent on the wind friction velocity only. Recent wavenumber spectrum measurements in this spectral domain and ocean conditions are analyzed. Toba´s spectral shape is shown to represent correctly these experimental data when updated with an equivalent amplitude factor. An expression for this factor is proposed. It is weakly wind friction velocity dependent, as observed by Mitsuyasu in the late 1970s. The proposed spectrum is then combined with a boundary perturbation model for electromagnetic scattering computations. Empirical scattering models and radar data collocated with assumed ground-truth data are used for comparison. This is shown to give consistent results for both C- and Ku-bands as well as large ranges of wind speeds and incidence angles. Comparisons of backscattering coefficients computed using other sea spectra from the literature are presented. The significant slope is found to be an important factor for scattering at low incidence angles. The proposed spectrum thus constitutes a useful basis for physically based inversion algorithms