Formulae for specular and diffuse forward scattering from a rough sea surface

Formulae for the specular and diffuse components of rough sea surface scattering over a wide range of grazing angles are derived from numerical simulations. A parabolic equation model is used to simulate scattering of an incident plane wave from a one-dimensional Pierson-Moskowitz sea surface. Individual components of the surface wave spectrum give scattering behaviour which can be explained in terms of diffraction secondary angles analogous to an acoustic array or Bragg diffraction. The angular spectrum of the scattered energy is used to calculate values to which curve fitting is applied to derive the formulae. The specular reflection loss predicted by the derived formula is compared with previously published measurements and formulae. Different power law dependencies are found to apply in the formula derived here, which leads to poor agreement with the comparison formulae at high wind speeds and frequencies, though there is reasonable agreement at low wind speeds and frequencies. Examples are shown as to how the specular and diffuse components can be used to construct scattering matrices for use in modelling ocean-acoustic propagation.