New statistical formulation for an inhomogeneous ocean surface

The authors summarize a recently proposed statistical formulation for a stationary inhomogeneous ocean surface fully described in angular-spectral domain. This formulation is akin to the formulation that is found in the theory of radiative energy transfer and in the theory of the optical coherence. Unlike the conventional formalism of ocean wave statistics, this theory gives explicit definitions of the spectra that characterize the statistically inhomogeneous (spatially nonstationary) surface. The authors show that there are two types of basic spectra in the statistically inhomogeneous surface. If the surface is homogeneous in space, however, the two spectra are identical and there is a unique spectrum that characterizes the homogeneous surface. The theory gives a physical basis for the fetch-limited wave spectral models, for example, JONSWAP spectrum, Mitsuyasu spectrum, and Wallops spectrum, each model of which describes the surface by the position-dependent directional spectrum. A number of formulas for the cross spectrum and the correlation function for the surface displacement are shown in connection with the basic spectra. By using an adequate wave spectral model and by using the present formalism, it is possible to treat an ocean surface as a light emitting and light scattering object. Optical characteristic understanding for a random water surface is essential for an optical remote sensing of oceans