Wave spectrum and roughness spectrum for microwave observation of the oceans

The description of the ocean surface by a vertical displacement spectrum for microwave remote sensing applications, is discussed. Two kinds of spectra are in use: a spectrum defined as the Fourier transform of the autocovariance function of the displacement, and a spectrum defined by an expansion of the surface in plane waves. The first one is symmetric, the second one is not. An important consequence is that the up-wind down-wind asymmetry, observed in the azimuthal response of a wind scatterometer, cannot be explained by an asymmetry of the spectrum