Microwave vector radiative transfer equation of a sea foam layer by the second-order Rayleigh approximation

The microwave vector radiative transfer (VRT) equation of a coated spherical bubble layer is derived by means of the second-order Rayleigh approximation field when the microwave wavelength is larger than the coated spherical particle diameter. Meanwhile, the perturbation method is developed to solve the second-order Rayleigh VRT equation for the small ratio of the volume scattering coefficient to the extinction coefficient. As an example, the emissive properties of a sea surface foam layer, which consists of seawater coated bubbles, are investigated. The extinction, absorption, and scattering coefficients of sea foam are obtained by the second-order Rayleigh approximation fields and discussed for the different microwave frequencies and the ratio of inner radius to outer radius of a coated bubble. Our results show that in the dilute limit, the volume scattering coefficient decreases with increasing the ratio of inner radius to outer radius and decreasing the frequencies. It is also found that the microwave emissivity and the extinction coefficient have a peak at very thin seawater coating and its peak value decreases with frequency decrease. Furthermore, with the VRT equation and effective medium approximation of densely coated bubbles, the mechanism of sea foam enhancing the emissivity of a sea surface is disclosed. In addition, excellent agreement is obtained by comparing our VRT results with the experimental data of microwave emissivities of sea surface covered by a sea foam layer at L-band (1.4 GHz) and the Camps’ model.