Effective medium approximation model of sea foam layer microwave emissivity of a vertical profile

Abstract

A sea foam layer produced by wave breaking consists of seawater-coated air bubbles, fluid water, and air. The non-uniformity and microstructure of the air–water mixture in a foam layer can cause some important effects on microwave or optical properties. Considering the vertical non-uniformity of the air–water volume, the air-volume fraction is derived as a function of the foam depth variable, coated air bubble velocity, and foam temperature using the gas convection–diffusion equation. For a vertical graded profile of the air volume fraction, we discuss the effects of the coated air bubble velocity parameter and the air–sea temperature difference on the air volume fraction. The results show that the coated air bubble velocity is a key parameter that widely modulates the air volume fraction. Furthermore, an effective medium approximation (EMA) of spherical shell microstructures is proposed to investigate the graded foam effective permittivity and the emissivity of the sea surface covered with the foam layer of the graded air volume fraction in a vertical profile, and good agreement is obtained on comparing the EMA results with the experimental data of foam layer microwave emissivities at frequencies 1.4, 10.8, and 36.5 GHz. In our EMA model, the depth average of graded foam permittivity is adopted. This model can produce reasonable results by only tuning the air bubble velocity. It indicates that the EMA model can combine the effects of graded foam permittivity and foam microstructures into the coated air bubble velocity parameter. Meanwhile, we have qualitatively discussed the influence of air–sea temperature difference on the brightness temperature of the foam layer. It is shown that a negative (or positive) air–sea temperature difference enhances (or reduces) the sea surface brightness temperature, and the brightness temperature difference increases with an increase in microwave frequency.