Skin depth at microwave frequencies of sea foam layers with vertical profile of void fraction

To develop a foam emissivity model, we started a systematic investigation of sea foam properties at microwave frequencies from 1 to 37 GHz. We first examined various permittivity formulae to find the most suitable one for obtaining the dielectric constant of sea foam. This paper presents an investigation of the skin depth of vertically structured foam layers for the first time. Various void fraction profiles representing variations of foam properties within the foam thickness are examined. The skin depth of foam layer thicknesses from 0.2 cm to 10 cm is obtained. The dependence of foam skin depth on frequency and foam layer thickness is investigated and compared to seawater skin depth. It was found that for exponential void fraction profile ranging from 99% at the air-foam interface to 1% at the foam-seawater boundary, the foam skin depth varies from 0.17 cm to no more than 7 cm. Possible variations of the foam skin depth due to permittivity formula choice, seawater temperature and salinity, and shape of void fraction profile, as well as its upper and lower limits, are presented. Analyses of the results help explain the sensitivity of microwave frequencies to foam layer thicknesses, infer the formation of the emissivity signal and its variations from foam-covered surfaces, infer implications for the passive remote sensing of whitecaps, discuss modeling approaches for vertically structured foam layers, and infer qualitatively the relative contributions of different foam structures to the absorption and emission of electromagnetic radiation. These findings give conceptual understanding of foam emissivity.