Physical Model and Experimental Results for Millimeter-Wave Emissivity of Seawater Foam at W-Band

In the field of seawater surface target monitoring, accurate modeling of seawater foam emissivity is essential for retrieving seawater parameters. Current research primarily focuses on frequency bands below 40 GHz, with a few studies addressing emissivity characteristics at higher frequencies. This article develops a physical emissivity model for seawater foam at W-band. In the foam-covered region, the emissivity is characterized and calculated by employing a three-layer planar structure comprising the atmosphere, foam, and seawater, utilizing the wave approach method. In the foam-free region, the scattering properties of the rough sea surface are characterized by the second-order small perturbation method (SPM) under laboratory conditions. For real-world sea states, the Kirchhoff approximation method (KAM) is utilized to maintain practical relevance. The hybrid modeling framework constructed in this study effectively unifies the electromagnetic radiation modeling of both foam-covered and foam-free regions. By introducing foam coverage (F_c), the difference in emissivity between foam-covered and foam-free regions is quantitatively evaluated. To validate the model, extensive measurements were conducted at three sites using a portable millimeter-wave radiometer, and quantitative comparisons were made with ten experimental datasets. Results show that the fitting root mean square error (RMSE) remains below 2.5%, and the correlation coefficient (R) is generally above 0.94. The polarization ratio (PR) exhibits strong fitting performance, with the R consistently around 0.97, confirming the high accuracy and robustness of the model. Further analysis of physical parameters related to seawater foam emissivity reveals that an increase in the product of foam void fraction (F_a) and F_c significantly enhances emissivity. Additionally, seawater temperature and salinity indirectly affect emissivity by altering the dielectric constant and the bubble microstructure. Particularly at W-band, the extremely small skin depth causes the emissivity of seawater foam to approach saturation due to the influence of the foam layer thickness.