782 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 4, APRIL 2003 Microwave Emission and Scattering of Foam Based on Monte Carlo Simulations of Dense Media Dong Chen, Leung Tsang, Fellow, IEEE, Lin Zhou, Steven C. Reising, William E. Asher, Louis Allen Rose, Kung-Hau Ding, Member, IEEE, and Chi-Te Chen Abstract—The foam-covered ocean surface is treated as densely packed air bubbles coated with thin layers of seawater. We apply Monte Carlo simulations of solutions of Maxwell’s equations to calculate the absorption, scattering, and extinction coefficients at 10.8 and 36.5 GHz. These quantities are then used in dense-media radiative transfer theory to calculate the microwave emissivity. Numerical results of the model are illustrated as a function of foam parameters. Results of emissivities for both horizontal polarization and vertical polarizations at 10.8 and 36.5 GHz are compared with recent experimental measurements. Index Terms—Dense-media radiative transfer, electromagnetic wave scattering, microwave emissivity, Monte Carlo simulations, ocean foam. I. INTRODUCTION T O ESTIMATE the effect of the foam on the ocean sur- face due to wave breaking on passive microwave remote sensing measurements, various empirical microwave emissivity models have been used [1]–[5]. Williams [1] measured emissivi- ties of foam in a waveguide and found that at X-band, the emis- sivity of foam depends strongly on the thickness of the foam layer. Wilheit’s model [2] treats foam as having neither polar- ization nor viewing angle dependence. In Pandey’s empirical emissivity model [3], the effect of foam was taken into account by coupling of the theoretical expressions of specular ocean sur- face emissivity with empirical expressions from ocean tower observations and from the analysis of published measurements. Smith [4] measured the brightness temperature of the foam-cov- Manuscript received August 9, 2002; revised December 4, 2002. This work was supported by the Office of Naval Research under Grant N00014-99-1-0190 to the University of Washington, and the City University of Hong Kong under Grant 9380034. The experimental measurements were also supported by the Office of Naval Research under Award N00014-00-1-280 to the University of Massachusetts, Award N00014-00-0152 to the University of Washington, and Award N0001400WX21032 to the Naval Research Laboratory. D. Chen is with the Department of Electronic Engineering, City University of Hong Kong, Hong Kong. L. Tsang is with the Department of Electronic Engineering, City University of Hong Kong, Hong Kong and also with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA (e-mail: eeltsang@cityu.edu.hk). L. Zhou and W. E. Asher are with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA. S. C. Reising is with the Microwave Remote Sensing Laboratory, University of Massachusetts at Amherst, Amherst, MA 01003 USA. L. A. Rose is with the Remote Sensing Division, Naval Research Laboratory, Washington, DC 20375 USA. K.-H. Ding is with the Air Force Research Laboratory, Hanscom Air Force Base, Bedford, MA 01731 USA. C.-T. Chen is with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA and is also with the Intel Corporation, Sacramento, CA 95827 USA. Digital Object Identifier 10.1109/TGRS.2003.810711 ered ocean from an aircraft at a 50 incidence angle. He related the emissivities of foam at the three channels (vertical polariza- tion at 19 GHz and both polarizations at 37 GHz) to one an- other by linear regression. Stogryn [5] used a least squares fit of a polynomial to measurements of artificially generated and naturally occurring foam available as of 1971 and derived an expression for the foam emissivity as a function of incidence angle and frequency. All of these models are empirical fitting procedures using experimental data. The empirical models do not take into account the physical microstructure of foam and the foam layer thickness. The subject of foam dynamics has attracted great attention. Huang and Jin [6] discussed a composite model of foam scat- terers and two-scale wind-driven rough sea surface. Controlled field experiments were performed to measure foam dynamics and the microwave emissivity of calm seawater [7], [8]. Recently, a physically based approach was proposed to model foam as air bubbles coated with seawater [9]. In this approach, wave scat- tering and emission in a medium consisting of densely packed coated particles are solved using the quasi-crystalline approx- imation in combination with dense-medium radiative transfer (DMRT) theory [10], [11]. The quasi-crystalline approximation takes into account the effects of dense media, a method that has been verified by controlled laboratory experiments [12], [13]. In this paper, we apply Monte Carlo simulations of solu- tions of Maxwell’s equations of densely packed coated parti- cles to analyze the microwave emission and scattering of foam. The absorption, scattering, and extinction coefficients are cal- culated. These quantities are then used in DMRT theory to cal- culate the microwave emissivity. In order to model high-density packing, we use a face-centered-cubic (fcc) structure to place the air bubbles. In Section II, we describe the physical and geometric proper- ties of foam, both measured and modeled. In Section III, inde- pendent scattering results for absorption and scattering are pre- sented. In Section IV, the Monte Carlo simulation and DMRT theory are described. By applying Monte Carlo simulations, we calculate numerical results for absorption rate, scattering rate, and effective permittivity of densely packed air bubbles coated with seawater in a fcc structure. In the Monte Carlo simulations, the volume integral equation is used. The simulation results for emissivity with typical foam parameters at 10.8 and 36.5 GHz are illustrated in Section V. Salient features of the numerical results are 1) the absorption coefficients at 10.8 GHz are appre- ciable, and 2) the emissivities at 10.8 and 36.5 GHz are com- parable. These features are consistent with experimental mea- surements [8]. Comparisons are also made with experimental measurements [8] for vertical and horizontal polarizations. 0196-2892/03$17.00 © 2003 IEEE