Emissivities of rough surface over layered media in microwave remote sensing of snow

The rough surfaces in Greenland are exhibited as sastrugi. The roughness heights are less than 8 cm for much of the year except in late winter and spring, when they increase to 25 cm or less. Roughness profiles were also related to snow and firn ventilation. WindSat, launched in January 2003, was the first spaceborne polarimetric radiometer to measure all 4 elements of Stokes vector, viz., the vertical polarized brightness temperatures, the horizontal polarized brightness temperatures, and the real and imaginary part of the cross-correlations of the vertical and horizontal polarizations. It was shown by Tsang (1984, 1990) that azimuthal asymmetry will create nonzero third and fourth Stokes parameter in passive microwave remote sensing. Thus the third and fourth Stokes parameters contain information of the azimuthal structure. Usually the third and fourth Stokes parameters are quite small between 0.5 K to 1 K over land and less than plusmn2.5 K over ocean. However, measurements of third and Stokes parameters over Greenland show surprising values of 10 K for the third Stokes parameter and between -10 K and 20 K for the fourth Stokes parameter. In this paper, we use physically based electromagnetic model to study the passive polarimetric remote sensing of snow in Greenland by consider the scattering and emission from a random rough surface over multi-layered media. We consider the random rough surface varied in only one horizontal direction so that azimuthal asymmetry exists in the 3-D problem. Dyadic Green´s functions of multilayered medium (Tsang et al., 2000) is used to formulate the surface integral equation so that the polarization dependence of emission and scattering is accounted for systematically. The surface integral equations are solved by using the method of moments in conjunction with fast numerical algorithms such as the multilevel UV method. Numerical results of brightness temperatures are illustrated for all four Stokes parameters to demonstrate the si- gnatures of sastrugi in passive microwave remote sensing. To account for the large third and fourth Stokes parameters, we also consider the case of anisotropic scatterers in volume scattering. Full multiple volume scattering are studied with numerical solutions of the radiative transfer equations for non-spherical scatterers with preferred orientation.