Abstract: An approach to a two-dimensional vector thermal radiative transfer equation for a layer of spatially inhomogeneous atmospheric rain and cloud is developed. By using the Fourier transformation in discrete form and matrix expression, 1-D radiative transfer equation is derived. Employing an iterative approach, the zeroth- and first-order solutions from integral radiative transfer equation are obtained. Numerical results of polarized brightness temperature of atmospheric rain and cloud with a Gaussian fractional volume are obtained. The functional dependence of brightness temperature to inhomogeneous scale, frequency, polarization, and other parameters are discussed.!
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