非均匀极化平面大气辐射转移的离散球谐函数法
A Discrete Spherical Harmonics Method for Radiative Transfer Analysis in Inhomogeneous Polarized Planar Atmosphere
摘要：
采用离散球谐函数法求解了非均匀偏振平面大气中的辐射转移问题。该方法将Stokes矢量和相位矩阵展开为有限级数的广义球函数，得到的矢量辐射转移方程表示为一组极坐标。因此，可以确定在任何极方向和方位角的大气内的辐射的偏振特性，而无需线性化和/或插值。利用谱切比雪夫方法解决了问题的空间依赖性。出射和透射的辐射强度和偏振度的瑞利和米氏散射的预测。使用36个流的离散球谐函数方法的预测结果与基准文献结果吻合良好。对于瑞利散射和米氏散射，当极向绝对值大于0.1时，本文方法与文献结果的最大偏差分别小于0.5%和0.9%。对于瑞利散射和米氏散射，接近于零的方向的这些偏差分别约为3%和10%。
英文摘要：
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for absolue value of the polar directions greater than 0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10 % for Rayleigh and Mie scattering, respectively.
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