Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium

Yoshihide Takano Department of Meteorology, University of Utah. Salt Lake City. Utah

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Kuo-Nan Liou Department of Meteorology, University of Utah. Salt Lake City. Utah

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Abstract

We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and transmitted intensities. Various optical features can be produced only by horizontally oriented plates and columns. For the polarization of sunlight reflected by ice crystals, the neutral point is independent of the solar zenith angle as well as the optical depth. We have also closely matched the polarization patterns observed for Martian white clouds, as well as cirrus clouds, with the results from the present multiple-scattering computations for ice crystals. Finally, it is noted that the polarization configuration is extremely sensitive to the shape of the particles. Thus, its full information content should be explored for applications to the remote sounding of clouds.

Abstract

We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and transmitted intensities. Various optical features can be produced only by horizontally oriented plates and columns. For the polarization of sunlight reflected by ice crystals, the neutral point is independent of the solar zenith angle as well as the optical depth. We have also closely matched the polarization patterns observed for Martian white clouds, as well as cirrus clouds, with the results from the present multiple-scattering computations for ice crystals. Finally, it is noted that the polarization configuration is extremely sensitive to the shape of the particles. Thus, its full information content should be explored for applications to the remote sounding of clouds.

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