Terrestrial atmospheres are neither isotropic nor homogeneous. In this chapter, we first take up a model of anisotropic scattering in an inhomogeneous slab, assuming that the local scattering is described by a function of only the incident and scattered polar angles and the vertical coordinate. This function is readily parameterized to approximate phase functions that vary from isotropic to highly elongated and anisotropic. Next we discuss a phase function that can be expanded in a series of Legendre polynomials and Cauchy problems for reflection and transmission functions that are also expanded in a similar series. Such a series approximation is appropriate for mildly anisotropic phase functions. Then we consider some inverse problems of estimating phase functions based on radiation measurements. There are also some approximate formulas that are rather useful and accurate. Finally, we take up diffuse reflection in a three-dimensional medium. Numerical results are presented in graphs and tables.
KeywordsPolar Angle Phase Function Optical Thickness Legendre Polynomial Azimuth Angle
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