Light scattering by nonspherical ice crystals: Theoretical study by finite-difference time domain technique and geometric optics methods

The finite-difference time domain (FDTD) and geometric ray-tracing methods are developed for the computations of light scattering and absorption by hexagonal ice crystals. A numerical scheme, which avoids the complex calculations arising from the imaginary refractive index when particle is absorptive, is developed for the computation of near-field by the FDTD method. In truncating the domain of near-field, highly absorbing boundary conditions are developed to suppress the artificial reflection from the boundary of the computational domain. The transformation of near-field to far-field is made in accordance with a volume-integration technique. The FDTD method is validated by applying it to scattering problems involving infinitely long circular cylinders and spheres. Maximum deviations of the FDTD results from the exact solutions are less than 5% in terms of the total scattered energy. As a reliable method, the FDTD technique has been used to solve the complete scattering phase matrix for hexagonal ice crystals.; We have also developed a new geometric optics model to overcome a number of shortcomings in the conventional ray-tracing method which is applicable only to sizes of the particles much larger than the incident wavelength. The new model uses the ray-tracing technique to solve the near-field on the particle surface which is then transformed to far-field on the basis of the electromagnetic equivalence theorem. The model, referred to as GOM2, can be applied to size parameters as small as 15. Moreover, an intensity-mapping algorithm for field transformation is also developed to reduce the computational effort. The conventional geometric ray-tracing method breaks down at the size parameter on the order of 40-100, depending on whether the calculations are for cross sections or phase function.; The numerical models and results presented in this investigation are significant in terms of understanding the impact of small ice crystals in cirrus clouds on the radiation budget and climate of the earth's atmosphere. They are also critical for applications to remote sensing of cirrus clouds and for parameterization of the radiative properties of ice clouds in climate models.