This thesis is made up of three parts on the computation of scattering properties of nonspherical particles in the atmosphere. In the first part, a new crystal type-droxtal-is introduced to make a better representation of the shape of small ice crystals in the uppermost portions of midlatitude and tropical cirrus clouds. Scattering properties of droxtal ice crystals are investigated by using the Improved-Geometric Optic (IGO) method. At the visible wavelength, due to the presence of the hexagonal structure, all elements of the phase matrix of droxtal ice crystals share some common features with hexagonal ice crystals, such as 220 and 460 halos. In the second part of this thesis, the possibility of enhancing the performance of current Anomalous Diffraction Theory (ADT) is investigated. In conventional ADT models, integrations are usually carried out in the domain of the particle projection. By transforming the integration domain to the domain of scaled projectile length, the algorithm of conventional ADT models is enhanced. Because the distribution of scaled projectile length is independent of the particle's physical size as long as the shape remains the same, the new algorithm is especially efficient for the calculation of a large number of particles with the same shape but different sizes. Finally, in the third part, the backscattering properties of nonspherical ice crystals at the 94GHz frequency are studied by employing the Finite-Difference Time- Domain (FDTD) method. The most important factor that controls the backscattering cross section is found to be the ratio of the volume-equal radius to the maximum dimension of the ice crystal. Substantial differences in backscattering cross sections are found between horizontal orientated and randomly oriented ice crystals. An analytical formula is derived for the relationship between the ice water (IWC) content and the radar reflectivity ( e Z ). It is shown that a change to the concentration of ice crystals without any changes on the size distribution or particle habits leads only to a linear e Z IWC - relationship. The famous power law e Z IWC - relationship is the result of the shift of the peak of particle size distribution.