The algorithm based on the physical-geometric optics method is developed to compute the linearization of single-scattering properties, such as extinction, absorption and scattering cross-sections, and the scattering phase matrix. The algorithm can be applied to any convex facet particles, where a new beam-splitting technique is employed. With the introduction of the winding number method, beams incident on multiple facets can be precisely divided into independent parts that are incident on single facets. The linearization algorithm is verified by the finite-difference method using the regular hexagonal prism. The sensitivities of single-scattering properties with respect to size, aspect ratio, and refractive index are discussed.
The linearized invariant-imbedding T-matrix method (LIITM) and linearized physical-geometric optics method (LPGOM) were applied on regular hexagonal prisms from small to large sizes to obtain the scattering properties and their partial derivatives. T-matrices and their derivatives from the LIITM are presented and discussed in the expansion order, where the minor diagonal elements are dominant. The simulation results of single-scattering properties and their corresponding linearization from both methods are compared. The mutual agreements can be treated as further verification of both linearized methods. Using extinction efficiency as the criterion, the LPGOM are convergent at the LIITM for the particle size parameter larger than 130 with a relative difference of less than 1%, with errors of about 3% and 5% for particle sizes of 50 and 30, respectively. The capability and convergence of the LIITM and LPGOM are discussed in detail based on linearized properties.
Accurate description of the single scattering properties of atmospheric particles can be an essential factor influencing the remote sensing of atmospheric microphysics. In this paper, a database for the linearized single scattering properties of ice particles was developed in the visible to infrared spectral region of 0.4–15 μm and for size parameters ranging from 0.5 to 500. The linearized invariant imbedding T-matrix method and linearized physical-geometric optics method were jointly applied. A full set of integral scattering properties including extinction efficiency, single scattering albedo, asymmetry factors, and differential scattering properties, including six phase matrix elements, were the basic scattering parameters in the database. Furthermore, the Jacobians of these regular scattering properties with respect to refractive index (real and imaginary parts) and effective radius were also included and used for sensitivity determinations. The spectral and size-dependent variations and changing rates of the derivative characteristics with actual application values, such as backscattering depolarization ratios, were also discussed.
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