## Approximation of Single Scattering Properties of Ice and Snow Particles for...

*J. Atmos. Sci., 61*, 2441-2456.

As satellite high-frequency passive microwave data have recently become available, there is an increasing demand for an accurate and computationally efficient method to calculate the single scattering properties of nonspherical ice particles, so that it may be used in radiative transfer models for physical retrievals of ice water path and snowfall rate. In this study, two such approximations are presented for calculating the single scattering properties of three types of large ice particles: bullet rosettes, sector snowflakes, and dendrite snowflakes, for the frequency range of 85 to 220 GHz, based on results of discrete-dipole approximation (DDA) modeling. By analyzing the DDA modeling results, it is noted that, for nonspherical ice particles, the scattering and absorption cross sections and the asymmetry parameter have a magnitude between those of the two imaginary equal-mass spheres. One is a solid sphere, and the other is an ice–air mixed soft sphere whose diameter equals the particle’s maximum dimension. Therefore, the first approximation involves substituting the single scattering properties of a nonspherical ice particle with those of an equal-mass sphere, which can be calculated by Lorenz–Mie theory, with an effective dielectric constant derived by mixing ice and air using the Maxwell–Garnett formula. The diameter of such an equal-mass sphere D is bigger than the diameter of the solid sphere D 0 , but smaller than the particle’s maximum dimension Dmax . Defining a softness parameter SP ϭ (D Ϫ D 0 )/(Dmax Ϫ D 0 ), it is found that the best-fit equal-mass sphere has an SP value of 0.2 ϳ 0.5 for calculating the volume scattering coefficient, depending on frequency and particle shape. At 150 GHz, the best-fit softness parameter is found to be ϳ1/3 when averaging over all particle shapes. For calculating the asymmetry parameter, the DDA model results show that the best-fit softness parameter is close to 0 (i.e., the same as the solid sphere) for frequencies higher than 150 GHz, while it is about 0.3 for 85.5 GHz. The second approximation presented is a polynomial fit to the scattering and absorption cross sections and the asymmetry parameter using the particle size parameter as an independent variable. For the scattering cross section, three fitting curves are derived for, respectively, rosettes, sector snowflakes, and dendrite snowflakes. For the absorption cross section, a single curve is used to fit all particle shapes. For the asymmetry parameter, two curves are derived, one for rosettes and one for snowflakes. The best-fit softness parameter for three particular frequencies (85.5, 150, and 220 GHz) and for three particle shapes in the first approximation, as well as the coefficients of the polynomial fit in the second approximation, are presented. After implementing these approximations in a radiative transfer model, radiative transfer simulations are carried out for a snowfall and an ice cloud case. The simulated brightness temperatures based on the two approximations agree with each other within 3 K, but are significantly different from those based on the solid- and the soft-sphere approximations.