Radar backscattering computations for fractal-shaped snowflakes

Abstract

We propose a model for large snowflakes based on the fractal nature of their particle shapes. Monte Carlo simulations were conducted to make particles with a fractal dimension of 1.8 to 2.4. The roundness parameter for the projected images of the modeled particles was derived, and an average roundness of approximately 0.4 for particles with fractal dimension 2.1 was indicated; this average roundness matched reported values measured for large ice aggregates. The finite difference time domain method was used to calculate the backscattering cross-sections of ice particles with a fractal dimension of 2.1 and a particle diameter of up to ∼20 mm at microwave frequencies of 95 GHz, 35 GHz, and 9.8 GHz. The results were compared with those of equivalent-volume spheres and randomly oriented equivalent-volume hexagonal columns. Our snowflake model had smaller values of radar backscattering cross-sections than did the equivalent-volume spheres in the size range out of the Rayleigh regime. Furthermore, large differences in backscattering cross-sections between the snowflake model and the equivalent-volume hexagonal column were confirmed, in particular at a frequency of 35GHz. © 2008, Meteorological Society of Japan.