Dielectric constant adjustments in computations of the scattering properties of solid ice crystals using the Generalized Multi-particle Mie method

Abstract

Ice crystal scattering properties at microwave radar wavelengths can be modeled with the Generalized Multi-particle Mie (GMM) method by decomposing an ice crystal into a cluster of tiny spheres composed of solid ice. In this decomposition the mass distribution of the tiny spheres in the cluster is no longer equivalent to that in the original ice crystal because of gaps between the tiny spheres. To compensate for the gaps in the cluster representation of an ice crystal in the GMM computation of crystal scattering properties, the Maxwell Garnett approximation is used to estimate what the dielectric function of the tiny spheres (i.e., the inclusions) in the cluster must be to make the cluster of tiny spheres with associated air gaps (i.e., the background matrix) dielectrically equivalent to the original solid ice crystal. Overall, compared with the T-matrix method for spheroids outside resonance regions this approach agrees to within mostly 0.3dB (and often better) in the horizontal backscattering cross section σhh and the ratio of horizontal and vertical backscattering cross sections σhh/σvv, and 6% for the amplitude scattering matrix elements Re{S22−S11} and Im{S22} in the forward direction. For crystal sizes and wavelengths near resonances, where the scattering parameters are highly sensitive to the crystal shape, the differences are generally within 1.2dB for σhh and σhh/σvv, 20% for Re{S22−S11} and 6% for Im{S22}. The Discrete Dipole Approximation (DDA) results for the same spheroids are generally closer than those of GMM to the T-matrix results. For hexagonal plates the differences between GMM and the DDA at a W-band wavelength (3.19mm) are mostly within 0.6dB for σhh, 1dB for σhh/σvv, 11% for Re{S22−S11} and 12% for Im{S22}. For columns the differences are within 0.3dB for σhh and σhh/σvv, 8% for Re{S22−S11} and 4% for Im{S22}. This method shows higher accuracy than an alternative method that artificially increases the thickness of ice plates to provide the same mass as the original ice crystal.