Petty and Huang (2010)

A investigation of the scattering properties of realistic aggregates of dendrites and needles compared to soft-sphere methods


Grant W. Petty; Wei Huang



Petty, G. W., and W. Huang, 2010: Microwave Backscatter and Extinction by Soft Ice Spheres and Complex Snow Aggregates. J. Atmos. Sci.67, 769–787,

Particle types

aggregates of dendrites and needles


125 microns to 10 millimeters


13.4 to 89 GHz




Scattering method


Coupled-dipole approximation (CDA) calculations of microwave extinction and radar backscatter are presented for nonhomogeneous (soft) ice spheres and for quasi-realistic aggregates of elementary ice crystal forms, including both simple needles and real dendrites. Frequencies considered include selections from the Dual-Frequency Precipitation Radar (DPR; 13.4 and 35.6 GHz) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI; 18.7, 36.5, and 89.0 GHz), both slated for orbit on the GPM mission.

The computational method is first validated against Mie theory using dipole structures representing solid ice spheres as well as stochastically generated “soft” ice spheres of variable ice–air ratio. Neither the traditional Bruggeman nor Maxwell Garnett dielectric mixing formula is found to correctly predict the full range of CDA results for soft spheres. However, an excellent fit is found using the generalized mixing rule of Sihvola with ν = 0.85.

The suitability of the soft-sphere approximation for realistic aggregates is investigated, taking into account the spectral dependence of backscatter and/or extinction per unit mass at key DPR and GMI frequencies. Even when spheres of nonequal mass are considered, there is no single combination of fraction and mass that simultaneously captures all the relevant radiative properties. All four aggregate models do, however, exhibit a predictable power-law dependence of the mass extinction coefficient on the total particle mass. Dual-frequency mass extinction ratios are only very weakly dependent on particle masses; moreover, the ratio is found to be approximately proportional to frequency raised to the power 2.5.

The dual-frequency backscatter ratio is found to be a predictable function of the aggregate mass for particles smaller than 3 mg. Above this size, the ratio is strongly sensitive to aggregate shape, a finding that raises concerns about the utility of dual-frequency backscatter ratio measurements whenever larger particles might be present in a volume of air.

The validity of the Rayleigh–Gans approximation applied to radar backscatter from snow aggregates was also examined. Although the dual-frequency backscatter ratio was reasonably well reproduced, the absolute magnitude was not.

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